MPC Seminar

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== Spring 2019 ==
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== Spring 2020 ==
  
The seminar talks are held in '''Keck Center for Science and Engineering, KC 171''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.
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The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.
 
Sometimes there will be a change of time or venue and the announcement will reflect this change.
 
Sometimes there will be a change of time or venue and the announcement will reflect this change.
  
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=== Thursday, May 16, 2019 at 3 pm, in Keck 370, tea and cookies at 2:40pm (same room) ===
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=== Wednesday, April 29th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===
  
==== ''Speaker:'' '''Dr. Purbita Jana, The Institute of Mathematical Sciences, Chennai, India''' ====
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==== ''Speaker:'' '''Sean Carroll, Caltech, Pasadena, CA''' ====
 
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''Title:'' '''TBA'''
''Title:'' '''Intuitionistic topological systems and their connections with Heyting algebra and Gödel algebra'''
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''Abstract:'' (joint work with Antonio Di Nola and Revaz Grigolia) This talk will suggest a new approach of representation of a Heyting algebra as an I-topological system. I-topological systems will be introduced following the notion of topological system introduced by S. Vickers which is a triple (X, |=, A) consisting of a non-empty set X, a frame A and a relation between X and A satisfying logic of finite observations or geometric logic. It is well known that frame is the Lindenbaum algebra of geometric logic where as the Lindenbaum algebra of intuitionistic logic is a Heyting algebra. Hence to define I-topological systems, intuitionistic logic plays a crucial role. Moreover, we will focus on the categorical relationships between the I-topological system, Esakia space and Heyting algebra (and its particular case of Gödel algebra).
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=== Tuesday, April 16, 2019 at 5 pm, in Keck 370, tea and cookies at 3:40pm (same room) ===
 
  
==== ''Speaker:'' '''Dr. Michele Piazzai, University of Amsterdam, Netherlands''' ====
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=== Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room) ===
  
''Title:'' '''The Ecology of Ideas: Computational Evidence of Self-Organization'''
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==== ''Speaker:'' '''Christian Williams, University of California at Riverside''' ====
  
''Abstract:'' Concepts are cognitive structures that people use to categorize objects and organize their knowledge of the world. Common examples include food and furniture, but also rock'n'roll, quantum physics, and blockchain. For individuals, concepts are the main tools of learning and inference; for groups of individuals (i.e., social systems), they are indispensable instruments of coordination and exchange. But how can the idiosyncratic knowledge of individuals in a social system converge on shared concepts, so as to allow coordination? Conventional wisdom in social science suggests that designated mediators, such as music critics, facilitate this convergence by endorsing the learning and usage of particular concepts. By contrast, I will argue that rational decisions embedded in everyday social interaction provide the necessary and sufficient conditions for concepts' convergence. No mediators are needed for the agents to develop a shared conceptual structure: as commonly occurs in complex adaptive systems, design emerges in the absence of centralized designers. Simulation results are presented that illustrate this point.
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''Title:'' '''Predicate Calculus for Algebraic Theories'''
  
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''Abstract:'' There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.
  
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We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.
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=== Thursday, April 11, 2019 at 4 pm, in Keck 370, tea and cookies at 3:40pm (same room) ===
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==== ''Speaker:'' '''Dr. Michele Piazzai, University of Amsterdam, Netherlands''' ====
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The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.
  
''Title:'' '''The Ecology of Ideas: Empirical Evidence of Evolutionary Pressure'''
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The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.
  
''Abstract:'' Building on the notion that the collective cognition of agents engaged in social interaction constitutes a complex adaptive system, I present a theoretical framework to describe agents' shared conceptual structure as a self-replicating network of objects, ideas, and decisions. Finite cognitive resources at the agents' disposal create a competitive environment where concepts vie to be assigned to objects in categorization decisions, so as to survive in the agents' memory. This struggle for survival gives the socio-cognitive system traits characteristic of an ecology. I identify two sources of ecological interdependence among concepts, including horizontal relations between concepts located at the same level of abstraction and vertical relations between concepts located at different levels. An empirical model is developed to test whether these relations affect the selection of concepts in agents' decisions and the evolution of their shared conceptual structure. To test this model, I analyze one decade's worth of categorization decisions made by users of a crowd-sourced music encyclopedia whose objective is sorting records into genres and sub-genres.
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[http://math.chapman.edu/~jipsen/seminarposters/Christian_Williams_pcat_2020-02-21.pdf Slides from the talk]
  
  
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=== Thursday, March 28, 2019 at 5 pm, in Keck 171, tea and cookies at 4:40pm (same room) ===
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=== Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===
  
==== ''Speaker:'' '''Prof. Giovanni Sambin, University of Padova, Italy''' ====
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==== ''Speaker:'' '''Simon Cho, University of Michigan''' ====
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''Title:'' '''A categorical perspective on persistent and magnitude homology'''
  
''Title:'' '''Half way to Grothendieck's aim (embedding of pointwise topology into pointfree topology)'''
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''Abstract:'' We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.
 
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''Abstract:'' For a mathematician, the most interesting motivation for a different foundation is when it offers a new perspective or even a solution to an old problem. Developing topology over a very "weak" foundation offers a precise mathematical expression and proof to the expectation, which is well present since the time of Grothendieck, of a notion of space generalising that of topological space.
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The well-known link between pointfree and standard topology (with points) is a categorical adjunction between topological spaces Top and locales Loc. Using a "weak" foundation to develop topology, one is compelled to preserve more information than usual, and thus replace topological spaces with "concrete spaces", and locales with "positive topologies". Contrary to a common expectation, it is precisely this "useless" information what offers a solution to Grothendieck's aim. That is,  the above adjunction becomes a categorical embedding of concrete spaces into positive topologies.
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This embedding does not look possible without exploiting the presence of the new (intrinsically existential) notion of positivity relation.
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Half way because this leaves the problem open of finding a suitable notion of positivity (formal closed subsets) in the framework of arbitrary Grothendieck topologies.
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=== Wednesday, March 13, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===
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=== Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===
 
