Tensor triangulated geometry on derived categories of algebraic varieties
演讲者
时间
2024年05月23日 15:00 至 16:00
地点
A6-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
In this talk I will provide a brief summary of tensor triangulated geometry as initiated by Balmer, and I will discuss a number of interactions and potential research directions in algebraic geometry. Our interest lies in understanding the different tensor structures one can equip the derived category of a variety with, and how this question reflects the geometry of the space in the same fashion as the study of Fourier-Mukai partners. Additionally we will discuss the use of higher category theory to approach this problem and provide a result describing spaces of tensor structures with certain fixed data.
演讲者介绍
I grew up in Mexico where I went to get a bachelors in pure mathematics at the National Autonomous University of Mexico and where I first got interested in noncommutative ring theory. I then obtained a double masters degree in mathematics at the University of Padova and the University of Bordeaux under the ALGANT Master program, and where I focused in arithmetic geometry. For my PhD I moved to Nice where I worked under the supervision of Carlos Simpson at the Université Côte d'Azur and where I graduated with a thesis titled "Spaces of tensor products on the derived category of a variety".
I'm mainly interested in questions involving derived categories in algebraic geometry with a focus on noncommutative derived algebraic geometry. This in particular usually involves questions in the realm of derived algebraic geometry broadly defined and the formal homotopy theory of different flavors of higher categories. I think a lot about the interactions of these topics with tensor triangulated geometry and potential applications towards homological mirror symmetry.
I'm mainly interested in questions involving derived categories in algebraic geometry with a focus on noncommutative derived algebraic geometry. This in particular usually involves questions in the realm of derived algebraic geometry broadly defined and the formal homotopy theory of different flavors of higher categories. I think a lot about the interactions of these topics with tensor triangulated geometry and potential applications towards homological mirror symmetry.