Gauged Linear Sigma Models

29 Jun 2026, 09:30 → 3 Jul 2026, 17:00 Europe/Berlin

02.430 (Mainz Institute for Theoretical Physics, Johannes Gutenberg University)

Registration closed on 02 March 2026.

 

One of the most important tools to quantitatively describe families of two-dimensional conformal field theories are gauged linear sigma models (GLSMs). As such they offer a powerful and indispensable method to study string compactifications and their phase structures from a worldsheet perspective. Over the years, the scope of GLSMs has developed much further, namely not only as a methodology to study string theories, but also to address fundamental questions of (supersymmetric) quantum field theories, in particular in two, three and four dimensions. That is to say, GLSMs have provided key insights into numerous aspects of mathematical physics, offering a bridge to various fields in mathematics such as enumerative and algebraic geometry and category theory. The aim of this workshop is to bring together experts from physics and mathematics in order to address topical research questions and to identify new applications for GLSMs. 

Monday 29 June

09:30 Check-in

1 Cyril Closset, TBA

Speaker: Cyril Closset

11:00 Break

2 Ilka Brunner, TBA

Speaker: Ilka Brunner

14:30 Break

3 Thorsten Schimmanek

Speaker: Thorsten Schimmanek

Tuesday 30 June

4 Albrecht Klemm, TBA

Speaker: Albrecht Klemm

10:30 Break

5 Ed Segal, TBA

Speaker: Ed Segal

6 Pyry Kuusela, Physics Applications of Hodge Theory and Arithmetic Geometry

This talk is an overview of recent progress in applying techniques from arithmetic geometry to physics. Many interesting physics constructions in various theories, such as CFTs and SUGRAs, can be related to non-trivial Hodge theoretic problems. Some number theoretic results and conjectures, generalising the celebrated modularity theorem in various directions, imply that these problems can be solved by using arithmetic geometry. After reviewing these connections, I give a quick overview of techniques I have developed together with collaborators to efficiently compute arithmetic geometry data, and give various examples of applications to physics.

Time permitting, I will give some comments on recent work, questions, and speculation on how the correspondence between arithmetic geometry and physics can be taken beyond the context of Hodge theory.

Speaker: Pyry Kuusela

14:30 Break

7 Yann Proto, TBA

Speaker: Yann Proto

Wednesday 1 July

8 Xiaohan Yan, TBA

Speaker: Xiaohan Yan

10:30 Break

9 YP Lee, Quantum elliptic cohomology: a progress report

Among the generalized cohomology theories associated with 1-dimensional groups are ordinary cohomology (additive group), complex K-theory (multiplicative group), and elliptic cohomology (elliptic curve). In the late 1980s and early 1990s, physicists initiated quantum cohomology (Gromov-Witten theory) as the enumerative geometry associated with ordinary cohomology. A decade later, A. Givental and I introduced quantum K-theory. In this joint work with E. Bouaziz and I. Huq-Kuruvilla, I will report on recent progress toward establishing a mathematical framework for quantum elliptic cohomology.

Speaker: YP Lee

10 Kentaro Hori, TBA

Speaker: Kentaro Hori

14:30 Break

11 Jirui Guo, Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double β-Grothendieck polynomials

The GL(N) asymmetric five vertex model is an integrable system that generalizes the spin-1/2 five vertex model. In this talk, I will explain why the Bethe ansatz equations of this model encode the ring relations of the equivariant quantum cohomology and K-theory ring of partial flag varieties, which are the OPE rings of the 2D and 3D quiver GLSMs. I will also show how the Bethe ansatz states of the integrable model generate the double β-Grothendieck polynomials interpolating the double Schubert polynomials and the double Grothendieck polynomials, which are representatives of the Schubert classes.

Speaker: Jirui Guo

Thursday 2 July

12 Muteeb M. Nouman, TBA

Speaker: Mouteeb Nouman

10:30 Break

13 Melissa Liu, TBA

Speaker: Melissa Liu

14 Tyler Kelly, TBA

Speaker: Tyler Kelly

14:30 Break

Friday 3 July

15 Emanuel Scheidegger, TBA

Speaker: Emanuel Scheidegger

10:30 Break

16 Ilarion Melnikov, The spectral flow operator in (2,2) Calabi-Yau GLSMs

The (2,2) GLSM Lagrangian allows for a simple presentation of a number of deformations of the IR SCFT obtained as the endpoint of the RG flow defined by the gauge theory path integral.
Typically, this only covers a subset of the deformations. In this talk I will review some work on describing the missing, so-called “non-toric” and “non-polynomial”, deformations as operators in the chiral algebra of the Lagrangian theory, and I will explain the key challenge through a construction, found together with Ronen Plesser, of a special holomorphic operator—the chiral spectral flow operator—in terms of the GLSM fields.

Speaker: Ilarion Melnikov

14:00 Break; in-person checkout by 14:30.