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==== ''Speaker:'' '''Dr. Matt Pusey, University of Oxford''' ====
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''Title:'' '''Anomalous weak values and contextuality: robustness and imaginary
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==== ''Speaker:'' '''Stephon Alexander, Brown University, Rhode Island''' ====
parts'''
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''Title:'' '''The Quantum Cosmological Constant'''
  
''Abstract:'' I will discuss extensions to my previous work linking anomalous weak
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''Abstract:'' The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar,
values with contextuality. In particular, I will show that using
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I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that
transformation noncontextuality obviates the experimentally
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paves new directions that invites us to rethink the quantum nature of vacuum energy.
problematic requirement that the post-selection is projective. I will
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also discuss the status of the imaginary part of weak values. My talk
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will be based on joint work with Ravi Kunjwal and Matteo Lostaglio:
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https://arxiv.org/abs/1812.06940
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=== Wednesday, February 27, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===
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=== Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===
  
==== ''Speaker:'' '''Prof. Christos Tzounis, California State Polytechnic University, Pomona''' ====
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==== ''Speaker:'' '''Pedram Roushan, Google Inc., Santa Barbara, CA''' ====
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''Title:'' '''Quantum supremacy using a programmable superconducting processor'''
  
''Title:'' '''Metric of an Evaporating Black Hole'''
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''Abstract:'' The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements.  
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''Abstract:'' We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state.
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=== Wednesday, February 13, 2019 at 4 pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===
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== Fall 2019 ==
  
==== ''Speaker:'' '''Prof. Peter Rakitzis, Institute of Electronic Structure and Laser, Heraklion, Greece''' ====
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The seminar talks are held in '''Keck Center for Science and Engineering, KC 370''' (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), '''usually on Wednesday at 4 pm'''.
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Sometimes there will be a change of time or venue and the announcement will reflect this change.
  
''Title:'' '''Ultrahigh-Density Spin-Polarized H and D Atoms Observed via Magnetization Quantum Beats'''
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See [http://www.chapman.edu/about/maps-directions/index.aspx Maps
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''Abstract:'' We measure nuclear and electron spin-polarized H and D densities of at least $10^{20}$ cm$^{−3}$ and $10^{19}$ cm$^{−3}$, i.e., at pressures of 5 bar and 0.5 bar, respectively, with ∼10-50 ns lifetimes, from the photodissociation of HBr and DI with circularly polarized UV light pulses. We observe the hyperfine quantum beating of the H and D magnetization with a pickup coil, i.e., the respective 0.7 and 3 ns periodic transfer of polarization from the electrons to the nuclei and back. These pulsed densities are ∼7 orders of magnitude higher than that produced by conventional continuous-production methods, and are sufficient for three novel applications: (a) laser-driven ion acceleration of spin-polarized electrons, protons, or deuterons, (b) the preparation of nuclear-spin-polarized molecules, and (c) the demonstration of spin-polarized D-T or D$^{-3}$He laser fusion at large laser facilities such as NIF, for which a reactivity enhancement of ∼50% is expected.
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=== Tuesday, February 5 -- Saturday, February 9, 2019  in Keck 370 ===
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==== '''11th Annual Chapman University CECAT Workshop on Pointfree Mathematics''' ====
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TUESDAY, February 5th:
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1:00 - 2:00pm '''M. Andrew Moshier''', ''Chapman University'', Weakening relations
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THURSDAY, February 7th:
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10:30 - 11:30am: '''Peter Jipsen''', ''Chapman University'', Involutive residuated lattices and relation algebras
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11:30 - 12:30pm: '''Sara Vannucci''', ''University of Salerno'', Semiring and Semimodule Issues in Residuated Lattices
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1:00 - 2:15pm: '''Rick Ball''', ''University of Denver'', Pointfree Integration
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2:15 - 3:15pm: '''Anna Laura Suarez''', ''University of Birmingham'', D-frames and frame coproducts
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3:30 - 4.30pm: '''Alex Kurz''', ''Chapman University'', On the duality theory of weakening relations
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FRIDAY, February 8th
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10:30 - 11:30am: '''Ales Pultr''', ''Charles University'', Strong Hausdorff properties of frames
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11:30 - 12:30pm: '''Diego Valota''', ''University of Milan'', [http://math.chapman.edu/~jipsen/cecat/11th-Pointfree-Mathematics-Workshop/DiegoValota2019.pdf Computing Spectra via Dualities in the MTL hierarchy]
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2:00 - 3:00pm: '''Olim Tuyt''', ''University of Bern'', Algebraic finite model property of a modal Gödel logic
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3:00 - 4:15pm: '''Rick Ball''', ''University of Denver'', Pointfree Integration, continued
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SATURDAY, February 9th
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1:00 - 5:00pm: Discussion session
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== Fall 2018 ==
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The seminar talks are held in Keck Center for Science and Engineering, KC 171 (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.).
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Sometimes there will be a change of venue and the announcement will reflect this change.
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See [http://www.chapman.edu/discover/maps-directions/index.aspx Maps
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and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf  
 
and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf  
 
Campus map]
 
Campus map]
 
  
  
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=== Thursday, December 6th 2018 at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370===
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=== Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===
  
==== ''Speaker:'' ''' Dr. Bogdan Suceava, CSUF ''' ====
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==== ''Speaker:'' '''Alí Guzmán Adán, Universiteit Gent, Belgium''' ====
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''Title:'' '''Pizzetti and Cauchy formulae for higher dimensional surfaces: a
 +
distributional approach'''
  
