# Algebra Seminar

This seminar is held on Tuesdays at 4pm in 210 University Hall.

### Fall Quarter, 2022

- October 11,
**Song Yu** (Columbia University)

Open Crepant Transformation Conjecture for toric Calabi-Yau 3-orbifolds
**Abstract**: The Crepant Transformation Conjecture of Ruan proposes an identification of the quantum cohomologies and Gromov-Witten theories of K-equivalent manifolds or orbifolds. In this talk, I will discuss various formulations and known cases of the conjecture, and focus on its extension to open Gromov-Witten theory. I will further present an approach to the conjecture for toric Calabi-Yau 3-orbifolds based on techniques from mirror symmetry. The talk is based on joint work with Bohan Fang, Chiu-Chu Melissa Liu, and Zhengyu Zong.

- October 20,
**Konstantin Aleshkin** (Columbia University)

**Special Time/Location**: 10am in 260 Tykeson Hall

Central charges in abelian GLSM
**Abstract**: GLSMs are enumerative theories associated to critical loci of functions in GIT quotients and generalize Gromov-Witten theory. A large part of structure of such a theory can be captured by certain generating series of genus 0 invariants called central charges which depend on a matrix factorization of the GLSM.

These generating series remarkably have two integral representations: Euler type and Mellin-Barnes type. In this talk I will outline our construction of central charges and explain how the integral representations lead to mirror symmetry, Higgs-Coulomb correspondence and wall crossing phenomena for GLSM invariants.

- November 15,
**Siu-Cheong Lau** (Boston University)

Mirror symmetry for quiver algebroid stacks
**Abstract**: Quiver algebroid stacks provide a unified setting for SYZ and noncommutative mirror symmetry. In this talk, I will first provide the background about SYZ and quiver mirror constructions. Then I will explain the terminologies of quiver algebroid stacks and twisted complexes. Finally, I will explain how such geometric objects arise from our mirror construction.

- November 29, Algebra course meeting

**Previous years**: 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005