The New York City Category Theory Seminar Department of Computer Science Department of Mathematics The Graduate Center of The City University of New York Some talks will be in-person (with a Zoom connection) and some talks will only be on Zoom. Time: Wednesdays 02:00-3:00 PM Eastern Time (US and Canada) NOTICE NEW TIME!!! IN-PERSON INFORMATION: 365 Fifth Avenue (at 34th Street) map (Diagonally across from the Empire State Building) New York, NY 10016-4309 Room 4214.03 NOTICE NEW ROOM!!! There will be a Zoom link to join us on in-person talks. This means that from now on, in-person talks will be hybrid. ZOOM INFORMATION: https://brooklyn-cuny-edu.zoom.us/j/84134080992?pwd=MNvAvOfYemk2bh7qCtI9I5zQ... Meeting ID: 841 3408 0992 Passcode: NYCCTS Seminar web page. Videoed talks. Previous semesters. List of previous speakers. Researchseminars.org page. Co-organizers: Emilio Minichiello and Noson S. Yanofsky. Contact E. Minichiello<mailto:eminichiello67@gmail.com> or N. Yanofsky<mailto:nosony@brooklyn.cuny.edu> to schedule a speaker or to add a name to the seminar mailing list. ________________________________ ________________________________ Spring 2026 ________________________________ ________________________________ • Speaker: Sergei Artemov, The CUNY Graduate Center. • Date and Time: Wednesday February 4, 2026, 2:00 - 3:30 PM. IN-PERSON TALK • Title: Non-compact proofs. • Abstract: Non-compact proofs are used in mathematics but overlooked in the analysis of (un)provability of consistency. We focus on arithmetical proofs of universal statements (*) "for any natural number n, F(n)." A proof of (*) is compact if all proofs of F(n)'s for n=0,1,2,... fit into some finitely axiomatized fragment of Peano Arithmetic PA. An example of non-compact reasoning is the standard proof of Mostowski's 1952 reflexivity theorem: PA proves the consistency of its finite fragments. It turns out that Gödel's Second Incompleteness Theorem, G2, prohibits compact proofs but does not rule out non-compact proofs of PA-consistency formalizable in PA. This explains why and how the recent proofs of PA-consistency in PA work: they essentially formalize in PA the explicit version of Mostowski's non-compact proof and use Gödelian provable explicit reflection to rid redundant provability operators. These findings yield a new foundational reading of G2: "the consistency of PA is not provable within a finite fragment of PA," complemented with the positive message: "the consistency of PA is provable within the whole PA." This perspective suggests that Gödel's theorem does not represent a failure of the system to "know" its own consistency, but rather a structural limit on how that knowledge can be packaged into a single finite string. ________________________________ • Speaker: David Ellerman, University of Ljubljana. • Date and Time: Wednesday February 11, 2026, 2:00 - 3:30 PM. ZOOM TALK • Title: A Fundamental Duality in the Exact Sciences: An Introduction to Mathematical Metaphysics. • Abstract: There is a fundamental duality that runs through the exact sciences. At the logical level, it is the duality between (Boolean) logic of subsets and the logic of partitions. The quantitative versions of the dual logics are logical probability theory and logical information theory. The duality accounts for the duality in the category of Sets and its opposite Sets^{op}. The partial order in the two dual logics gives the two fundamental canonical functions and the claim is that all canonical morphisms in Sets arise from those two morphisms. In physics, there is the notion of "definiteness all the way down" which arises in classical physics (Boolean logic of subsets) and dually there is the notion of definiteness only down to a certain level and then objective indefiniteness that arises in quantum physics (logic of partitions). ________________________________ • Speaker: Ellis Cooper . • Date and Time: Wednesday February 18, 2026, 2:00 - 3:30 PM. IN-PERSON TALK • Title: Algebraic String Diagrams and a Manifest Covariance Theorem. • Abstract: Book titles such as "Covariant Physics" (Moataz H. Emam) and "Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory" (Carlo Rovelli and Francesca Vidotto) shout the important of covariance in modern mathematical physics. In categorical terms, covariance is a family of natural isomorphisms of pairs of functors defined on the groupoid of diffeomorphisms in a category of ``domains." "Manifest covariance" is a syntactic concept arising from preservation of covariance of basic covariant tensor calculations combined by composition and product maps. Differential geometry and general relativity theory calculations are expressed by algebraic string diagrams, including the Einstein Curvature Tensor. Physical nature is categorically natural. ________________________________ • Speaker: James Austin Myer, CUNY. • Date and Time: Wednesday March 4, 2026, 2:00 - 3:30 PM. IN-PERSON TALK • Title: The Bloch Material: a Simplicial Set Whose Homology is the Higher Chow Groups of Spencer Bloch. • Abstract: To this day, it is still unknown whether every variety enjoys a resolution of its singularities. Dennis Sullivan suggests in a 2004 memorial article for René Thom that the obstructions constructed to attack Steenrod’s problem could be adapted to handle the outstanding scenario in positive characteristic. We will discuss a