The seminar meets on Fridays from 10:30 am -12:00 am at the room 2-361 (MIT).

02.15. Organization meeting.

03.01. Tudor Padurariu : K-theoretic Hall algebras for quivers with potential

For a quiver with potential, Kontsevich and Soibelman defined an algebra called the cohomological Hall algebra. After work of Davison and Meinhardt, the CoHA is actually a localized bialgebra and in many cases it satisfies a PBW theorem. We study a version of the Hall algebra defined using the K_0 group of certain categories of singularities associated to the quiver with potential, and explain that similar definitions as the ones used for CoHA put a localized bialgebra structure on this algebra. We also prove a PBW theorem for this algebra using semi-orthogonal decompositions inspired by the work of Spenko and van den Bergh.

03.08. Dori Bejleri: Moduli of stable maps in genus 1 and logarithmic geometry

Reference:

Ranganathan, Santos-Parker, and Wise: Moduli of stable maps in genus 1 and logarithmic geometry I

https://arxiv.org/pdf/1708.02359.pdf

03.15. Kai Huang: Log Calabi-Yau fibrations

Reference:

Birkar: Log Calabi-Yau fibrations

https://arxiv.org/pdf/1811.10709.pdf

03.22 Friday before spring break and AGNES...

03.29 Spring break

04.05. Chun Hong Lo: Towards an algebraic theory of Welschinger invariants

Reference:

Levine: Towards an algebraic theory of Welschinger invariants

https://arxiv.org/pdf/1808.02238.pdf

04.12. Zhiyuan Li (SCMS & Fudan University): Tautological cycles on moduli spaces of IHS manifolds

I will discuss the recent work on studying the cycle theory on moduli of polarized IHS manifolds, such as generalized Franchetta conjecture and the tautological conjecture. Besides, I will talk about the properties of the tautological ring and further questions.

04.19. Yu Zhao: Categorifacation of 2-dim Cohomological Hall Algebras

Reference:

F. Sala and M. Porta: Categorifacation of 2-dim Cohomological Hall Algebras

https://arxiv.org/pdf/1903.07253.pdf

04.26. Guodu Chen: ACC for minimal log discrepancies of exceptional singularities

Reference:

J. Han, J. Liu, and V. Shokurov: ACC for minimal log discrepancies of exceptional singularities

https://arxiv.org/pdf/1903.04338.pdf

05.03. Yau Wing Li: Geometric Langlands duality and representations of algebraic groups over commutative rings

Reference:

I.Mirkovic, K. Vilonen: Geometric Langlands duality and representations of algebraic groups over commutative rings

https://arxiv.org/pdf/math/0401222.pdf

05.17. Svetlana Makarova: Derived categories of Grassmannians and modular representation theory

Reference:

A. Efimov: Derived categories of Grassmannians and modular representation theory

https://arxiv.org/pdf/1410.7462.pdf