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Emilio Minichiello (Feb 06 2024 at 15:12):Not sure if this should go here, but the NYC Category Theory seminar is starting up for the semester tomorrow.
Here are the details, note that the time is EST.
ZOOM INFORMATION:
https://brooklyn-cuny-edu.zoom.us/j/83479113097?pwd=Wis5OG80WUdScFQwcXdFRlVQdjZoZz09
Meeting ID: 834 7911 3097
Passcode: NYCCTS
Speaker: Saeed Salehi, Univeristy of Tabriz.
Date and Time: Wednesday February 7, 2024, 11:00AM - 12:00 NOON. NOTICE SPECIAL TIME!!! ZOOM TALK!!!
Title: On Chaitin's two HP's: (1) Heuristic Principle and (2) Halting Probability.
Abstract: Two important achievements of Chaitin will be investigated: the Omega number, which is claimed to be the halting probability of input-free programs, and the heuristic principle, which is claimed to hold for program-size complexity. Chaitin's heuristic principle says that the theories cannot prove the heavier sentences; the sentences and the theories were supposedly weighed by various computational complexities, which all turned out to be wrong or incomplete. In this talk, we will introduce a weighting that is not based on any computational complexity but on the provability power of the theories, for which Chaitin's heuristic principle holds true. Also, we will show that the Omega number is not equal to the halting probability of the input-free programs and will suggest some methods for calculating this probability, if any.
Emilio Minichiello (Feb 06 2024 at 15:13):Here is the seminar website : https://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.html
Morgan Rogers (he/him) (Feb 06 2024 at 15:16):It definitely should go here :innocent:
Emilio Minichiello (Mar 05 2024 at 18:09):Forgot to post last week. Here is the Youtube video for last week's talk.
There is a talk tomorrow, here are the details. Note the talk is in person, time is EST, and the location is the CUNY Graduate Center. See the seminar website for more information.
Speaker: Jean-Pierre Marquis, Universite de Montreal.
Date and Time: Wednesday March 6, 2024, 7:00 - 8:30 PM (EST). IN PERSON TALK!
Title: Hom sweet Hom: a sketch of the history of duality in category theory.
Abstract: Duality, in its various forms and roles, played a surprisingly important part in the development of category theory. In this talk, I will concentrate on the development of these forms and roles that lead to the categorical formulation of Stone-type dualities in the 1970s. I will emphasize the epistemological gain and loss along the way.
Emilio Minichiello (Mar 18 2024 at 11:28):We have a seminar this Wednesday over Zoom. See seminar website for more information.
Speaker: Sina Hazratpour, Johns Hopkins University.
Date and Time: Wednesday March 20, 2024, 4:00 - 5:30 PM. NOTE SPECIAL TIME. ZOOM TALK!!!
Title: Fibred Categories in Lean.
Abstract: Fibred categories are one of the most important and useful concepts in category theory and its application in categorical logic. In this talk I present my recent formalization of fired categories in the interactive theorem prover Lean 4. I begin by highlighting certain technical challenges associated with handling the equality of objects and functors within the extensional dependent type system of Lean, and how they can be overcome. In this direction, I will demonstrate how we can take advantage of dependent coercion, instance synthesis, and automation tactics from of the Lean toolbox. Finally I will discuss a formalization of Homotopy Type Theory in Lean 4 using a fired categorical framework.
Lean formalization repository.
Emilio Minichiello (Apr 07 2024 at 13:43):We have a seminar this Wednesday in person! See seminar website for more information.
· Speaker: Ellis D. Cooper.
· Date and Time: Wednesday April 10, 2024, 7:00 - 8:30 PM. IN-PERSON
· Title: Pulse Diagrams and Category Theory.
· Abstract: ``Pulse diagrams'' are motivated by the ubiquity of pulsation in biology, from action potentials, to heartbeat, to respiration, and at longer time-scales to circadian rhythms and even to human behavior. The syntax of the diagrams is simple, and the semantics are easy to define and simulate with Python code. They express behaviors of parts and wholes as in categorical mereology, but are missing a compositional framework, like string diagrams. Examples to discuss include cellular automata, leaky-integrate-and-fire neurons, harmonic frequency generation, Gillespie algorithm for the chemical master equation, piecewise-linear genetic regulatory networks, Lotka-Volterra systems, and if time permits, aspects of the adaptive immune system. The talk is more about questions than about answers.
Emilio Minichiello (May 06 2024 at 12:33):We have a seminar this Wednesday over Zoom. See seminar website for more information.
Emilio Minichiello (May 13 2024 at 16:10):We have a seminar this Wednesday in person! See seminar website for more information.
Abstract: In previous talks at this Category seminar and at the Topology, Geometry and Physics seminar, Arthur Parzygnat showed how Bayesian inversion and its generalization to quantum mechanics may be interpreted as a functor on a suitable category of states which satisfies certain axioms. Such a functor is called a retrodiction and Parzygnat and collaborators conjectured that retrodiction is unique. In this talk, I will present a proof of this conjecture for the special case of classical probability theory on finite state spaces.
In this special case, the category in question has non-degenerate probability distributions on finite sets as its objects and stochastic matrices as its morphisms. After preliminary definitions and lemmas, the proof proceeds in three main steps.
In the first step, we focus on certain groups of automorphisms of certain objects. As a consequence of the axioms, it follows that these groups are preserved under any retrodiction functor and that the restriction of the functor to such a group is a certain kind of group automorphism. Since this group is isomorphic to a Lie group, it is easy to prove that the restriction of a retrodiction to such a group must equal Bayesian inversion if we assume continuity. If we do not make that assumption, we need to work harder and derive continuity "from scratch" starting from the positivity condition in the definition of stochastic matrix.
In the second step, we broaden our attention to the full automorphism groups of objects of our category corresponding to uniform distributions. We show that these groups are generated by the union of the subgroup consisting of permutation matrices and the subgroup considered in the first step. From this fact, it follows that the restriction of a retrodiction to this larger group must equal Bayesian inversion.
In the third step, we finally consider all the objects and morphisms of our category. As a consequence of what we have shown in the first two steps and some preliminary lemmas, it follows that retrodiction is given by matrix conjugation. Furthermore, Bayesian inversion is the special case where the conjugating matrices are diagonal matrices. Because the hom sets of our category are convex polytopes and a retrodiction functor is a continuous bijection of such sets, a retodiction must map polytope faces to faces. By an algebraic argument, this fact implies that the conjugating matrices are diagonal, answering the conjecture in the affirmative.