Bagels talks - Fall 2020
| Date | Speaker | Title |
| August 26th | Yen-An | Automorphism Groups of Foliations
Abstract: Recently, a powerful theory for the birational classification of foliated surfaces has been developed by Brunella, McQuillan, and others. It is well-known that (birational) automorphism group of a variety of general type is finite. So it is natural to ask if (birational) automorphism group of a foliation of general type is also finite. In this talk, I will introduce the foliation and its properties and sketch the proof of finiteness of (birational) automorphism groups of foliated surfaces of general type. |
| September 2nd | Marin | Kuznetsov component of the Veronese double cone
Abstract: The derived category of coherent sheaves has been a widely used tool in the last 20 years. If the variety is of Fano type, the derived category determines it entirely. Moreover, a particular subcategory called the Kuznetsov component carries much of its geometry. A powerful method developed by Bayer, Lahoz, Macri, and Stellari produces stability conditions on the Kuznetsov component of Fano threefolds. We use this technique to study moduli spaces on the Kuznetsov component of the Veronese double cone. |
| September 9th | You-Cheng | Introduction to Gromov-Witten Theory
Abstract: In this talk, I will define Gromov-Witten potential and show that it satisfies WDVV equation. As an application, we answer the following question in enumerative geometry: How many degree d rational curves passing through 3d-1 points in general position in P^2? If time permitted, I will say some parallel construction in K-theoretic Gromov-Witten Theory. |
| September 16th | No Talk |
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| September 23rd | Jose | The Kawamata - Morrison conjecture
Abstract: In this talk, we will talk about the Kawamata - Morrison conjecture which relates the structure of the Nef and Movable cones with the group of Automorphisms and Birational Automorphisms of a Calabi - Yau manifold. |
| September 30th | Junpeng | On fibrations and Minimal Model Program
Abstract: Suppose X\rightarrow Z is a fibration with good property, we will show that there are some relations on some birational invariants between X and Z, such as canonical model, good minimal model and Zariski decomposition. |
| October 7th | Seungsu | Properties of Global F-regular/F-split Pairs
Abstract: It is known that globally F-regular/F-splits varieties (and pairs) enjoy nice properties. In this talk, we will see reasons why they are good and introduce several properties including vanishing theorems for globally F-regular/F-splits varieties/pairs. |
| October 14th | No Talk |
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| October 21th | Peter | Derived splinters in prime characteristic
Abstract: In characteristic zero, splinters and derived splinters give alternative characterizations of normal schemes and schemes with rational singularities respectively. In this talk, we’ll introduce (derived) splinters and discuss a result of Bhatt (https://arxiv.org/abs/1109.0354) showing that these notions coincide in positive characteristic. Along the way, we’ll look at some examples and, time permitting, apply this result to some vanishing theorems. |
| October 28th | Qingyuan | An introduction to complements
Abstract: Introduced by Shokurov, complements play an important role in birational geometry, especially in some recent progress of birational geometry, e.g. in the proof of BAB conjecture. In this talk, I will give a brief introduction of this concept, and proof a baby case of BAB conjecture. Time permitting, I will also introduce more about the theory of complements and some other applications. |