Bagels talks - Spring 2020
| Date | Speaker | Title |
| January 16th | Jose | Introduction to numerical dimensions of divisors
Abstract: An important invariant to study divisors is their Iitaka dimension. This is not a numerical invariant, so different analogous notions of the dimension of divisors have been proposed that depend only on the numerical class. In this talk I will introduce some of these definitions, along with properties, and also some questions that arise from recent results. |
| January 23rd | Yen-An | Introduction to Canonical Models of Foliated Surfaces
Abstract: Recently, a powerful theory for the birational classification offoliated surfaces has been developed by Brunella, McQuillan and others. Inthis talk, I will introduce the foliation (on surfaces) and its properties, and how to get to the nef/canonical model. If time permits, I will talk about the boundedness of foliated surfaces. |
| January 30th | Marin | Linear spaces contained in two quadrics and vector bundles on curves
Abstract: I will talk about the classical correspondence between intersections of two even dimensional quadrics and hyperelliptic curves. This connection was also realized on the level of their derived categories by Bondal and Orlov. Using this, one can recognize linear subspaces of two quadrics as vector bundles on the associated hyperelliptic curve. Given time, I will discuss the case of two odd-dimensional quadrics, and associated orbifold curve. |
| February 6th | You-Cheng | Bivariant intersection theory and Riemann-Roch for singular varieties
Abstract: For any morphism of schems, we can define the corresponding bivariant group. There are three basic operations (product, pull-back, and push-forward) on the bivariant groups. The compatibilities among these three operations allow one to manipulate bivariant classes symbolically with homology and cohomology in topology. Then I will state Riemann-Roch for singular varieties. |
| February 13th | Seungsu | Etale fundamental groups on strongly F-regular singularities
Abstract: It is well known that log terminal singularities are closely related to strongly F-regular varieties after characteristic p reduction. In this talk, we will discuss how they are related and see that etale fundamental group is finite on strongly F-regular singularities. |
| February 20th | No talk | |
| February 27th | Vaibhav | Cohomological dimension of ideals defining Veronese subrings
Abstract: Given a polynomial ring over an 'arbitrary domain', we will show that the geometric measure of the size of the ideals defining any of its Veronese subrings, i.e. codimension, is the same as its homological measure, i.e. cohomological dimension. This will generalize a result of Ogus where he proves the above statement for fields. |
| March 5th | Hanlin | Almost purity theorem in char p > 0
Abstract: Tilting functor induces an equivalence between the category of finite extensions of a perfectoid field K and its tilt K^\flat. One key step is to establish the almost purity theorem, which relies on Faltings' theory of almost mathematics. Though proving almost purity theorem in char 0 is hard, proving it in char p > 0 is quite straightforward. I'll talk about the proof of almost purity theorem in char p. |
| March 12th | Spring break | No talk |
| March 19th | Lingyao | TBD
Abstract: |
| March 26th | Matteo | TBD
Abstract: |
| April 2nd | Qingyuan | TBD
Abstract: |