Algebra Seminar (higher categories)
Speaker: Merlin Christ (Paris Cite U)
Time: 10:00-11:00am, Aug. 22, 2024
Place: Shuangqing C654
Title: Relative Calabi-Yau structures and perverse schobers
Abstract: We will consider relative Calabi-Yau structures, which generalize the usual Calabi-Yau structures on dg-categories/linear stable infinity-categories. Similar to Calabi-Yau categories, they have remarkable connections with many topics, such as cluster theory, stability conditions, Fukaya categories and shifted symplectic/Lagrangian structures on moduli stacks of objects. Besides a general introduction to the topic, we will explain in this talk how relative Calabi-Yau structures naturally arise from categorified perverse sheaves (called perverse schobers) on surfaces with boundary.
Speaker: Chen Dawei (Boston College)
Title: Differentials and Singularities
Time: 3:30-4:30pm, Aug. 20, 2024
Place: C654
Abstract: We introduce a stratification of moduli spaces of differentials. Each stratum corresponds to a class of isolated and smoothable curve singularities with Gm-action that possess the same numerical invariants. We discuss applications to the minimal model program for the moduli space of curves. This is joint work in progress with Fei Yu.
Date: 2024/06/27 下周四 10-11am
Place: 双清C546
Speaker: 谭桔（波士顿大学）
Title: Mirror construction for Nakajima quiver varieties.
Abstract: Quiver possesses a rich representation theory. On the one hand, it exhibits a deep connection between instantons and coherent sheaves as illuminated by the ADHM construction and the works of many others. On the other hand, quivers also capture the formal deformation space of a Lagrangian submanifold. In this talk, we will discuss these relations more explicitly from the perspective of SYZ mirror symmetry. In particular, we will introduce the notion of framed Lagrangian immersions, the Maurer-Cartan spaces of which are Nakajima quiver varieties. And we will realize the ADHM construction as a mirror symmetry phenomenon. This talk is based on the joint work with Jiawei Hu and Siu-Cheong Lau.
Time:6月20日 10-11am
Speaker: 黄靖尹(Jingyin Huang), Associate Professor, The Ohio State University
Title: The K(pi,1)-conjecture for Artin groups via combinatorial non-positive curvature
Place: 双清C546
Abstract: The K(pi,1)-conjecture for reflection arrangement complements, due to Arnold, Brieskorn, Pham, and Thom, predicts that certain complexified hyperplane complements associated to infinite reflection groups are Eilenberg MacLane spaces. We establish a close connection between a very simple property in metric graph theory about 4-cycles and the K(pi,1)-conjecture, via elements of non-positively curvature geometry. We also propose a new approach for studying the K(pi,1)-conjecture. As a consequence, we deduce a large number of new cases of Artin groups which satisfies the K(pi,1)-conjecture.
Time: 6月18日 10-11am
Speaker: 黄靖尹(Jingyin Huang), Associate Professor, The Ohio State University
Title: Introduction to Artin groups and K(pi,1)-conjecture
Place：双清C548
Abstract: A hyperplane arrangement in C^n is the manifold obtained by removing a collection of affine complex dimension one hyperplanes from C^n. Despite the simplicity of the definition and the long history of studying them, even basic questions on their fundamental groups still remain open. One important scenario of studying, is that the collection of hyperplanes has extra symmetry - namely there is a group acting on C^n permuting the hyperplanes. We will explain how this is related to the study of reflection groups, and braided versions of reflection groups - Artin groups. We will also discuss some background on one central conjecture in this direction, namely the K(pi,1)-conjecture for reflection arrangement complements.
