Add Headings and they will appear in your table of contents.
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