''Title:'' ''' Strictly Convex Hypersurfaces Satisfying Weingarten-Type Inequalities '''
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''Abstract:'' In this talk, we study Pizzetti-type formulas for Stiefel
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manifolds and Cauchy-type formulas for the tangential Dirac operator
''Abstract: '' Linear Weingarten surfaces in three-dimensional ambient space satisfy a relation between mean curvature and Gaussian
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from a distributional perspective. First, we illustrate a general
curvature: aH^2+bK=c. We investigate whether for hypersurfaces invariant to inversions of dimensions 3, 4, and 5, there are
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distributional method for integration over manifolds in R^m defined by
curvature inequalities similar to the classical Weingarten condition. We also consider the globalization of these pointwise
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means of k equations. We apply this method to derive an alternative
inequalities. This question is suggested by the investigations of Bang-Yen Chen’s fundamental inequalities, as we reflect
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proof of the Pizzetti formulae for the real Stiefel manifolds
on the geometric interpretations of these relations.Additionally, we plan to discuss other related inequalities, investigated in recent
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SO(m)/SO(m-k). Besides, a distributional interpretation of invariant
works written with Mihaela Vajiac, Nicholas Brubaker, and Leonard Giugiuc, respectively.
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oriented integration is provided. In particular, we obtain a
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distributional Cauchy theorem for the tangential Dirac operator on an
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embedded (m-k)-dimensional smooth surface.
  
  
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=== Friday, November 30th 2018 at 2:00pm, in Keck 171, tea and cookies at 1:30pm in Keck 370===
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=== Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===
  
==== ''Speaker:'' ''' Dr. Apostolos Tzimoulis, Chapman University postdoc ''' ====
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==== ''Speaker:'' '''Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota''' ====
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''Title:'' '''Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system'''
  
''Title:'' ''' Proof theory and algebraic semantics for predicate logics '''
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''Abstract:'' Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands;  here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.
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''Abstract: '' I will start with recasting classical first-order logic in an algebraic and proof-theoretic framework based on Lawvere's theory of hyperdoctrines. Then I will discuss the problem of obtaining general semantics for predicate non-classical logics, provide some examples, and argue that algebraic and proof-theoretic insight can help us understand better and solve this problem.
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=== Thursday, November 29th 2018 at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370===
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=== Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room) ===
  
==== ''Speaker:'' ''' Dr. Sabine Hossenfelder (Frankfurt Institute for Advanced Studies)''' ====
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==== ''Speaker:'' '''Raphael Drumond, Universidade Federal de Minas Gerais, Brazil''' ====
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''Title:'' '''The basics of Quantum Darwinism (and its relationship with non-Markovianity)'''
  
''Title:'' ''' Do women get fewer citations than men? '''
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''Abstract:'' Some aspects of physical systems described by quantum
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mechanics, most notably the possibility of violating a Bell inequality,
''Abstract: '' I will talk about the results of a citation analysis on
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suggests (to some) or unavoidably implies (to others) that certain
publication data from the arXiv and inspire in which we explored gender
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properties of microscopic systems, like the precise values of position
differences. I will further explain how we can use bibliometric analysis
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and momentum of a fundamental particle, do not have an objective
to improve the efficiency of knowledge discovery.
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reality. This strongly contrasts with the objectivity of properties of
   
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everyday macroscopic systems like the (rough estimate of) position and
 
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momentum of a baseball. Now, how can this objectivity of the
There is also a public talk at 7pm, See [https://www.facebook.com/events/2293901217497764/ Public Talk, Argyros Forum, 7pm]
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macroscopic world emerge from a theory where, apparently, not all
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aspects of physical systems are objective? The notion of quantum
 +
Darwinism, put forward and popularized by Wojciech Zurek, is a path in
 +
that direction.  In this talk I will discuss the main ideas behind
 +
quantum Darwinism, explore it in some simple models, and briefly discuss
 +
its relationship (or the lack of it) with the notion of non-Markovianity
 +
of quantum dynamical systems.
  
  
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=== Conference: Monday to Friday, November 12th to November 16th in Sandhu Conference Center ===
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=== Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room) ===
  
==== ''Speaker:'' ''' Advances in operator theory with applications to mathematical physics ''' ====
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==== ''Speaker:'' '''Sandu Popescu, University of Bristol, UK''' ====
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''Title:'' '''Exploring the limits of no-backward-in-time signaling'''
  
''CONFERENCE:'' ''' Advances in operator theory with applications to mathematical physics '''
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''Abstract:'' One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.
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''Abstract: '' For a complete schedule, and a list of abstracts, see: [http://www1.chapman.edu/~alpay/conf2018/conf2018.html Conference Webpage].
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=== Monday, November 5th 2018 at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370===
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==== ''Speaker:'' ''' Dr. Uwe Kahler, Universidade de Aveiro, ''' ====
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''Title:'' '''  Curvature detection using Taylorlets  '''
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''Abstract: '' The problem in detection of nodules in medical images consists of two parts: the detection of edges and the detection of curvature. For the detection of edges as elements of the wavefront set of an image shearlets appeared in the last decade as the principal approach based on approximation. But elements of the wavefront set have a problem in the sense that they are singularities with prescribed direction, but not prescribed curvature. To overcome this problem higher order shearlets, so-called Taylorlets were introduced. While we will discuss them in this talk we will also point out and discuss a principal mathematical problem arising in their application: the problem of construction of a Schwartz function with infinitely many generalized vanishing moments. We will show that Meyer’s frequency-based approach does not fit this case and provide a space-based method for its generation.
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=== Thursday, November 1st 2018 at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370===
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=== Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room) ===
  
==== ''Speaker:'' ''' Dr. Roman Buniy, Chapman University ''' ====
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==== ''Speaker:'' '''Fredrik Dahlqvist, University College London, UK''' ====
 
