Tue, 20 Oct 2026
15:30
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, 10 Nov 2026
15:30
15:30
L4
HKR theorem for Deligne-Mumford stacks
Mauro Porta
(Strasbourg)
Abstract
The classical Hochschild-Kostant-Rosenberg (HKR) theorem supplies an identification of Hochschild homology groups in terms of differential forms. In the setting of derived geometry, Ben Zvi and Nadler and Toën and Vezzosi supplied a geometric interpretation of the HKR theorem in terms of an equivalence between the derived loop space and the shifted tangent bundle of a scheme. There is however a nontrivial problem in globalising this equivalence from schemes to stacks, and it is well known that derived loops and shifted tangent bundle do not agree already on Deligne-Mumford stacks. Ben Zvi and Nadler provided an infinitesimal version that holds for Artin stacks ; on the other hand, Arinkin Caldararu and Hablicsek [ACH] provided a global formula for smooth global quotient Deligne-Mumford stacks. In joint work with Fu, Scherotzke and Sibilla we extended this global formula to general derived Deligne-Mumford stacks, establishing a coordinate-free version of the previous result of [ACH]. In this talk I will explain the main ideas as well as some more recent developments.
Tue, 03 Nov 2026
15:30
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.
Tue, 27 Oct 2026
15:30
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.