Author Archives: Victoria Hain

March 13, 2023 TITLE: Generalized symmetries from string theory ABSTRACT: String theory provides a systematic way of constructing quantum field theories (QFTs) via geometric engineering. In particular, this can involve non-compact Calabi-Yau spaces in various dimensions, as well as other special holonomy manifolds. I will describe the dictionary between the generalized symmetry data of the […]

Lakshya Bhardwaj: Lectures

March 13, 2023 TITLE: Overview of Generalized Symmetries ABSTRACT: I will provide an overview of various types (higher-form, higher-group and non-invertibles) of generalized symmetries and how they arise in gauge theories. This will set stage for later talks that will describe how generalized symmetries are encoded in geometric engineering.

Federico Bonetti: Lectures

March 14, 2023 TITLE: SymTFTs, Differential Cohomology, and Geometric Engineering ABSTRACT: The symmetry data of a quantum field theory (QFT) in d spacetime dimensions is conveniently captured by an auxiliary topological field theory in d+1 spacetime dimensions, referred to as the Symmetry Topological Field Theory (SymTFT). After a brief introduction to the SymTFT, I will […]

Saman Habibi Esfahani: Lectures

5/16/2024: On the Donaldson-Scaduto conjecture 3/16/2023: Towards a Monopole Fueter Floer Homology May 16, 2024 TITLE: On the Donaldson-Scaduto conjecture ABSTRACT: Motivated by G2-manifolds with coassociative fibrations in the adiabatic limit, Donaldson and Scaduto conjectured the existence of associative submanifolds homeomorphic to a three-holed 3-sphere with three asymptotically cylindrical ends in the G2-manifold X×ℝ3, or […]

Constantin Teleman: Lectures

March 13, 2023 TITLE: Introduction to topological symmetries and higher groups ABSTRACT: I will review the setting of an algebra of symmetries acting on a QFT. Special emphasis will be placed on symmetries arising from finite homotopy types (aka higher finite groups) and the way homotopical calculations quantize to a ‘higher categorical group ring’ of […]

Victoria Hoskins: Lectures

January 9, 2023 TITLE: Motivic mirror symmetry for Higgs bundles ABSTRACT: Moduli spaces of Higgs bundles for Langlands dual groups are conjecturally related by a form of mirror symmetry. For SLn and PGLn, Hausel and Thaddeus conjectured a topological mirror symmetry given by an equality of (twisted orbifold) Hodge numbers, which was proven by Groechenig-Wyss-Ziegler […]

Oscar Garcia-Prada: Lectures

January 10, 2023 TITLE: Vinberg pairs and Higgs bundles ABSTRACT: A finite order automorphism of a complex semisimple Lie group determines a cyclic grading of its Lie algebra. Vinberg’s theory is concerned with the geometric invariant theory associated to this grading. Important examples include the case of involutions and representations of cyclic quivers. After reviewing […]

Katrin Wendland: Lectures

January 11, 2023 TITLE: An application of folding ADE to BCFG ABSTRACT: We consider families of Calabi-Yau threefolds which are obtained from the deformation spaces of ADE type surface singularities. For these non-compact Calabi-Yau threefolds, Diaconescu, Donagi and Pantev discovered in 2007 that the associated Calabi-Yau integrable systems agree with the ADE type Hitchin integrable […]

Timo Weigand: Lectures

January 12, 2023 TITLE: Tower Counting for the Weak Gravity Conjecture ABSTRACT: This talk presents recent advances in our understanding of the Tower Weak Gravity Conjecture (WGC) in string compactifications with minimal supersymmetry. The underlying mathematics involves aspects of the Kahler and enumerative geometry of Calabi-Yau manifolds, in particular modular properties of partition functions of […]

Matt Turner: Lectures

January 9, 2023 (jointly with Johannes Nordström) TITLE: Examples of asymptotically conical G2-instanstons ABSTRACT: We present examples of G2-instantons with dilation-invariant asymptotics on the “C7” asymptotically conical G2-metric on the anticanonical bundle of CP1 x CP1. The examples have cohomogeneity one which reduces the problem to solving an ordinary differential equation. We find solutions to […]