Logo

Mathematical Sciences Research Institute

Home » Workshop » Schedules » Birational geometry for d-critical loci and wall-crossing in Calabi-Yau 3-folds

Birational geometry for d-critical loci and wall-crossing in Calabi-Yau 3-folds

Structures in Enumerative Geometry March 19, 2018 - March 23, 2018

March 22, 2018 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Yukinobu Toda (Kavli Institute for the Physics and Mathematics of the Universe )
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

15-Toda

Abstract

In this talk, I will discuss birational geometry for Joyce’s d-critical loci, by introducing notions such as ‘d-critical flips’, ‘d-critical flops’, etc. I will show that several wall-crossing phenomena of moduli spaces of stable objects on Calabi-Yau 3-folds are described in terms of d-critical birational geometry, e.g. certain wall-crossing diagrams of Pandharipande-Thomas stable pair moduli spaces forma a d-critical minimal model program. I will also show the existence of semi-orthogonal decompositions of the derived categories under simple d-critical flips satisfying some conditions. This is motivated by a d-critical analogue of Bondal-Orlov, Kawamata’s D/K equivalence conjecture, and also gives a categorification of wall-crossing formula of Donaldson-Thomas invariants

Supplements No Notes/Supplements Uploaded
Video/Audio Files

15-Toda

H.264 Video 15-Toda.mp4 429 MB video/mp4 rtsp://videos.msri.org/data/000/030/972/original/15-Toda.mp4 Download
Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture. The videos are sold at cost for $20USD (shipping included). Please Click Here to send an email to MSRI to purchase the DVD.

See more of our Streaming videos on our main VMath Videos page.