### 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,
you may subscribe to the
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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 |
---|---|---|

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 | Natalie Paquette (Stanford) | TBA |

Abstract forthcoming | ||

November 7Tuesday, 2pm, 02/104 |
Arnav Tripathy (Harvard) | Special cycles and BPS jumping loci |

I'll sketch an attempt to bring the theory of special cycles, a deep part of number theory, into the domain of supersymmetric string compactifications. I'll describe a construction based on jumping loci for BPS state counts -- a separate phenomenon from the better-known wall-crossing! -- and explain in what cases these jumping loci generalize some parts of the theory of special cycles. Finally, I'll conclude with a host of physical and mathematical conjectures raised by this line of investigation. | ||

November 20 | Minhyong Kim (Oxford) | TBA |

Abstract forthcoming | ||

November 21
Tuesday, 2pm, 02/104 |
Minhyong Kim (Oxford) | 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