Regularized integrals and manifolds with log corners
 Dupont, C Panzer, E Pym, B (29 Dec 2023)
Mon, 04 Mar 2024
14:15
L4

Significance of rank zero Donaldson-Thomas (DT) invariants in curve counting theories

Sohelya Feyzbakhsh
(Imperial College London)
Abstract
Fix a Calabi-Yau 3-fold X of Picard rank one satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as the quintic 3-fold. I will first describe two methods to achieve explicit formulae relating rank zero Donaldson-Thomas (DT) invariants to Pandharipande-Thomas (PT) invariants using wall-crossing with respect to weak Bridgeland stability conditions on X. As applications, I will find sharp Castelnuovo-type bounds for PT invariants and explain how combining these explicit formulas with S-duality in physics enlarges the known table of Gopakumar-Vafa (GV) invariants. The second part is joint work with string theorists Sergei Alexandrov, Albrecht Klemm, Boris Pioline, and Thorsten Schimannek.
Mon, 04 Mar 2024
15:30
L4

Rigidity of ideal symmetric sets

Stephan Stadler
(Max Planck Institute for Mathematics)
Abstract

A subset in the ideal boundary of a CAT(0) space is called symmetric if every complete geodesic with one ideal boundary point
in the set has both ideal boundary points in the set. In the late 80s Eberlein proved that if a Hadamard manifold contains a non-trivial closed symmetric  subset in its ideal boundary, then its holonomy group cannot act transitively. This leads to rigidty via
the Berger-Simons Theorem. I will discuss rigidity of ideal symmetric sets in the general context of locally compact geodesically complete
CAT(0) spaces.
 

Convergence and stability results for the particle system in the Stein
gradient descent method
 Carrillo, J Skrzeczkowski, J Mathematics of Computation http://arxiv.org/abs/2312.16344v1
Convergence of boundary layers of chemotaxis models with physical
boundary conditions~I: degenerate initial data
 Carrillo, J Hong, G Wang, Z SIAM Journal on Mathematical Analysis (08 Jul 2024) http://arxiv.org/abs/2401.01437v1
The Collisional Particle-In-Cell Method for the Vlasov-Maxwell-Landau
Equations
 Bailo, R Carrillo, J Hu, J Journal of Plasma Physics (09 Jul 2024) http://arxiv.org/abs/2401.01689v2
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