When and Where? : Tuesdays at 2:00 pm in DRL 4C8

The goal of this seminar is to provide a supportive and inclusive place for all to learn more about algebraic geometry and related areas. The setting is informal, the intention is to foster discussion and learning in a low stakes environment.  In addition to algebraic geometry, talks can be from adjacent areas such as complex geometry, number theory, arithmetic geometry, etc.

We need volunteers to give talks!  At the beginning of the semester we collected a list of topics that people would like to hear about.  If you'd like to add something to this list, or if you'd like to give a talk, please let one of the organizers know. (Organizers: Andrew, Emmett, and Deependra)

For other ideas of talks, check out these two other sources: https://www.daniellitt.com/crag and https://wiki.math.wisc.edu/index.php/Graduate_Algebraic_Geometry_Seminar.

Fall 2023 topics wishlist:

• toric varieties

• (p-adic) Hodge Theory

• Tate's thesis (Fourier analysis on number fields)

• K3 surfaces

• moduli spaces+problems

• rigid/formal geometry

• Hecke operators/correspondences (translating NT and geo)

• vertex algebras

• combinatorial Hodge theory

• arakelov theory

• derived AG

• log geometry

• tropical geometry

• classification of surfaces (over C)

• what is... (geometric) Langlands? a stack? a motive? a perfectoid space?

• Mumford's GIT

• Intro to Schubert calculus

• (algebraic) K-theory

• Hilbert Irreducibility and generalizations

• McKay correspondence

• F-theory

Spring 2023 topics wishlist:

• What is Etale cohomology? 

• Weil conjectures

• What are motives? (Explain like I am 5)

• Geometry and arithmetic of K3 surfaces

• Brauer-Manin obstruction for K3 surfaces 

• Toric varieties for dummies

• p-adic Hodge theory for beginners

• Arithmetic schemes/surfaces (Arakelov theory)

• Who were the Fields medalists? (pick a Fields medalist and introduce their work)

• Perfectoid spaces

• Mazur’s theorem on torsion in elliptic curves

• Duality theorems in topology, AG and arithmetic

• Monodromy representations

• Moduli of curves - introduction and the irreducibility theorem

• Gromov-Witten theory

• Kodaira-Parshin construction (related to moduli of curves + Mordell conjecture)

• What are Chow rings?

• Fano varieties and Fano problems

• Top 10 things you need to know about rational points on varieties

• What are Neron models?

• Good reduction of abelian varieties (Serre - Tate)

• Jouanolou device

• Bridgeland stability

• Hensel’s lemma, Henselian rings

• Tate’s thesis

• Modular forms

• Fermat’s theorem / Galois representation

• Knots and primes

• Iwasawa theory

• Inverse Galois theory (Shafrevich’s theorem on solvable groups)

• Bruhat-Tits

• What is a Calabi-Yau manifold?

• Inflexion of linear series on curves

• Fukaya category

• Representation Theory of Reductive p-adic groups (or harmonic analysis on p-adic groups)