### Info

This seminar features recent results at the intersection of high-energy physics, string theory, and geometry and topology.

** Prerequisites:** None. Everyone is welcome. To receive announcements for
this seminar, and for the advertisement of other talks at the intersection of physics and
geometry in Heidelberg,
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** Time and Place:** Regularly: Monday, 2 p.m.s.t., MATHEMATIKON
SR 3

Alternatively: Tuesday or Thursday, 2 p.m.s.t., various locations (or as noted below).

### Schedule

Date | Speaker | Title, Abstract |
---|---|---|

April 10 | Ingmar Saberi (Heidelberg) | Holographic lattice field theories |

Recent developments in tensor network models (which are, roughly speaking, quantum circuits designed to produce analogues of the ground state in a conformal field theory) have led to speculation that such networks provide a natural discretization of the AdS/CFT correspondence. This raises many questions: just to begin, is there any sort of lattice field theory model underlying this connection? And how much of the usual AdS/CFT dictionary really makes sense in a discrete setting? I'll describe some recent work that proposes a setting in which such questions can perhaps be addressed: a discrete spacetime whose bulk isometries nevertheless match its boundary conformal symmetries. Many of the first steps in the AdS/CFT dictionary carry over without much alteration to lattice field theories in this background, and one can even consider natural analogues of BTZ black hole geometries. | ||

Tuesday, April 11 2 p.m.s.t. |
Michael Gekhtman (Notre Dame) | Higher pentagram maps via cluster mutations and networks on surfaces |

The pentagram map that associates to a projective polygon a new one formed by intersections of short diagonals was introduced by R. Schwartz and was shown to be integrable by V. Ovsienko, R. Schwartz and S. Tabachnikov. M. Glick demonstrated that the pentagram map can be put into the framework of the theory of cluster algebras, a new and rapidly developing area with many exciting connections to diverse fields of mathematics. In this talk I will explain that one possible family of higher-dimensional generalizations of the pentagram map is a family of discrete integrable systems intrinsic to a certain class of cluster algebras that are related to weighted directed networks on a torus and a cylinder. After presenting necessary background information on Poisson geometry of cluster algebras, I will show how all ingredients necessary for integrability - Poisson brackets, integrals of motion - can be recovered from combinatorics of a network. The talk is based on a joint project with M. Shapiro, S. Tabachnikov and A. Vainshtein. | ||

May 29 | Jon Keating (Bristol) | The Riemann hypothesis and physics — a perspective |

I will give an overview of some connections, mostly speculative, between the Riemann Hypothesis, random matrix theory, and quantum chaos. | ||

July 3 | Alex Turzillo (Caltech) | Spin TQFT and fermionic gapped phases |

I will discuss state sum constructions of two-dimensional Spin TQFTs and their G-equivariant generalizations. These models are related to tensor network descriptions of ground states of fermionic topological matter systems. We will revisit the classification of fermionic short range entangled phases enriched by a finite symmetry G and derive a group law for their stacking. | ||

July 10 | Markus Banagl (Heidelberg) | Intersection homology and the conifold transition |

Abstract forthcoming | ||

September 25 | Du Pei (QGM Aarhus and Caltech) | Can one hear the shape of a drum? |

Much like harmonics of musical instruments, spectra of quantum systems contain wealth of interesting information. In this talk, I will introduce new invariants of three- and four-manifolds using BPS spectra of quantum field theories. While most of them are completely novel, some of the new invariants categorify well-known old invariants such as the WRT invariant of 3-manifolds and the Donaldson invariant of 4-manifolds. This talk is based on arXiv:1701.06567 and ongoing work with Sergei Gukov, Pavel Putrov and Cumrun Vafa. | ||

October 16 | Laura Schaposnik (UIC) | On Cayley and Langlands type correspondences for Higgs bundles. |

The Hitchin fibration is a natural tool through which one can understand the moduli space of Higgs bundles and its interesting subspaces (branes). After reviewing the type of questions and methods considered in the area, we shall dedicate this talk to the study of certain branes which lie completely inside the singular fibres of the Hitchin fibrations. Through Cayley and Langlands type correspondences, we shall provide a geometric description of these objects, and consider the implications of our methods in the context of representation theory, Langlands duality, and within a more generic study of symmetries on moduli spaces. | ||

November 6 | Arnav Tripathy (Harvard) | TBA |

Abstract forthcoming |

### Organizers

Prof. J. Walcher, walcher@uni-heidelberg.de

Dr. Richard Eager, eager@mathi.uni-heidelberg.de

Dr. Ingmar Saberi, saberi@mathi.uni-heidelberg.de