construction en route to the realization of this dream: to each variety, we prescribe a simplicial set whose homology is the higher Chow groups of (Spencer) Bloch. In particular, this simplicial set recovers the topology of the analytic space associated to a variety over the complex numbers ________________________________ • Speaker: Kristaps John Balodis, University of Calgary. • Date and Time: Wednesday March 11, 2026, 2:00 - 3:30 PM. ZOOM TALK • Title: A geometric introduction to the local Langlands correspondence. • Abstract: In this talk I will provide a non-traditional introduction to the local Langlands program for p-adic groups by framing the so-called "Galois side" geometrically. For simplicity, the primary focus will be on the "unramified" version for GL(n). The ultimate goal will be to articulate the p-adic Kazhdan-Lusztig hypothesis with accompanying examples. Along the way, I will stop to discuss some categorical aspects of the theory. ________________________________ • Speaker: Morgan Rogers, University of Sorbonne. • Date and Time: Wednesday March 25, 2026, 2:00 - 3:30 PM. ZOOM TALK • Title: Ultrarings. A categorical approach to unifying boolean and algebraic descriptive complexity. • Abstract: The presentation of a commutative ring by generators and relations is (at least superficially) similar to the presentation of a first order theory in terms of sorts, function/relation symbols and axioms. More concretely, we can associate categories to rings and to theories: * In commutative algebra we can associate to a ring its category of finitely generated projective modules, which is a monoidal category with coproducts (over which the monoidal product distributes) having several further special properties. * Classical first-order theories are classified by Boolean lextensive categories. That is, if we take a first order theory 𝕋, we can associate to it a category ℬ𝕋 (its "syntactic category") with finite limits and finite (pullback-stable, disjoint) coproducts in which every subobject has a complement, such that models of 𝕋 in the category of sets correspond to functors ℬ𝕋 → Set preserving all that structure. Of course, there are many other categories we could have chosen on each side, but these particular constructions admit a mutual generalization which we call ultrarings. In this talk we explain what ultrarings are, how their presentations generalize those of commutative rings and first-order theories, and how they connect to the logical approach to complexity theory (descriptive complexity). We will also sketch how we hope to exploit this connection in the future to transport tools from algebraic geometry. This talk is based on work with Baptiste Chanus and Damiano Mazza, https://doi.org/10.4230/LIPIcs.FSCD.2025.13, with slightly updated definitions. ________________________________ • Speaker: Michael Lesnick, University at Albany -- SUNY. • Date and Time: Wednesday April 15, 2026, 2:00 - 3:30 PM. IN-PERSON TALK • Title: Limit Computation Over Posets via Minimal Initial Functors. • Abstract: Joint work with Tamal Dey, Department of CS, Purdue University. It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic implications of this idea for diagrams indexed by a finite poset. We say an initial functor $F\colon C\to D$ with $C$ small is \emph{minimal} if the sets of objects and morphisms of $C$ each have minimum cardinality, among the sources of all initial functors with target $D$. For $Q$ a finite poset or $Q\subseteq \mathbb{N}^d$ an interval (i.e., a convex, connected subposet), we describe all minimal initial functors $F\colon P\to Q$ and in particular, show that $F$ is always a subposet inclusion. We give efficient algorithms to compute a choice of minimal initial functor. In the case that $Q\subseteq \mathbb{N}^d$ is an interval, we give asymptotically optimal bounds on $|P|$, the number of relations in $P$ (including identities), in terms of the number $n$ of minima of $Q$: We show that $|P|=\Theta(n)$ for $d\leq 3$, and $|P|=\Theta(n^2)$ for $d>3$. We apply these results to give new bounds on the cost of computing $\lim G$ for a functor $G \colon Q\to \mathbf{Vec}$ valued in vector spaces. For $Q$ connected, we also give new bounds on the cost of computing the \emph{generalized rank} of $G$ (i.e., the rank of the induced map $\lim G\to \operatorname{colim} G$), which is of interest in topological data analysis. ________________________________ • Speaker: Gabriel Goren Roig, TBA. • Date and Time: Wednesday April 22, 2026, 2:00 - 3:30 PM. ZOOM TALK • Title: TBA. • Abstract: TBA ________________________________ • Speaker: Emilio Minichiello, CUNY CityTech. • Date and Time: Wednesday May 13, 2026, 2:00 - 3:30 PM. IN-PERSON TALK • Title: Introduction to locally presentable categories. • Abstract: This will be an expository talk about locally presentable categories and surrounding ideas, corresponding to Appendix C of my notes https://arxiv.org/pdf/2503.20664. ________________________________ ________________________________ You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/groups/groupsubscription?source=EscalatedMessage&action=files&smtp=categories%40mq.edu.au&bO=true&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/groups/groupsubscription?source=EscalatedMessage&action=leave&smtp=categories%40mq.edu.au&bO=true&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>