# Recent seminars

## 29/11/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Shira Chapman, Ben Gurion University of the Negev
Holographic Complexity and de Sitter Space

We compute the length of spacelike geodesics anchored at opposite sides of certain double-sided flow geometries in two dimensions. These geometries are asymptotically anti-de Sitter but they admit either a de Sitter or a black hole event horizon in the interior. While in the geometries with black hole horizons, the geodesic length always exhibit linear growth at late times, in the flow geometries with de Sitter horizons, geodesics with finite length only exist for short times of the order of the inverse temperature and they do not exhibit linear growth. We comment on the implications of these results towards understanding the holographic proposal for quantum complexity and the holographic nature of the de Sitter horizon.

## 08/11/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Joerg Teschner, University of Hamburg
Mathematical structures of non-perturbative topological string theory: from GW to DT invariants

We study the Borel summation of the Gromov-Witten potential for the resolved conifold. The Stokes phenomena associated to this Borel summation are shown to encode the Donaldson-Thomas invariants of the resolved conifold, having a direct relation to the Riemann-Hilbert problem formulated by T. Bridgeland. There exist distinguished integration contours for which the Borel summation reproduces previous proposals for the non-perturbative topological string partition functions of the resolved conifold. These partition functions are shown to have another asymptotic expansion at strong topological string coupling. We demonstrate that the Stokes phenomena of the strong-coupling expansion encode the DT invariants of the resolved conifold in a second way. Mathematically, one finds a relation to Riemann-Hilbert problems associated to DT invariants which is different from the one found at weak coupling. The Stokes phenomena of the strong-coupling expansion turn out to be closely related to the wall-crossing phenomena in the spectrum of BPS states on the resolved conifold studied in the context of supergravity by D. Jafferis and G. Moore.

## 18/10/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Sergey Mozgovoy, Trinity College Dublin
Attractor invariants, brane tilings and crystals

Given a CY3-fold $X$, we define its refined DT invariants $\Omega_Z(d)$ by counting objects in the derived category $D^b(X)$, semistable with respect to a stability condition $Z$ and having Chern character $d$. Attractor invariants $\Omega_*(d)$ correspond to a special stability condition that depends on the Chern character $d$. They usually have a particularly simple form. If known, attractor invariants can be used to determine DT invariants for all other stability conditions using wall-crossing formulas or flow tree formulas. A wide class of non-compact toric CY3-folds is encoded by combinatorial data called brane tilings or by associated quivers with potentials. In this setting the derived category of $X$ can be substituted by the derived category of a quiver with potential and the counting problems can be reduced to representation theoretic problems and then solved under suitable conditions. I will survey known results about DT invariants and some new conjectures about attractor invariants in this setting. I will also explain how these formulas in the unrefined limit correspond to the counting of molten crystals associated with brane tilings.

## 04/10/2021, Monday, 16:15–17:15 Europe/Lisbon — Online

Ben Heidenreich, University of Massachusetts, Amherst
The Weak Gravity Conjecture and BPS Particles

Motivated by the Weak Gravity Conjecture, we uncover an intricate interplay between black holes, BPS particle counting, and Calabi-Yau geometry in five dimensions. In particular, we point out that extremal BPS black holes exist only in certain directions in the charge lattice, and we argue that these directions fill out a cone that is dual to the cone of effective divisors of the Calabi-Yau threefold. The tower and sublattice versions of the Weak Gravity Conjecture require an infinite tower of BPS particles in these directions, and therefore imply purely geometric conjectures requiring the existence of infinite towers of holomorphic curves in every direction within the dual of the cone of effective divisors. We verify these geometric conjectures in a number of examples by computing Gopakumar-Vafa invariants.

Unusual hour!

## 19/07/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

ChunJun Cao, University of Maryland
Building Bulk Geometry from the Tensor Radon Transform

Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS$_3$/CFT$_2$. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.