# Planned seminars

## 24/05/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Daniel Waldram, Imperial College London

“G-algebroids” are natural extension of Lie and Courant algebroids that give a unified picture of the symmetries that underlie generalised and exceptional geometry as well as new “non-exact” versions. We analyse their structure in the exceptional case, and translate the problem of finding maximally supersymmetric consistent truncations to a relatively simple algebraic condition. We then show how Poisson-Lie U-duality is encoded in this framework and prove, in particular, that it is compatible with the supergravity equations of motion.

## 07/06/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Syo Kamata, National Centre for Nuclear Research, Warsaw

We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with $N$ minima on $S^{1}$. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of $N$-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with 't Hooft anomaly for even $N$ and global inconsistency for odd $N$. By using Delabaere Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.

This talk is based on:

1. On exact-WKB analysis, resurgent structure, and quantization conditions, N.Sueishi, S.K, T.Misumi, and M.Ünsal, arXiv:2008.00379.
2. Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$, N.Sueishi, S.K, T.Misumi, and M.Ünsal, arXiv.2103.06586

## 21/06/2021, Monday, 11:30–12:30 Europe/Lisbon — Online

Sven Krippendorf, LMU Munich

Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of relevant structures, the Lax pair and Lax connection respectively. By formulating this search as an optimization problem, we are able to identify appropriate structures via machine learning techniques. We test our method on standard systems of classical integrability and find that we can distinguish between integrable and non-integrable deformations of a system. Due to the ambiguity in defining a Lax pair our algorithm identifies novel Lax pairs which can be easily verified analytically.

## 05/07/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Ingmar Saberi, University of Heidelberg

We consider a class of holographic quantum error-correcting codes, built from perfect tensors in network configurations dual to Bruhat-Tits trees and their quotients by Schottky groups corresponding to BTZ black holes. The resulting holographic states can be constructed in the limit of infinite network size. We obtain a $p$-adic version of entropy which obeys a Ryu-Takayanagi like formula for bipartite entanglement of connected or disconnected regions, in both genus-zero and genus-one $p$-adic backgrounds, along with a Bekenstein-Hawking-type formula for black hole entropy. We prove entropy inequalities obeyed by such tensor networks, such as subadditivity, strong subadditivity, and monogamy of mutual information (which is always saturated).