When Calabi-Varieties degenerate: analytic invariants and singularities

：Gerard Freixas i Montplet（法国国家科学研究中心）
：2026-04-28 10:50
：海韵园行政楼C802

报告人：Gerard Freixas i Montplet（法国国家科学研究中心）

时  间：2026年4月28日10:50

地  点：海韵园行政楼C802

内容摘要:

Families of geometric spaces often develop singularities when they degenerate. A basic question is whether such singular fibers can be replaced, after a suitable change of parameter, by a smooth model. For Calabi–Yau varieties, this turns out to be a subtle and fascinating problem.

In this talk, I will explain how ideas from several different areas (complex geometry, singularity theory, and spectral invariants) come together to shed light on this question. The main character is analytic torsion, a delicate invariant built from the spectrum of natural differential operators. Although analytic in nature, it turns out to detect surprisingly precise information about singularities.

I will describe recent joint work with Dennis Eriksson showing that the asymptotic behaviour of analytic torsion is closely tied to classical numerical invariants of singularities. This leads to new evidence for, and extensions of, a conjecture of Durfee, and provides new obstructions to smoothing degenerations of Calabi-Yau varieties.

个人简介：

Gerard Freixas i Montplet，法国国家科学研究中心（CNRS）研究主任，巴黎综合理工学院教授。2001年于巴塞罗那大学获得学士学位（同等学历），2007年于巴黎第十一大学与巴塞罗那大学获得博士学位。他的研究聚焦于代数几何和算术几何，特别是Arakelov理论、相交理论和模空间，成果发表在 Journal für die Reine und Angewandte Mathematik, Duke Mathematical Journal, Compositio Mathematica, Journal of the European Mathematical Society, Annales Scientifiques de l'École Normale Supérieure 等重要期刊上，曾获得2019年法国科学院Thérèse Gautier奖以及Knut and Alice Wallenberg教授席位等奖励和荣誉。

 

联系人：刘文飞