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''Title:'' ''' Tripartite entanglement of qudits '''
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''Abstract: '' We provide an in-depth study of tripartite entanglement of qudits. We start with a short review of tripartite entanglement invariants, prove a theorem about the complete list of all allowed values of three (out of
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the total of four) such invariants, and give several bounds on the
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allowed values of the fourth invariant. After introducing several
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operations on entangled states (that allow us to build new states from
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old states) and deriving general properties pertaining to their
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invariants, we arrive at the decomposition theorem as one of our main
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results. The theorem relates the algebraic invariants of any
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entanglement class with the invariants of its corresponding components
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in each of its direct sum decompositions. This naturally leads to the
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definition of reducible and irreducible entanglement classes. We
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explicitly compute algebraic invariants for several families of
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irreducible classes and show how the decomposition theorem allows
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computations of invariants for compounded classes to be carried out
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efficiently. This theorem allows us to compute the invariants for the
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infinite number of entanglement classes constructed from irreducible
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components. We proceed with the complete list of the entanglement
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classes for three qutrits with decompositions of each class into
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irreducible components, and provide a visual guide to interrelations of
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these decompositions. We conclude with numerous examples of building
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classes for higher spin qudits.
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=== Friday, October 26th at 3:00pm, in Keck 171, tea and cookies at 2:30pm in Keck 370 ===
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''Title:'' '''A probabilistic approach to floating point arithmetic'''
  
==== ''Speaker:'' ''' Dr. Askery Canabarro, Federal University of Alagoas - BRAZIL ''' ====
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''Abstract:'' Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval.
  
''Title:'' ''' Statistical and Machine Learning for physicists, but not just Physics (part 2) '''
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Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.
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''Abstract: '' Machine Learning has become one of the most exciting areas of modern research and application. In these talks we provide an introduction to the core concepts and tools of machine learning in a way easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning, for instance: ensemble deep learning, auto ML and so on. We illustrate the ideas with problems we are currently involved in.  
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Part 2 of a series of 2 talks.
 
 
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=== Thursday, October 25th at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===
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=== Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===
  
==== ''Speaker:'' ''' Dr. Askery Canabarro, Federal University of Alagoas - BRAZIL ''' ====
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==== ''Speaker:'' '''Jacques Pienaar, International Institute of Physics in Natal, Brazil''' ====
  
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''Title:'' '''The new question in quantum foundations: what is causality?'''
  
''Title:'' ''' Statistical and Machine Learning for physicists (part 1)  '''
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''Abstract:'' Work in quantum foundations has tended to concentrate on Bell's Theorem,
 +
but recently a particular aspect of that theorem has taken on a life of
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its own: the question of what "causality" means in quantum mechanics,
 +
and how to model it. This movement has been driven in large part by
 +
recent advances in causal modeling in the statistical and Artificial
 +
Intelligence communities, which have had a heavy influence on quantum
 +
causal modeling. These "classical" approaches tend to define causality
 +
as a probabilistic and action-centered concept, which fits well with
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modern information-theoretic treatments of quantum mechanics. However,
 +
the classical approaches also tend to emphasize notions of underlying
 +
determinism and objective mechanisms that do not sit so well in the
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quantum context. In this talk I will step back from most of the
 +
technical jargon and try to get to the heart of some of the conceptual
 +
issues involved in "quantizing" the concept of causality, critically
 +
reviewing some key findings, pointing out potential inconsistencies and
 +
outlining possible directions for further inquiry into this fascinating
 +
problem.
  
''Abstract: '' Machine Learning has become one of the most exciting areas of modern research and application. In these talks we provide an introduction to the core concepts and tools of machine learning in a way easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning, for instance: ensemble deep learning, auto ML and so on. We illustrate the ideas with problems we are currently involved in.
 
  
 
Part 1 of a series of 2 talks.
 
 
----
 
----
 
----
 
----
  
=== Friday, October 19th at 1:00pm, in Keck 171, tea and cookies at 2:00pm in Keck 370 ===
+
=== Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room) ===
 +
 
 +
==== ''Speaker:'' '''Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel''' ====
  
==== ''Speaker:'' ''' Dr. Erik Linstead, Chapman University ''' ====
+
''Title:'' '''The past of a quantum particle'''
  
''Title:'' ''' A Convoluted Talk '''
+
''Abstract:'' Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.
+
''Abstract: '' Convolutional neural networks (CNNs) represent the current state-of-the-art in machine learning for computer vision. In this talk we will discuss some interesting applications of CNNs to non-traditional domains, as well as explore what happens to CNNs when we ignore computational efficiency to more closely align with neural physiology.
+
  
  
 
----
 
----
 
----
 
----
=== Thursday, October 18th at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===
 
  
==== ''Speaker:'' ''' Dr. Sandu Popescu, IQS, Chapman University ''' ====
+
=== Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room) ===
  
''Title:'' ''' Dynamical quantum non-locality '''
+
==== ''Speaker:'' '''Prof. Thomas Curtright, University of Miami''' ====
+
''Abstract: '' During the 50 years since its discovery, the Aharonov–Bohm effect has had a significant impact on the development of physics. Its arguably deepest implication, however, has been virtually ignored.
+
  
Next year will be the 60th anniversary of the discovery of the Aharonov–Bohm (AB) effect, one of the most surprising and quintessential effects in quantum mechanics. Since its discovery in 1959, the AB effect has made a significant impact on the development of physics. It has been generalized in a variety of directions — from a rather straightforward dual effect such as the Aharonov–Casher effect, to the celebrated Berry phase, to non-Abelian gauge theories, to Wilson loops, to anyons. During these past 60 years the impact of the AB effect has been significant indeed.
+
''Title:'' '''Massive Dual Gravity Revisited'''
  
And during all these past 60 years, what I believe to be by far the deepest implication of the AB effect (discovered by Yakir Aharonov and described in his Tel Aviv University lecture notes and elsewhere) has been virtually ignored. It is an implication that transcends the specific context from which it originates, and goes directly to the very core of quantum physics: the quantum equations of motion are non-local. Without appreciating this fact, it is safe to say that no real understanding of the nature of quantum mechanics is possible.
+
''Abstract:'' I will describe a highly speculative model of gravity as a massive,
 +
pure spin 2 field, which is "dual" to the usual description in terms of
 +
a spacetime metric tensor.
  
