BAGELS 2024 Spring

BAGELS (Best Algebraic Geometry Eating and Learning Seminar) is a students-running algebraic geometry seminar. We meet weekly and share our knowledge and research on algebraic geometry and related areas. You can give a talk about what you are studying, reading, or researching. For past BAGELS talks, see BAGELS Spring 2023

During 2024 Spring semester, we meet on Wednesdays from 3:30-4:30 in JWB 308.


Jan. 24 Organizational Meeting
Feb. 14Yu-Ting HuangThe Boundedness of Complements for Log Surfaces
Abstract: Shokurov posed the idea of complements in his work, 3-fold Log Flips, 1992. Since then, the theory of complements has played an essential role in birational geometry. People are concerned about the existence as well as the boundedness of complements. In the past 20 years, lots of related works have been done. For example, Birkar proved that the complements are bounded for Fano type morphisms in his well-known paper, Anti-pluricanonical System on Fano Varieties, 2019. In this talk, I will define the complement and prove the existence and boundedness of log Fano type surfaces.
Feb. 21Rahul AjitBertini Properties over finite field
Abstract: I will present Poonen’s Sieve methods and sketch a proof of Bertini for smoothness over finite fields. Time permitting, I’ll sketch a proof of Bertini property for irreducibility due to Charles-Poonen. Then I’ll give a survey of known result and mention open questions in this direction. Finally, I’ll briefly talk about my joint projects with Matthew Bertucci and Daniel Apsley. I won’t assume any prerequisites outside basic AG.
Feb. 28Zach MereArc spaces and the Nash problem
Abstract: Nash viewed the theory of arc spaces as a tool for studying the singularities of a complex variety. In 1968, he predicted a bijection between families of arcs through singularities and so-called “essential” divisors, which appear as exceptional in every resolution of singularities. This problem was wide open until recently. The correspondence has since been shown to hold for surfaces, but to fail in general in higher dimensions. However, certain partial results have been proven true in all dimensions, suggesting that a slightly different formulation might work. In this talk, we’ll discuss this recent progress towards a solution to the Nash problem.
Mar. 13Joseph SullivanAbstract:
Mar. 20Yi-Heng TsaiAbstract:
Mar. 27Daniel ApsleyAbstract:
Apr. 3Jonathon FleckAbstract:
Apr. 10Will LeggAbstract:
Apr. 17Qingyuan XueAbstract: