Reading Seminar : Toric Geometry in Mirror Symmetry 

Welcome to the official seminar page for Toric Geometry in Mirror Symmetry. This seminar series aims to explore the interactions between algebraic geometry, symplectic geometry, and string theory, focusing on toric methods in mirror symmetry. 

• Start Date: 5/22/2025

•  Format: In-person 

• Time: Thursday, 3:30pm - 4:30pm

• Location: Leconte 103

• Organizers: Anirban Bhaduri, Pankaj Singh and Matthew Booth

                                                               Reading List (Books and Papers)

We will follow the following resources throughout the seminar series. Participants are encouraged to review these materials before each session.

• Toric Varieties 

• Mirror Symmetry and algebraic Geometry

• A Gentle Introduction to Homological Mirror Symmetry

• Mirror Symmetry:(Lectures: Professor Bernd Siebert )

• The Coherent-Constructible Correspondence and Homological Mirror Symmetry for Toric Varieties

• Some Notes 

1. Mirror Symmetry and Fukaya Categories

2. Algebra + homotopy = operad

3. What are Operads?∗

4. Introduction to  a-infinity algebras and modules

                                                                        Speakers and Schedule 

Below is a list of confirmed talks in the series: 

Title:  Introduction to toric varieties

speaker:  Pankaj Singh

Date: 5/22/2025 and 5/29/2025

Abstract:  We will begin by introducing and reviewing the background and key definitions related to toric varieties. Next, we will explore their connection with fans to understand the combinatorial structure. We will then revisit the orbit-cone correspondence and, if time permits, cover additional related material. 

Title:  Introduction to Quiver

speaker:   Lecture by Anirban Bhaduri

Date: 6/5/2025

Abstract:  In this talk, we focus on quivers and their representation. Quivers have been crucial to the study of algebraic geometry, representation theory, and OfCourse, Mirror Symmetry. Here we talk about quivers which are Acyclic and of both finite and infinite representation type. We discuss their path algebra and relate it to ideas in algebraic geometry. We explicitly compute modules over path algebras of ADE quivers. 

Title:  Introduction to A-infinity Categories

speaker:  Lectures by Matthew Booth 

Date: 6/19/2025 and 6/26/2025

Abstract:  An A∞-algebra is an algebra over an A∞-operad. An A∞-operad is a special kind of operad which parameterizes multiplication operations that are associative (the letter “A”) up to all higher homotopies (the “∞” subscript). General operads in turn have their origin in algebraic topology and were first (formally) introduced in the late 1960s to characterize iterated loop spaces. Interest in operad theory was renewed in the 1990s when M. Kontsevich and others discovered that some duality phenomena observed in rational homotopy theory could be explained using Koszul duality of operads.

Our aim in this talk is to develop the rudiments of operads and understand their basic construction and properties. This is in anticipation of a subsequent talk in which we direct our attention to A∞-operads, A∞-algebras, and A∞-categories, as these concepts have a close connection with homological mirror symmetry.