Tue, 20 Oct 2026
15:30
L4

The logarithmic derived category

Patrick Kennedy-Hunt
(Cambridge)
Abstract
As a scheme undergoes a simple normal crossing degeneration its coherent sheaves - and their derived category - behave unpredictably. In this talk I will describe a proposal for a category of logarithmic (quasi-)coherent sheaves associated to such a degeneration. The corresponding derived category exhibits Grothendieck-Neeman duality with the expected dualizing complex, and has a perfect diagonal (the categorical signature of smoothness).  Structures on the logarithmic derived category of the central fibre most closely resemble the smooth situation when considered relative a tropical derived category. This category is compatible with Maulik and Ranganathan’s logarithmic Donaldson—Thomas theory and has an associated (logarithmic) moduli stack of logarithmic coherent sheaves.
 
Based on joint work with De Deyn, Dell, Hu, Manali-Rahul, and Schimpf, and on separate joint work with Poiret, and Song for the moduli stack.



 

Tue, 03 Nov 2026
15:30
L4

Smash-nilpotence: algebraic, tropical and symplectic

Alexia Corradini
(Cambridge)
Abstract
In algebraic geometry, two useful ways of classifying cycles are up to rational equivalence, or up to a weaker equivalence relation known as algebraic equivalence. Using the dictionary of mirror symmetry, these correspond to classifications of Lagrangians in the mirror symplectic manifold: Sheridan—Smith showed that rational equivalence is related to a version of Lagrangian cobordism, and in previous work I introduced an equivalence relation called alg-cobordism as a Lagrangian counterpart to algebraic equivalence.
In the early 90’s, Voevodsky and Voisin independently proved the following surprising Theorem: if an algebraic cycle Z in an algebraic variety Y is algebraically trivial, then for k sufficiently large, Z^k is rationally trivial in Y^k. I will present joint work with Danil Kozevnikov, in which we translate their Theorem into the symplectic realm: if a Lagrangian L is alg-nullcobordant, then for k sufficiently large, L^k is null-cobordant.
 
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Tue, 27 Oct 2026
15:30
L4

Coproducts on 3d CoHAs

Sarunas Kaubrys
(IPMU Tokyo)
Abstract

In this talk I will discuss different types of coproducts on cohomological Hall algebras associated to 3-Calabi-Yau categories, as recently defined by Kinjo-Park-Safronov and Descombes. In general, these are actually a more exotic structure we call a vertex coproduct. I will explain the important special case of a quiver with potential. In this case, these coproducts are related to deformed Drinfeld coproducts on Yangians. I will also discuss how vertex coproducts are related to factorization type coproducts, recently defined in work of Davison-Hennecart-Kinjo-Schiffmann-Vasserot. This is joint work with Jindal and Latyntsev and work in progress with Latyntsev and Descombes.

Thu, 23 Jul 2026
09:00
L4

TBA

Sarunas Kaubrys
(IPMU Tokyo)
Tue, 13 Oct 2026
15:30
L4

In search of theta-stratifications on the stack of curves

Jessica Jackson
(Cambridge)
Abstract

In their recent ICM address, Dan Halpern-Leistner and Jarod Alper posed the question: does the stack of canonically polarized curves admit a theta-stratification whose semistable locus is the moduli space of stable curves? In other, perhaps more familiar, language: is there some notion for curves that understands instability the way Harder-Narasimhan type does for vector bundles/coherent sheaves?

I will explain some joint work with Dave Swinarski that solves the analogous problem for certain rational curves, and then sketch out an argument that I think should solve the problem in general.

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