Fri, 13 Oct 2023
12:00
L3

Modular bootstrap for compact Calabi-Yau threefolds

Sergey Alexandrov
(Université de Montpellier)
Abstract
BPS indices encoding entropy of supersymmetric black holes in compactifications of Type II string theory on compact Calabi-Yau threefolds coincide with generalized Donaldson-Thomas invariants whose computation represents an outstanding problem. I'll show how this problem can be solved for a set of one-parameter threefolds by combining a direct integration of topological string, modular properties of rank 0 DT invariants counting D4-D2-D0 BPS states, and wall-crossing relations between rank 1 and rank 0 DT invariants. In particular, one obtains explicit (mock) modular functions encoding infinite sets of D4-D2-D0 BPS indices and new boundary conditions for the holomorphic anomaly equation allowing to overcome the limitations of the direct integration method.
 
Wed, 11 Mar 2020
16:00
C1

Horocyclic product of Gromov hyperbolic spaces.

Tom Ferragut
(Université de Montpellier)
Abstract

Gromov hyperbolicity is a property to metric spaces that generalises the notion of negative curvature for manifolds.
After an introduction about these spaces, we will explain the construction of horocyclic products related to lamplighter groups, Baumslag solitar groups and the Sol geometry.
We will describe the shape of geodesics in them, and present rigidity results on their quasi-isometries due to Farb, Mosher, Eskin, Fisher and Whyte.

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