Northeast Conference on Categorical Methods

About this event

Northeast Conference on Categorical Methods

Dates: November 6– 7 , 2026

Location: CMSA G10, 20 Garden St., Cambridge MA 02138

This conference is intended to bring together researchers in all areas of mathematics and mathematical physics whose work involves the use of methods from categorical algebra, abstract homotopy theory, and higher category theory. Our goal is to showcase new, exciting research and offer an avenue for researchers from the Northeast US to discuss their work and collaborate with people in this ever-growing community.

There will be time for 4 short talks by early-career mathematicians.

Registration for in-person participation and funding is now closed.

Remote participation is still available. Sign up using this link: Zoom Webinar Registration

Cambridge Links

• Recommended Lodging

• Restaurants

• Transportation: MBTA

Invited Speakers

• Andrew Blumberg, Columbia University

• Soren Galatius, Columbia University

• Tony Pantev, University of Pennsylvania

• Nick Rozenblyum, University of Toronto

• Tomer Schlank, Harvard University

• Brian Williams, Boston University

• Inna Zakharevich, Cornell University

Early-career Speakers

• Alexandra Ballow, Montana State University

• Connor Malin, MPIM

• Azélie Picot, Columbia University

• Shubhankar Sahai, UCSD

Organized by Dan Freed , Harvard Math & CMSA; Owen Gwilliam , UMass Amherst; and Lorenzo Riva , Harvard CMSA

Schedule

Friday, November 6, 2027

8:30 – 9:00 am

Breakfast

9:00 – 10:00 am

Tomer Schlank, Harvard

tba

10:00 – 10:15 am

Break

10:15 – 11:15 am

Tony Pantev, University of Pennsylvania

Title: The pushforward theorem and its applications

Abstract: I will discuss the notion of a relative shifted symplectic structure along the stalks of a constructible sheaf of derived stacks on a stratified space. I will describe a general pushforward theorem producing relative shifted symplectic forms and will explain explicit techniques for computing such forms. As an application I will describe a universal construction of Poisson structures on derived moduli of Stokes data on smooth varieties and will explain how symplectic leaves arise from fixing irregular types and local formal monodromies at infinity. This is a joint work with Dima Arinkin and Bertrand Toen.

11:15 – 11:30 am

Break

11:30 am – 12:00 pm

Azelie Picot, Columbia

Title: The cobordism category for Poincaré Duality spaces

Abstract: Cobordism categories conveniently package closed manifolds of a given dimension as objects and moduli spaces of their cobordisms as morphisms. On the other hand, Poincaré duality spaces are spaces whose homology satisfies Poincaré duality. We can again define a cobordism category for Poincaré duality spaces. In this talk, I will discuss some of its key features.

12:00 – 1:30 pm

Break

1:30 – 2:00 pm

Connor Malin, MPIM Bonn

Title: An application of nonabelian Poincaré duality to embedding calculus

Abstract: The Isotopy Extension Theorem (IET) is one of the fundamental tools in the study of spaces of embeddings and diffeomorphisms. It states that an isotopy of a submanifold can be extended to an isotopy of its complement. Surprisingly, for embedding calculus IET has only been proven under very restrictive conditions. I will talk about how to remove these conditions using Tillmann-Weiss’s nonabelian Poincaré duality between embedding calculus and Goodwillie calculus. This is joint work with Samuel Muñoz-Echániz.

2:00 – 2:15 pm

Break

2:15 – 3:15 pm

Brian Williams, Boston University

Title: Higher central charges and a universal Grothendieck–Riemann–Roch theorem

Abstract: Mumford’s computation of determinant line bundles in CFT relates the Virasoro central charge to the geometry of moduli spaces of curves. In joint work with Zhengping Gui, we prove a local, universal Grothendieck–Riemann–Roch theorem extending this relationship to higher dimensions. Our categorical starting point is the functorial construction of Tate complexes from derived sections of natural bundles on punctured formal disks. We compute the induced central extension of global derived vector fields in terms of the Todd class and Chern character, connecting categorical determinant constructions with higher Virasoro symmetries and anomalies in holomorphic QFT.

3:15 – 3:30 pm

Break

3:30 – 4:30 pm

Inna Zakharevich, Cornell

Title: “The category of schemes is abelian” and other obviously-false true statements

Abstract: The category of schemes is clearly not abelian, as, for example, there is no additive structure on the hom-sets of the category. However, from the perspective of algebraic K-theory, there turn out to be many respects in which the category of schemes behaves akin to an abelian category. In this talk we will discuss the notion of an “ACGW category,” which is a generalizations of abelian categories which allows us to use the methods of abelian categories inside the category of schemes. In particular, we will prove Quillen’s d\’evissage for ACGW-categories and explain implications of this to analyses inside combinatorial K-theory.

Saturday, November 7, 2026

8:30–9:00 am

Breakfast

9:00 – 10:00 am

Andrew Blumberg, Columbia

tba

10:00 – 10:15 am

Break

10:15 – 11:15 am

Soren Galatius, Columbia

tba

11:15 – 11:30 am

Break

11:30 am– 12:00 pm

Alexandra Ballow, Montana State University

Title: Derived Turaev-Viro

Abstract: We aim to integrate a 2-category over a (framed) surface: this is a purely combinatorial implementation of factorization homology. We will discuss intuitively what factorization homology is, focusing first on a combinatorial definition of factorization homology over the circle. This example is interesting in its own right as a generalized Hochschild homology. To extend this definition to surfaces, we define 2-dimensional quivers and consider representations of such in a 2-category. We finish with a discussion of string-nets to motivate the correspondence between factorization homology of a surface and a version of the TQFT Turaev-Viro on surfaces.

12:00 – 1:30 pm

Break

1:30 – 2:00 pm

Shubhankar Sahai, UCSD

Title: Tannakian reconstruction in derived algebraic geometry

Abstract: In the early 2010s, Lurie, Bhatt and Bhatt–Halpern-Leistner (building on a ‘relative’ perspective introduced by Lurie a decade earlier) proved strong reconstruction results for maps of spectral stacks from (certain) symmetric monoidal functors between their derived categories of quasi-coherent sheaves. Motivated by recent work in p-adic Hodge theory and Hochschild homology, one asks whether such reconstruction results exist in derived geometry, where the basic geometric objects are spectra of animated (i.e. simplicial commutative) rings rather than E_\infty-rings. In this talk we will explain how to answer this question positively using the recently invented Theta-categories of Nuiten–Toën. This is joint work with Joshua Mundinger.

2:00 – 2:15 pm

Break

2:15 – 3:15 pm

Nick Rozenbluym, University of Toronto

Title: Categorical representations and higher traces

Abstract: I will give an overview of the theory of categorical representations of algebraic groups and relate them to ordinary representations via higher categorical trace. This procedure allows to extract concrete consequences of higher structures. For instance, I will explain how the theory of iterated traces applied to an appropriate (∞,3)-category gives a conceptual proof of a character formula for Deligne-Lusztig representations of finite groups of Lie type. This is joint work with D. Gaitsgory and Y. Varshavsky.

From Dan Freed