 
+
In the dual description, for weak fields, the metric emerges as the
----
+
field strength of an underlying fundamental field. More generally, if
----
+
the gravitational field is not weak, the metric emerges as a nonlinear
 
+
mixture involving the energy momentum tensor.
=== Thursday, October 4th at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===
+
 
+
==== ''Speaker:'' ''' Dr. Justin Dressel, Chapman University ''' ====
+
 
+
''Title:'' ''' Strengthening weak measurements for qubit tomography and multitime correlators '''
+
+
''Abstract: '' We re-examine the measurement strength needed to perform two recent quantum information tasks with qubits: state tomography using weak values, and determining multitime correlators. Traditionally these protocols have required weak measurements that are minimally disturbing, meaning that the coupling between an investigated quantum system and a measurement device has no appreciable influence on the evolution of the system. We show that the weakness of the interaction is not in fact necessary when measuring qubits. For the case of state tomography, we report an experiment performed with neutron matter-waves that extends the notion of generalized eigenvalues for the neutron's path system to allow the exact determination of weak values using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones both for precision and accuracy. For the case of obtaining multitime correlators, we show a method that uses sequential generalized measurements. Specifically, if a correlator can be expressed as an average of nested (anti)commutators of operators that square to the identity, then that correlator can be determined exactly from the average of a measurement sequence of arbitrary strength. We show that both two-point and four-point (out-of-time-ordered) correlators belong to this useful class of qubit correlators.
+
  
  
Line 331: Line 237:
 
----
 
----
  
=== Thursday, September 27th at 4:15pm, in Keck 171, tea and cookies at 3:45pm in Keck 370 ===
+
=== Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room) ===
  
==== ''Speaker:'' ''' Dr. Matthew Leifer, Chapman University''' ====
+
==== ''Speaker:'' '''Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France''' ====
  
''Title:'' ''' Fine Tunings and the Nature of Quantum Reality '''
+
''Title:'' '''On planar web geometry'''
+
''Abstract: '' Despite many years of research, there is still no universally agreed upon realist interpretation of quantum theory. In this talk, I argue that the main problem is to deal with the fine-tunings implied by no-go theorems about realist approaches to quantum theory, such as Bell’s theorem. We should seek to either eliminate these fine tunings or explain them as emergent. I will give an overview of the various fine-tunings that exist in quantum theory, due to nonlocality, contextuality, lack of time-symmetry, and results on the reality of the quantum state. I will explain how we can quantify each fine tuning, and exploit them in quantum information processing tasks.  If time permits, I will outline two approaches to solve the fine-tuning problem based on block universe models with retrocausality and many-worlds.
+
  
 
+
''Abstract:'' Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented.  
----
+
----
+
 
+
=== Tuesday, September 18th at 4:15pm in Keck 171, tea and cookies at 3:45pm in Keck 370 ===
+
 
+
==== ''Speaker:'' ''' Professor H. Turgay Kaptanoglu, Department of Mathematics, Bilkent University, Ankara ''' ====
+
 
+
''Title:'' ''' Singular Integral Operators With Bergman-Besov Kernels on the ball '''
+
+
''Abstract: '' Although the boundedness of the Bergman-Besov projection operators from Lebesgue classes onto Bergman-Besov spaces has been studied for several decades, the study of the boundedness of the same operators as singular integral operators between different Lebesgue classes are rather new. Some initial work has recently been done by Cheng, Fang, Wang, Yu for the weighted Bergman operator on the unit disc and by Cheng, Hou, Liu for the Drury-Arveson operator. Also Zhao has investigated certain sub-cases of the same problem as Bergman projections. The methods they employ are sporadic and specific to the particular cases they are interested in.
+
  
  
Line 355: Line 249:
 
----
 
----
  
=== The 4th SYSMICS Workshop: Friday-Monday, September 14-17, in Sandhu Conference Center D1 ===
+
=== Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room) ===
  
==== ''Speaker:'' ''' The 4th SYSMICS Workshop  ''' ====
+
==== ''Speaker:'' '''Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics''' ====
  
''Title:'' ''' Topic of the workshop: "Duality in Algebra and Logic” '''
+
''Title:'' '''Entropic uncertainty relations for quantum-information scrambling'''
+
''Abstract: '' Workshop Webpage: http://math.chapman.edu/~jipsen/sysmics/
+
+
  
 +
''Abstract:'' How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.
  
----
+
NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8
----
+
 
+
=== Friday, August 31st at 3:30pm, in Beckman 404 ===
+
 
+
==== ''Speaker:'' ''' Dr. Philip Mannheim, Professor of Physics, University of Connecticut  ''' ====
+
 
+
''Title:'' ''' The Crisis  in Fundamental  Physics '''
+
+
''Abstract: '' Cosmology deals with the the astrophysical macroscopic universe on large
+
scales while fundamental  physics  deals with the particle physics
+
microscopic universe on small ones. Recently it has become apparent that
+
large and small scale physics  are actually intertwined leading to an
+
astro-particle picture of the universe. At the present time this picture
+
has achieved great success, but at the same time it has led to many open
+
questions and challenges, challenges which threaten to potentially
+
undermine the entire picture. These challenges include dark matter, dark
+
energy, the cosmological constant problem, quantum gravity, the status of
+
supersymmetry, the multiverse picture, extra space-time dimensions, and the nature of the Higgs boson. In this talk we review these issues and suggest that their resolution would require a paradigm shift in our view of the universe.
+
  
  
Line 389: Line 263:
 
----
 
----
  
=== Friday, August 31st at 1:00pm, Keck 171, lunch with the speaker in the Faculty Club at noon ===
+
=== Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room) ===
  
==== ''Speaker:'' ''' Dr. Philip Mannheim, Professor of Physics, University of Connecticut  ''' ====
+
==== ''Speaker:'' '''Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology''' ====
  
''Title:'' ''' Why physicists are interested in differential geometry '''
+
''Title:'' '''Computing Causal Relations at Scale    or    Causality: From Aristotle through Computing to Zebrafish'''
+
''Abstract: '' Ever since Einstein's development of gravity theory, general relativity and differential geometry have been central components of physics research and of our understanding of the universe. Of special interest is how gravity can interface with the other fundamental forces, the nuclear force, the weak force, and especially the electromagnetic force. In this talk we describe some of the motivation and central achievements for general relativity, and discuss some proposed generalizations of it such as torsion and Weyl geometry that might lead to a purely geometric unification of the fundamental forces.
+
  
 +
''Abstract:'' What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.
  
