When Calabi-Varieties degenerate: analytic invariants and singularities

Speaker：Gerard Freixas i Montplet (CNRS)

Time：2026-4-28 10:50

Location：Conference Room C802 at Administration Building at Haiyun Campus

Abstract:

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.