# Mathematical Sciences Research Institute

Home » Workshop » Schedules » Approximate cohomology

# Approximate cohomology

## Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017

May 01, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Tamar Ziegler (The Hebrew University of Jerusalem)
Location: MSRI: Atrium
Tags/Keywords
• cohomology

• Fourier analysis

• inverse conjecture for Gowers norms

• Gowers norm

• homogeneous multilinear forms

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### Ziegler

Abstract

Let V be an infinite vector space over a finite field k and let be an approximate homomorphism from V to End(V), i.e. the rank of f(x+y)-f(x)-f(y) is uniformly bounded by some constant r. We show that there is a homomorphism g such that f-g is of rank uniformly bounded by R(r).

We introduce a notion of a approximate cohomology groups and interpret this result as a computation of H^1 in a special case. Our proof uses the inverse theorem for the Gowers norms over finite fields; and an independent proof of this result (and some natural generalizations of it) would lead to a new proof of the inverse theorem. Joint work with D. Kazhdan

Supplements