**The New York City**

**Category Theory Seminar**

**
Department of Computer Science**

Department of Mathematics

The Graduate Center of The City University of New York

THE TALKS WILL ALL BE DONE ON ZOOM THIS SEMESTER.

Time: Wednesdays 07:00 PM Eastern Time (US and Canada)

https://us02web.zoom.us/j/84134331639?pwd=TVRzVjlaZW5CNVh5ampxOGJ0RE5QQT09

Meeting ID: 841 3433 1639

Passcode: NYCCTS

Usually our talks take place at

365 Fifth Avenue (at 34th Street) map

(Diagonally across from the Empire State Building)

New York, NY 10016-4309

Room 6417

Wednesdays 7:00 - 8:30 PM

Videoed talks.

Previous semesters.

Research seminars page.

Contact N. Yanofsky to
schedule a speaker

or to add a name to the
seminar mailing list.

**Fall 2021 **

Speaker: ** Gemma De las Cuevas, University of Innsbruck.**

Date and Time: ** Wednesday October 6, 2021, 7:00 - 8:30 PM., on Zoom.**

Title:** From simplicity to universality and undecidability.**

Abstract: Why is it so easy to generate complexity? I will suggest that this is due to the phenomenon of universality — essentially every non-trivial system is universal, and thus able to explore all complexity in its domain. We understand universality in spin models, automata and neural networks. I will present the first step toward rigorously linking the first two, where we cast classical spin Hamiltonians as formal languages and classify the latter in the Chomsky hierarchy. We prove that the language of (effectively) zero-dimensional spin Hamiltonians is regular, one-dimensional spin Hamiltonians is deterministic context-free, and higher-dimensional and all-to-all spin Hamiltonians is context-sensitive. I will also talk about the other side of the coin of universality, namely undecidability, and will raise the question of whether universality is visible

in Lawvere’s Theorem.

Speaker: ** Dan Shiebler, Oxford University.**

Date and Time: ** Wednesday October 20, 2021, 7:00 - 8:30 PM., on Zoom.**

Title:** Out of Sample Generalization with Kan Extensions.**

Abstract: A common problem in data science is use this function defined over this small set to generate predictions over that larger set.

Extrapolation, interpolation, statistical inference and forecasting all reduce to this problem. The Kan extension is a powerful tool in category theory that generalizes this notion. In this work we explore several applications of Kan extensions to data science.

Speaker: ** Dusko Pavlovic, University of Hawai‘i at Mānoa.**

Date and Time: ** Wednesday November 3, 2021, 7:00 - 8:30 PM., on Zoom.**

Title:** Geometry of computation and string-diagram programming in a monoidal computer.**

Abstract: A monoidal computer is a monoidal category with a distinguished type carrying the structure of a single-instruction programming language. The instruction would be written as "run", but it is usually drawn as a string diagram. Equivalently, the monoidal computer structure can be viewed as a typed lambda-calculus without lambda abstraction, even implicit. Any Turing complete programming language, including Turing machines and partial recursive functions, gives rise to a monoidal computer. We have thus added yet another item to the Church-Turing list of models of computation. It differs from other models by its categoricity. While the other Church-Turing models can be programmed to simulate each other in many different ways, and each interprets even itself in infinitely many non-isomorphic ways, the structure of a monoidal computer is unique up to isomorphism. A monoidal category can be a monoidal computer in at most one way, just like it can be closed in at most one way, up to isomorphism. In other words, being a monoidal computer is a property, not structure. Computability is thus a categorical property, like completeness. This opens an alley towards an abstract treatment of parametrized complexity, one-way and trapdoor functions on one hand, and of algorithmic learning in the other.

Speaker: ** Marco Schorlemmer, Spanish National Research Council.**

Date and Time: ** Wednesday November 17, 2021, 7:00 - 8:30 PM., on Zoom.**

Title:** A Uniform Model of Computational Conceptual Blending.**

Abstract: We present a mathematical model for the cognitive operation of conceptual blending that aims at being uniform across different representation formalisms, while capturing the relevant structure of this operation. The model takes its inspiration from amalgams as applied in case-based reasoning, but lifts them into category theory so as to follow Joseph Goguen’s intuition for a mathematically precise characterisation of conceptual blending at a representation-independent level of abstraction. We prove that our amalgam-based category-theoretical model of conceptual blending is essentially equivalent to the pushout model in the ordered category of partial maps as put forward by Goguen. But unlike Goguen’s approach, our model is more suitable to capture computational realisations of conceptual blending, and we exemplify this by concretising our model to computational conceptual blends for various representation formalisms and application domains.

Speaker: ** Robert Geroch, University of Chicago.**

Date and Time: ** Wednesday December 1, 2021, 7:00 - 8:30 PM., on Zoom.**

Title:** An Alien's Perspective on Mathematics (and Physics).**

Abstract: We describe what might be called a "point of view" toward mathematics. This view touches on such issues as how Godel's theorem might be interpreted, the relevance to physics of mathematical axioms such as the axiom of choice, and the possibility of using physics to "solve" unsolvable mathematical problems.

Related paper.

Speaker: ** Jens Hemelaer, University of Antwerp.**

Date and Time: ** Wednesday December 8, 2021, 7:00 - 8:30 PM., on Zoom.**

Title:** Toposes of presheaves on a monoid and their points.**

Abstract: In 2014, Connes and Consani constructed their Arithmetic Site, with as underlying topos the topos of presheaves on the monoid of nonzero natural numbers under multiplication. One of their surprising results is that the points of this topos are classified by a double quotient of the finite adeles, leading immediately to a link with number theory. Inspired by this, we will consider toposes of presheaves on various monoids, and discuss strategies of calculating their points. The most recent strategies (involving for example étale geometric morphisms and complete spreads) are based on joint work with Morgan Rogers.

Speaker: ** Samantha Jarvis, The CUNY Graduate Center.**

Date and Time: ** Wednesday December 15, 2021, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** Todd Trimble, Western Connecticut State University.**

Date and Time: ** Wednesday December 22, 2021, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

**Spring 2022 **

Speaker: ** Ralph Wojtowicz, Shenandoah University.**

Date and Time: ** Wednesday February 2, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** Emilio Minichiello, CUNY Graduate Center.**

Date and Time: ** Wednesday February 16, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** David Roberts, University of Adelaide.**

Date and Time: ** Wednesday February 23, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** Jin-Cheng Guu, Stony Brook University.**

Date and Time: ** Wednesday March 9, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** Topological Quantum Field Theories from Monoidal Categories.**

Abstract: We will introduce the notion of a topological quantum field theory (tqft) and a monoidal category. We will then construct a few (extended) tqfts from monoidal categories, and show how quantum invariants of knots and 3-manifolds were obtained. If time permits, I will discuss (higher) values in (higher) codimensions based on my recent work on categorical center of higher genera (joint with A. Kirillov and Y. H. Tham).

Speaker: ** TBA, TBA.**

Date and Time: ** Wednesday March 23, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** TBA, TBA.**

Date and Time: ** Wednesday March 30, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** TBA, TBA.**

Date and Time: ** Wednesday April 6, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** TBA, TBA.**

Date and Time: ** Wednesday April 13, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** TBA, TBA.**

Date and Time: ** Wednesday April 27, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** TBA, TBA.**

Date and Time: ** Wednesday May 4, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** TBA, TBA.**

Date and Time: ** Wednesday May 11, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract:

Speaker: ** TBA, TBA.**

Date and Time: ** Wednesday May 18, 2022, 7:00 - 8:30 PM., on Zoom.**

Title:** TBA.**

Abstract: