ICM 2026 Invited Section Lecture - Uri Bader

Item: ICM 2026 Invited Section Lecture - Uri Bader
Rating: 5
Author: PostSingularity Institute

by Uri Bader · View the channel on PSI

Formal & Physical Sciences Mathematics PBMathematics

🎙 Uri Bader 👥 61K 📅 October 5, 2026 ⏱ 38 min 👁 256 📄 expert opinion 🧭 2026-10-16

Available in: English (current) Français

Keywords

higher property TcohomologyBanach spaceproperty Tlattices

Summary

Uri Bader delivers an ICM invited lecture about higher Property T, a recent generalization of Kazhdan’s Property T to higher cohomological degrees. He starts with a motivating question about actions of SL(3,Z) on low-dimensional contractible complexes, noting that while it acts on a 3-dimensional complex, it is unknown whether it acts on a 2-dimensional one. He recalls the definition of Property T via almost invariant vectors and its cohomological reformulation using continuous cohomology, where vanishing of H^1 with unitary coefficients is equivalent to Property T. The lecture then introduces higher Property T (T_n), focusing on vanishing of cohomology up to degree n, and mentions his joint work with Roman Sauer proving that SL(n,Z) satisfies T_{n-2}. The talk extends to Banach representations, showing that for simple groups of higher rank, cohomology vanishes with L^p coefficients for all p, leading to fixed point properties for actions on low-dimensional complexes, proving a conjecture by Benson-Farb. Bader also discusses L^p cohomology of symmetric spaces, Pansu’s computation for hyperbolic spaces, and Gromov’s conjecture on higher rank. The lecture concludes with open questions and the interplay between cohomology, geometry, and unitary representations.

186 words

Critical Evaluation

Value of the Information & Strength of the Argument

The talk presents significant recent advances in understanding higher Property T and its applications. The argumentation is well-structured: it begins with concrete problems, motivates the definitions, and then demonstrates how the results solve conjectures and connect to other areas. The value lies in both the survey of known results and the presentation of new theorems, including the fixed-point property for lattices, which has geometric implications. The speaker supports his claims with references to his own work and that of Pansu, Gromov, and others, though details are streamlined for a general mathematical audience.

Scientific Rigor, Source Quality, Title Accuracy

The scientific rigor is high: the lecture is based on peer-reviewed research and the speaker names specific collaborators and relevant literature. The title, while generic about the event and speaker, accurately reflects the described topic in the video description, focusing on higher Property T, Banach representations, and applications. The content aligns with the title’s promise, justified by the detailed coverage of these themes.

170 words

Title / Content Match

The title is generic but the content matches the description, focusing on higher Property T and its applications.

Quality & Reliability

9/10

The speaker is a leading expert in group theory, the lecture presents recent peer-reviewed results with clear definitions and discussions. The theoretical content is rigorous, but as a survey, details are simplified.

Key Moments

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

Cited Sources

Joint work with Roman Sauer — Presented as recent work on higher Property T and vanishing of cohomology.
Joint work with Saar Bader, Shaked Bader and Roman Sauer — Banach representations and higher property T.

Contribution & Novelties

This lecture provides a clear synthesis of recent breakthroughs in higher Property T, including new vanishing theorems for cohomology with Banach coefficients and their geometric applications. The key novelty is the unified treatment of unitary and Banach representations, leading to a proof of the Benson-Farb conjecture. The talk also highlights open questions and connections to L^p cohomology, encouraging further exploration.

Pour aller plus loin :

Property T (Kazhdan’s property) — Foundational concept, relevant to the core topic.
Group cohomology — Essential framework for the cohomological interpretations.
Lattice (discrete subgroup) — Examples of groups with higher Property T.

97 words

Radar Profile

The radar profile indicates an extremely high technical level and excellent information quality, with very strong fiability and a good quantity of information, typical of an expert conference lecture.

Reliability 9/10