----
+
''Bio:'' Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.
----
+
 
+
=== Thursday, August 30th at 4:00pm, Keck 171, tea and cookies at 3:30pm in Keck 370===
+
 
+
==== ''Speaker:'' ''' Dr. Philip Mannheim, Professor of Physics, University of Connecticut  ''' ====
+
 
+
''Title:'' ''' Quantum Conformal Gravity '''
+
+
''Abstract: '' Conformal symmetry is a natural symmetry in physics since it is the full symmetry of the light cone. If all particles are to get their masses by symmetry breaking then conformal symmetry is the symmetry of the unbroken Lagrangian. Like Yang-Mills theories conformal symmetry has a local extension, namely conformal gravity, a pure metric-based candidate alternative to the non-conformal invariant standard Newton-Einstein theory of gravity. With its dimensionless coupling constant quantum conformal gravity is power counting renormalizable. Since its equations of motion are fourth-order derivative equations conformal gravity has long been thought to possess unacceptable ghost states of negative norm that would violate unitarity. However on constructing the quantum Hilbert space Bender and Mannheim found that this not to be the case. Conformal gravity is thus offered as a completely consistent and unitary quantum theory of gravity, one that requires neither the extra dimensions nor the supersymmetry of string theory. As formulated via local conformal invariance there is no intrinsic classical gravity, with gravity instead being intrinsically quantum-mechanical, with the observed classical gravity being output rather than input. The contribution of the graviton loops of conformal gravity enables conformal gravity to solve the cosmological constant problem. Like Yang-Mills the potential of conformal gravity contains both a Newtonian term and a linear potential. Together with a quadratic potential that the theory also contains conformal gravity is able to explain the systematics of galactic rotation curves  without any need for galactic dark matter. Since all mass is to be dynamical there cannot be a fundamental double-well Higgs potential in the theory. Instead, the Higgs boson is generated dynamically, with the hierarchy problem then being solved.
+
  
 +
His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.
  
  
Line 414: Line 279:
 
----
 
----
  
=== Thursday, August 23rd at 4:00pm, Keck 171, tea and cookies at 3:30pm in Keck 370===
 
  
==== ''Speaker:'' ''' Dr. Gunduz Caginalp, Professor of Mathematics, University of Pittsburgh''' ====
 
  
''Title:'' ''' Volatility Maxima as a Forecaster of Trading Price Extrema '''
+
== Previous Seminar talks ==
+
''Abstract: '' This is joint work with Carey Caginalp. The relationship between price volatility and a market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic setting, we obtain the implications of randomness in the supply and demand, rather than assuming that price has randomness on an empirical basis. Within a very general setting the volatility has a maximum that precedes the extremum of the price. A key issue is that randomness arises from the supply and demand, and the variance in the stochastic differential equation governing the logarithm of price must reflect this. Analogous results are obtained by further assuming that the supply and demand are dependent on the deviation from fundamental value of the asset.
+
  
 
+
* [[MPC Seminar 2019]]
----
+
----
+
 
+
 
+
== Previous Seminar talks ==
+
  
 
* [[MPC Seminar 2018]]
 
* [[MPC Seminar 2018]]

Latest revision as of 21:11, 11 March 2020

This is the homepage of the Chapman University Mathematics, Physics, and Computation Seminars (MPC Seminar)

Seminar Organizers: Roman Buniy and Peter Jipsen


Contents

Spring 2020

The seminar talks are held in Keck Center for Science and Engineering, KC 370 (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), usually on Wednesday at 4 pm. Sometimes there will be a change of time or venue and the announcement will reflect this change.

See [http://www.chapman.edu/about/maps-directions/index.aspx Maps and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf Campus map]




Wednesday, April 29th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

Speaker: Sean Carroll, Caltech, Pasadena, CA

Title: TBA





Friday, Feb 21st, 2020, noon - 1 pm in Keck 370, refreshments at 11:45 am (same room)

Speaker: Christian Williams, University of California at Riverside

Title: Predicate Calculus for Algebraic Theories

Abstract: There is a notion of predicate for algebraic theories, which admits a calculus of both logical and algebraic operations. We thereby extend equational logic by first-order logic, and provide a natural type theory for algebraic structures.

We demonstrate the idea with the theory of monoids, and derive the example predicate "prime". This and many algebraic examples are only useful when they are mapped from a theory into actual models. There is much to be done in this direction. However, the driving motivation of this work is the application to programming languages: we focus on applying the idea to a more general notion of theory with variable binding.

The construction is given in the topos of presheaves on a theory T: a "predicate" is a sieve on an object t of T, which corresponds to a subfunctor of the representable T(-,t). For each type t, these predicates form a Heyting algebra, providing the constructors of intuitionistic logic. The operations of T can be lifted to act on predicates, and we construct a model Pred(T): T -->HeyAlg. The correspondence between the operations of T and those in the image of Pred(T) gives that the former are "polymorphic" with respect to the types of the latter. This process can be understood as providing the theory T with a polymorphic type system.

The original motivation of this work is a logic for concurrency known as Namespace Logic. This applies to the reflective higher-order pi calculus, which is the language of the distributed computing platform RChain. We demonstrate the above framework by constructing namespace logic. This gives a glimpse into a large field of potential application.

