A Polynomial Bogolyubov type Result for the Special Linear Group

Channel:
United States Simons Institute for the Theory of Computing
Subscribers:
68,700
Published on ● Video Link: https://www.youtube.com/watch?v=nfzV9h95kPU


Duration: 1:04:15
244 views
5

Guy Kindler (Hebrew University of Jerusalem)
https://simons.berkeley.edu/talks/guy-kindler-hebrew-university-jerusalem-2023-07-26
Structural Results

For a subset A of a finite dimensional vector space over a finite field, It is known that 2A-2A must contain a subgroup of density that is quasi-polynomial in the density of A. We show an analogue result for the special linear group over a finite field, except we achieve a polynomial density for the subgroup. The main tool used is a new hyper-contractive estimate for the special linear group, that has origins in the study of 2-to-2 games.



Other Videos By Simons Institute for the Theory of Computing


2023-07-29Correspondence Colouring of Random Graphs
2023-07-28Structures in Random Graphs: New Connections
2023-07-28Noncommutativity and Rounding Schemes for Combinatorial Optimization Parts 1 & 2
2023-07-28Some Remarks About Quantum and Classical Local Hamiltonian Optimization and SDP Rounding
2023-07-28Structure of Communication | Richard M. Karp Distinguished Lecture
2023-07-28Randomized versus Deterministic Decision Tree Size
2023-07-28Fourier Growth of XOR-Fibers of Communication Protocols
2023-07-27Sign-rank vs Margin
2023-07-27Tight Space Complexity of the Coin Problem
2023-07-27A New Upper Bound for the Heilbronn Triangle Problem
2023-07-26A Polynomial Bogolyubov type Result for the Special Linear Group
2023-07-26Higher-dimensional Expansion of Random Geometric Complexes
2023-07-26Testing Thresholds for High-dimensional Sparse Random Geometric Graphs
2023-07-25An Improved Bound for Regular Partitions of Hypergraph of Bounded VC_2 Dimension
2023-07-25Larger Corner-free Sets in High Dimensions
2023-07-25Top-Down Lower Bounds for Depth-Four Circuits
2023-07-25P-smallness of Increasing Families
2023-07-24Nearly all k-SAT Functions are Unate
2023-07-21Session #3
2023-07-20Survey on Optimization in FL
2023-07-20Session #2


Tags:
Simons Institute
theoretical computer science
UC Berkeley
Computer Science
Theory of Computation
Theory of Computing
Structural Results
Guy Kindler