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.
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.