Slides from the talk




Wednesday, Feb 19th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

Speaker: Simon Cho, University of Michigan

Title: A categorical perspective on persistent and magnitude homology

Abstract: We define and explain both persistent homology and magnitude homology, and their respective roles in applications (in both pure and applied settings). We will exhibit how both arise as a "singular complex" of a metric space in essentially the same way, but for different values of a parameter.




Wednesday, Feb 12th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

Speaker: Stephon Alexander, Brown University, Rhode Island

Title: The Quantum Cosmological Constant

Abstract: The mysteries surrounding the Cosmological Constant presides at the interface of quantum mechanics and gravity. In this seminar, I will provide a pedagogical discussion of the many faces of the cosmological constant problem and discuss some current research that paves new directions that invites us to rethink the quantum nature of vacuum energy.




Tuesday, Jan 14th, 2020, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

Speaker: Pedram Roushan, Google Inc., Santa Barbara, CA

Title: Quantum supremacy using a programmable superconducting processor

Abstract: The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2^53 (about 10^16). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm. If time permits, I will present some of our more recent measurements.




Fall 2019

The seminar talks are held in Keck Center for Science and Engineering, KC 370 (Center St. Orange, CA 92866, intersection of Center St. And Sycamore St.), usually on Wednesday at 4 pm. Sometimes there will be a change of time or venue and the announcement will reflect this change.

See [http://www.chapman.edu/about/maps-directions/index.aspx Maps and directions], Keck Center is Building 28 on the Campus Map [https://www.chapman.edu/about/_files/maps-and-directions/current-maps/campus-map.pdf Campus map]




Thursday, Dec 12th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

Speaker: Alí Guzmán Adán, Universiteit Gent, Belgium

Title: Pizzetti and Cauchy formulae for higher dimensional surfaces: a distributional approach

Abstract: In this talk, we study Pizzetti-type formulas for Stiefel manifolds and Cauchy-type formulas for the tangential Dirac operator from a distributional perspective. First, we illustrate a general distributional method for integration over manifolds in R^m defined by means of k equations. We apply this method to derive an alternative proof of the Pizzetti formulae for the real Stiefel manifolds SO(m)/SO(m-k). Besides, a distributional interpretation of invariant oriented integration is provided. In particular, we obtain a distributional Cauchy theorem for the tangential Dirac operator on an embedded (m-k)-dimensional smooth surface.




Wednesday, Dec 11th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

Speaker: Arjendu K Pattanayak, Physics and Astronomy, Carleton College, Northfield, Minnesota

Title: Quantum entanglement and tunneling oscillations in a (few) many-body nonlinear spin system

Abstract: Quantum tunnelling permits recoherence or refocusing in real or phase space after the initial quantum state has seemingly delocalized, exhibiting so-called classically forbidden dynamics. For a nonlinearly interacting many-body spin system this interim state can be an entangled state. We report on recent results from investigations into this phenomenon for initially spin coherent pure states in the paradigmatic kicked top (vale Haake) system. This has a mixed regualar and chaotic phase space in the classical limit and exhibits the entanglement tunneling described above, including coherent dynamics between phase-space stability islands; here the interim state is maximally entangled. We map the dependence on various parameters including nonlinear spin and number of spins involved (focusing mostly on the remarkable special case N=4) using a metric that attempts to quantify the quality and rate of tunnelling. The calculations of tunneling rates using eigenvalues and eigenstates of the time evolution operator as a function of initial condition compared to classical space structures demonstrates several nontrivial ways in which quantum behavior transitions to classical as the size of the system grows.




Wednesday, Dec 4th, 2019, 4 - 5 pm in Keck 370, refreshments at 3:45 pm (same room)

Speaker: Raphael Drumond, Universidade Federal de Minas Gerais, Brazil

Title: The basics of Quantum Darwinism (and its relationship with non-Markovianity)

Abstract: Some aspects of physical systems described by quantum mechanics, most notably the possibility of violating a Bell inequality, suggests (to some) or unavoidably implies (to others) that certain properties of microscopic systems, like the precise values of position and momentum of a fundamental particle, do not have an objective reality. This strongly contrasts with the objectivity of properties of everyday macroscopic systems like the (rough estimate of) position and momentum of a baseball. Now, how can this objectivity of the macroscopic world emerge from a theory where, apparently, not all aspects of physical systems are objective? The notion of quantum Darwinism, put forward and popularized by Wojciech Zurek, is a path in that direction. In this talk I will discuss the main ideas behind quantum Darwinism, explore it in some simple models, and briefly discuss its relationship (or the lack of it) with the notion of non-Markovianity of quantum dynamical systems.




Thursday, Nov 21th, 2019, 12:30 - 1:30 pm in Keck 370, refreshments from 12:15 (same room)

Speaker: Sandu Popescu, University of Bristol, UK

Title: Exploring the limits of no-backward-in-time signaling

Abstract: One of the most routine observations that we make about our world is that we cannot signal backwards in time. So ubiquitous is this understanding that it is often taken as one of the basic laws of Nature. At first glance, this remark seems straightforward. However, as I will show, in probabilistic theories such as quantum mechanics, the consequences of such an assertion are far more involved. In fact, we will see that there is a surprising amount of liberty: some theories even allow the future to affect the past, nevertheless without signaling backwards in time.




Friday, Nov 8th, 2019, 3 - 4 pm in Keck 171, refreshments from 2:45 (same room)

Speaker: Fredrik Dahlqvist, University College London, UK

Title: A probabilistic approach to floating point arithmetic

Abstract: Finite-precision floating point arithmetic introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be extremely rare events in practice. Here we develop a probabilistic model of rounding errors with which it becomes possible to quantify the likelihood that the rounding error of an algorithm lies within a given interval.

