Class S theories and the geometric Langlands correspondence by Aswin Balasubramanian

Value of the Information & Strength of the Argument

The talk provides a valuable synthesis of a complex subject, connecting several distinct mathematical and physical frameworks. The argumentation is well-structured, moving from classical number theory (Ramanujan, Hecke) through the Langlands program to geometric Langlands and its physical realization in Class S theories. The speaker gives clear motivations for each step and explains the conceptual bridges, such as the role of Hecke operators and the equivalence of categories. However, the treatment is often cursory, and the speaker frequently mentions that many details are omitted or handwaved, which is typical of a survey talk. The discussion of his own contributions is somewhat informal, and the existing results are not presented with rigorous mathematical detail.

Scientific Rigor, Source Quality, Title Accuracy

The talk cites a wide range of works, including those of Ramanujan, Hecke, Peterson, Langlands, Arinkin, Gaitsgory, Kapustin, Witten, Teschner, Donagi, and others, without giving specific references. The description provides only the program link, which may contain further details. The title accurately reflects the content, and the talk is appropriate for an expert audience. There is no problematic discrepancy between the title and the actual material presented. The scientific rigor is appropriate for a review lecture, but the lack of explicit sources in the transcript limits the ability to verify claims independently.

The title accurately reflects the content: the talk indeed focuses on Class S theories and their connection to the geometric Langlands correspondence, with a detailed historical and mathematical context.

7/10

The talk is a high-level technical review given by a researcher at a specialized workshop. It covers a broad range of advanced topics and cites many relevant works, but the presentation is informal and the transcript contains digressions. While the content is likely accurate, the lack of explicit references and the rapid overview of many subjects limit its use as a standalone source.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction and talk outline; motivation for discussing geometric Langlands.
• 02:00Discussion of Ramanujan's tau function, its conjectured properties, and Hecke operators.
• 07:00Introduction to the Langlands program, dual groups, and the generalized Ramanujan conjectures.
• 15:00Overview of geometric Langlands, including abelian case and Jacobians, and non-abelian formulations.
• 25:00Recent progress on the unramified geometric Langlands correspondence by Gaitsgory and collaborators.
• 35:00Connection to physics: Kapustin-Witten and S-duality, and the role of 4D gauge theories.
• 45:00Introduction to Class S theories, their definition and relevance to geometric Langlands.
• 55:00Discussion of speaker's work with Teschner and Donagi, and conclusions.

• ICTS Monopole Moduli Program — Official program page for the workshop where this talk was given, containing background and links to related materials.