BAGELS is a weekly grad-student-led seminar on Algebraic Geometry, where bagels and mathematical ideas are shared. It takes place on Thursdays from 3:30-4:30pm in LCB 323. If you have any questions about the seminar (other than what BAGELS stands for), feel free email one of the organizers: Daniel Apsley and Rahul Ajit. (apsley(at)math.utah.edu, rahulajit(at)math.utah.edu)
| Date | Speaker | Title | Abstract |
| August 22 | N/A | Organizational 'Meeting' | N/A |
| August 29 | Rahul Ajit | Multiplier Ideals for NON-Q-Gorenstein Normal Varieties | Following de Fernex-Hacon, I'll explain how to define relative canonical divisor in a non-Q-Gorenstein setting. Then, I'll define the multiplier ideal sheaf in this general setup and prove some of its natural properties. Finally, following Urbinati, I'll mention interesting pathologies that appear in this setup. In the next talk, I'll essentially do a char p version of the above and mention open questions! |
| September 5 | Rahul Ajit | Multiplier and (big) Test ideal for non-Q-Gorenstein Varieties | Continuing the last talk, I'll define the multiplier ideal sheaf in this general setup and prove some of its natural properties. Then, following Schwede, I'll define (big) test ideal and prove a result similar to dFH. Finally, I'll mention several open questions asked by Schwede, Smith and Lazarsfeld. |
| September 12 | Will Legg | Motivic Integration and Calabi-Yau Varieties | Motivic integration is a powerful tool in algebraic geometry inspired by results in classical p-adic integration. This talk is a concrete introduction to the ideas and techniques of motivic integration. After spending some time setting up the machinery, we will apply our newfound knowledge to give a quick proof (due to Kontsevich) that birational Calabi-Yau varieties have the same Hodge numbers. |
| September 26 | Daniel Apsley | What is K-Stability? | In an effort to answer the titular question, I'll introduce some complex-geometric background to motivate the definition of K-Stability. Then, we'll discuss the definition of K-Stability via test configurations and give numerous examples. If there's time, I'd also like to mention some of the geometric consequences of K-Stability, indicate different approaches to the definition, and mention some open problems. |
| October 17 | Matthew Bertucci | Generalized Taylor Conditions over Finite Fields | For trying to do calculus over finite fields, we are punished with combinatorics. We'll walk through the history of classical Bertini theorems, explain "probability" in the Grothendieck ring of varieties, and define the sheaf of principal parts. Existing Bertini theorems over finite fields will be neatly packaged and served up for you, the consumer. |
| October 24 | Joseph Sullivan | Betti Beware---Syzygies Ahead! | Coherent sheaves on projective space (e.g. ideal sheaves or pushforwards of structures sheaves) carry invariants called (graded) Betti numbers coming from "minimal graded free resolutions" (of their corresponding modules). We will study how geometric properties constrain Betti numbers and vice versa, and depending on time we'll state some conjectures at the end. |
| October 31 | Zach Mere | A Friendly Introduction to Arc Spaces | In this talk, we'll define the arc space of a scheme of finite type over a field and go over the construction. Then we'll compute some simple examples. |
| November 21 | Yu-Ting Huang | Existence of Good Minimal Models for Fibered Varieties | In this talk, I will first introduce the fundamental concepts of the Minimal Model Program (MMP) and discuss the conjecture concerning the existence of good minimal models. I will then present results showing that varieties fibered by good minimal models possess a good minimal model in certain cases, specifically when the map is an Albanese morphism or an Iitaka fibration. Finally, I will outline how to pose this question in an analytic context and highlight potential issues that arise in this setting. |
| December 5 | Jonathon Fleck | TBD | TBD |