Given an input distribution, the model requires the distribution of rounding errors. We show how to exactly compute this distribution for low precision arithmetic. For high precision arithmetic we derive a simple but surprisingly useful approximation. The model is then entirely compositional: given a numerical program written in a simple imperative programing language we can recursively compute the distribution of rounding errors at each step and propagate it through each program instruction. This is done by applying a formalism originaly developed by Kozen to understand the semantics of probabilistic programs, for example how probability distributions gets transformed by assignments or "if then else" statements.




Wednesday, Nov 6th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room)

Speaker: Jacques Pienaar, International Institute of Physics in Natal, Brazil

Title: The new question in quantum foundations: what is causality?

Abstract: Work in quantum foundations has tended to concentrate on Bell's Theorem, but recently a particular aspect of that theorem has taken on a life of its own: the question of what "causality" means in quantum mechanics, and how to model it. This movement has been driven in large part by recent advances in causal modeling in the statistical and Artificial Intelligence communities, which have had a heavy influence on quantum causal modeling. These "classical" approaches tend to define causality as a probabilistic and action-centered concept, which fits well with modern information-theoretic treatments of quantum mechanics. However, the classical approaches also tend to emphasize notions of underlying determinism and objective mechanisms that do not sit so well in the quantum context. In this talk I will step back from most of the technical jargon and try to get to the heart of some of the conceptual issues involved in "quantizing" the concept of causality, critically reviewing some key findings, pointing out potential inconsistencies and outlining possible directions for further inquiry into this fascinating problem.




Friday, October 18th, 2019, 12 - 1 pm in Keck 370, refreshments from 11:45 (same room)

Speaker: Prof. Lev Vaidman, Alex Maguy-Glass Chair in Physics of Complex Systems, Tel Aviv University, Israel

Title: The past of a quantum particle

Abstract: Textbooks of quantum mechanics lack the concept of the past of quantum systems. Few years ago I proposed to define the past of a quantum particle according to the trace it leaves. While in many cases this definition provides a reasonable description, for a nested Mach-Zehnder interferometer it leads to a picture seemingly contradicting common sense: the particle leaves a trace in a place through which it could not pass. I will discuss recent theoretical and experimental studies of this controversial issue.




Friday, October 11th, 2019, 1 - 2 pm in Keck 370, refreshments from 12:45 (same room)

Speaker: Prof. Thomas Curtright, University of Miami

Title: Massive Dual Gravity Revisited

Abstract: I will describe a highly speculative model of gravity as a massive, pure spin 2 field, which is "dual" to the usual description in terms of a spacetime metric tensor.

In the dual description, for weak fields, the metric emerges as the field strength of an underlying fundamental field. More generally, if the gravitational field is not weak, the metric emerges as a nonlinear mixture involving the energy momentum tensor.




Wednesday, October 9th, 2019, 4 - 5 pm in Keck 370, refreshments from 3:45 (same room)

Speaker: Alain Hénaut, Institut de Mathématiques de Bordeaux, Université de Bordeaux, France

Title: On planar web geometry

Abstract: Web geometry deals with foliations in general position. In the planar case and the complex setting, a $d$-web is given by the generic family of integral curves of an analytic or an algebraic differential equation $F(x,y,y')=0$ with $y'$-degree $d$. Invariants of these configurations as abelian relations (related to Abel's addition theorem), Lie symmetries or Godbillon-Vey sequences are investigated. This viewpoint enlarges the qualitative study of differential equations and their moduli. In the nonsingular case and through the singularities, Cartan-Spencer and meromorphic connections methods will be used. Basic examples will be given from different domains including classic algebraic geometry and WDVV-equations. Standard results and open problems will be mentioned. Illustration of the interplay between differential and algebraic geometry, new results will be presented.




Thursday, September 5th, 2019, 4 - 5 pm in Keck 171, refreshments from 3:45 (same room)

Speaker: Nicole Yunger Halpern, Harvard-Smithsonian ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Harvard University Department of Physics

Title: Entropic uncertainty relations for quantum-information scrambling

Abstract: How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: (i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. (ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, spreads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements’ possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields—quantum information, condensed matter, and high-energy physics—can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots.

NYH, Bartolotta, and Pollack, Comms. Phys. 2, 92 (2019). https://www.nature.com/articles/s42005-019-0179-8




Monday, August 26, 2019, 7 - 8:30 pm, in Argyros Forum, Room 209 A&B, networking from 6:15 to 7pm (same room)

Speaker: Frederick Eberhardt, Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology

Title: Computing Causal Relations at Scale or Causality: From Aristotle through Computing to Zebrafish

Abstract: What causes what? How do we untangle the “why” behind processes that regulate the brain, the climate or the economy? If “Correlation does not imply causation" is the standard mantra in science, how can we ever discover causal relationships behind the data? Will it ever be possible for intelligent AI to make its own deductions and predictions? In recent years researchers have developed mathematical techniques that give us the power to infer the underlying “why” behind scientific data. What’s more, we’ve learned that we can discover these causes without performing experiments. Starting with a little practical example with lightbulbs that can be worked out by hand we will see how the problem scales as the number of variables increases. To compute the neural connections in a zebrafish brain, high performance computing is essential.

Bio: Frederick Eberhardt is Professor of Philosophy in the Division of the Humanities and Social Sciences at the California Institute of Technology. Before coming to Caltech he was Assistant Professor in the Philosophy-Neuroscience-Psychology (PNP) program and the Department of Philosophy at Washington University in St. Louis and a postdoc at the Institute of Cognitive and Brain Sciences at the University of California, Berkeley. As an undergraduate he attended the London School of Economics for a Bachelor in Philosophy & Mathematics. He received his PhD in philosophy from Carnegie Mellon University, where he also completed a Masters in Machine Learning.

His research interests lie at the intersection of philosophy of science, machine learning and statistics. He is particularly interested in the development of methods for causal discovery from statistical data.





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