Spring 2026

Spring 2026

Fall 2025

11/12/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Professor Eva Belmont (Case Western Reserve University)
Title: Associated graded of operadic bar constructions
Abstract: May’s recognition theorem says that every connected algebra X over an E_\infty operad is an infinite loop space: for every n, there is a space Y_n such that X ~ \Omega^n Y_n. The monadic bar construction associated to the monad of such an operad plays a role in the delooping construction. We consider monadic bar constructions on filtered spaces, and give an example in which the associated graded is related to the poset of partitions.

11/5/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Professor Mark Meckes (CWRU)
Title: Magnitude and magnitude homology of metric spaces
Abstract: Magnitude is a recently defined isometric invariant of metric spaces which is analogous, in a precise sense, to the Euler characteristic of (the classifying space of) a category. Even more recently, a homology theory for metric spaces, magnitude homology, was defined for which magnitude is the corresponding Euler characteristic. In a way that wouldn’t be surprising to category theorists, but can be surprising to other mathematicians, these ideas have turned out to be related to a wide variety of more classical ideas in geometry, graph theory, information theory, and topology. I will give a high-level introduction to these ideas, emphasizing the breadth of the connections we already know about, as well as the many things we still don’t know.

10/29/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Aaron Huntley (CWRU)
Title: Locally presentable categories
Abstract: The category of sets and functions has many nice properties, one of these is that elements of a set X can be characterised by maps out of the terminal object. The idea of presentability is to generalise this notion, to be able to understand objects of a category by understanding maps out of a collection of “nice” objects. We will see that a category which is locally presentable is “essentially algebraic”.

10/22/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Dr. Gabriel Angelini-Knoll (CWRU)
Title: Algebraic K-theory of prime division rings in homotopy theory
Abstract: In algebra, the prime division rings are the finite fields with p elements and the rationals. The algebraic K-theory groups of prime division rings are of fundamental importance. For example, algebraic K-theory groups of the rationals and finite fields can be used to recover the special values of the Riemann zeta function. This was originally conjectured by Lichtenbaum and Quillen in the 1970’s.

In stable homotopy theory, there are more prime division rings known as Morava K-theory depending on a height n and a prime p. These can be regarded as multiplicative cohomology theories, which are equipped with a Künneth isomorphism. Algebraic K-theory has been defined sufficiently generally by Waldhausen so that we can define algebraic K-theory of Morava K-theory. I will talk about some joint work with Jeremy Hahn and Dylan Wilson where we resolve a version of the conjecture of Lichtenbaum and Quillen, due to Ausoni and Rognes, for Morava K-theory at arbitrary heights and primes.

10/15/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Johnny Taylor (CWRU)
Title: Picard Infinity Groupoids
Abstract: The Stable Homotopy Hypothesis claims an equivalence between Picard n-groupoids equipped with categorical equivalences and stable homotopy n-types attached with stable equivalences. We have only one problem with this in the globular setting: there is no existing notion of Picard n-groupoid in the literature past n=2. We correct this and construct the first globular model of Picard Infinity groupoids.

10/8/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Runhan Wang (CWRU)
Title: Introduction to Bredon homology
Abstract: Homology is an algebraic invariant of spaces. Bredon homology is the analogous algebraic invariant of G-spaces (for a group G).

10/1/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Reeve Johnson (CWRU)
Title: Much to Chu On: A Recipe for *-Autonomous Categories
Abstract: Sometimes one ingredient in a dish makes all the difference, like a dash of Greek yogurt in your boxed mac and cheese. If one object in a symmetric closed monoidal category serves as a global dualizing object, then we have ourselves a robust, hearty, *-autonomous category. Sometimes we are missing that one special ingredient (Greek yogurt also makes for excellent smoothies), but there are still ways of making the intended dish delicious. The Chu construction takes any symmetric closed monoidal category and makes a *-autonomous category out of its components. How? Well, this abstract is just the appetizer! Come to the talk for the full course meal.

9/17/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Reeve Johnson (CWRU)
Title: All the Categories Who Independent: A *-autonomous category prime
Abstract: You’re familiar with the unit interval as a poset. You’ve seen that the double dual of a finite dimensional vector space is isomorphic to the vector space. You attended my talk on polycategories last semester. (Right?) What do all of these have in common? Why, *-autonomous categories, of course! In this talk, we will explore the structure of *-autonomous categories and dive into numerous examples.

9/10/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Jordan Sawdy (University of Kentucky)
Title: Generalized Character Theory via Monoidal Traces
Abstract: In linear algebra, the trace of a square matrix is defined to be the sum of its diagonal entries. Though quite simple to define, this operation enjoys several nice properties that make it useful for producing invariants of vector spaces and associated structures. One such invariant is the character of a group representation. In this talk, we will look at a generalization of the trace to symmetric monoidal categories introduced by Dold and Puppe and use it to define “generalized characters” (with the representation-theoretic character arising as a special case). We will see that these characters behave nicely with respect to certain adjunctions in a way that generalizes the formula for the character of an induced representation. Finally, I will mention my work on a bicategorical instantiation of this story and its algebro-geometric interpretation, following a 2021 paper of Hoyois, Safranov, Scherotzke, and Sibilla.

9/3/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Johnny Taylor (Case Western Reserve University)
Title: Globularly modelling E_infinity Spaces
Abstract: We construct a theory for globular symmetric monoidal infinity-groupoids and begin the
process of using them to model E_infinity spaces.

8/27/2025, Wed. 1-2 pm in AW Smith B01
Speaker: Johnny Taylor (Case Western Reserve University)
Title: Controlled Theories
Abstract: Classically, a Lawvere theory may be presented with generators and relations which determine the structure of its models. This is fine to handle notions of algebras in the category of Sets but fails in higher dimensions due to conflicting structure data in a Lawvere theory. Controlled theories as introduced by the speaker are a framework for
categorical algebra which extends Lawvere theories and consists of generators, relations and an additional control component which includes into the presentation. The control component ensures that the issue of conflicting structure data is non-existent. We begin to show that this extension serves as a natural framework to do higher categorical algebra.

Spring 2026

2/6/2026, Fri. 3:30-4:30 pm in Sears 541
Speaker: Jake Hinds (Case Western Reserve University)
Title: A fine way to do Linear Algebra without matrices
Abstract: Did you feel like Shiv’s talk had TOO many matrices? Were you annoyed that Shiv didn’t fully explain what Affine transformation means? Do you wish to shear but do not own sheep? This talk will walk you through an undergraduate research project that at one point you will realize this is just linear algebra from a mathematician who refuses to use a matrix at every turn, cause something something euclidean geometry doesn’t need a grid. Said mathematician is me.

1/30/2026, Fri. 3:30-4:30 pm in Nord 356
Speaker: Saravana Mauree (Case Western Reserve University)
Title: How I solved racism using Calculus and Linear Algebra
Abstract: This talk will walk you through an undergraduate project that started off as a sign language translation app and unexpectedly became a “social justice movement “(extreme hyperbole). The problem ultimately boiled down to classifying points in a finite Euclidean space using composition of linear maps and nonlinearity optimization.