Modern Algebraic Geometry Workshop
2026-06-05
Venue: B725, Shuangqing Complex Building A
Zoom Meeting ID: 262 865 5007
Passcode: YMSC
Recording: https://cloud.tsinghua.edu.cn/d/c17fbe549ec94dd2aa42/
Time: 10:00-11:00
Speaker: Joaquín Moraga (UCLA)
Title: Characterization of toric varieties and products of projective varieties
Abstract: There are dozens of different characterizations of the projective space from a topological perspective, geometric perspectives and differentiable perspectives. Many of them relate to the positivity of T_X or the positivity of -K_X. In the last few decades there has been some interest in finding similar characterizations for toric varieties and products of projective spaces. At the same time, refined decompositions of -K_X have been introduced in parallel developments of the MMP and birational geometry. In this talk, I will give an overview of some of these characterizations and present some new results regarding the characterization of products of projective spaces, as well as some conjectures for further research.
Lunch Break 11:00-13:00
Time: 15:30-16:30
Speaker: Karim Adiprasito (IMJ-PRG)
Title: Some polyhedral approaches to birational geometry
Abstract: I will survey two recent advances in algebraic geometry whose proofs rely on polyhedral and combinatorial constructions: the solution of the weighted version of Oda’s strong factorization conjecture; the resolution, in characteristic zero, of the Abramovich–Karu semistable reduction conjecture. The emphasis will be on the main ideas and geometric meaning rather than technical details. I will also discuss several open problems, both algebraic and combinatorial. The talk will be accessible to non-experts, and you can interrupt me at any point.
Time: 17:00-18:00
Speaker: Jihao Liu (PKU)
Title: Solving birational geometry questions using AI
Abstract: I will talk some of my recent works on solving birational geometry questions using AI, particularly the Rethlas system, and discuss the potentials.
