Tue, 28 Apr 2026

14:00 - 15:00
L5

A Fourier-theoretic Approach to Non-Abelian Additive Combinatorics: The LNS Conjecture and Beyond

Noam Lifshitz
(Hebrew University of Jerusalem)
Abstract

Since the foundational works of Diaconis, pointwise character bounds of the form \chi(\sigma) \le \chi(1)^\alpha have guided the study of growth in finite simple groups. However, this classical machinery hits an algebraic bottleneck when confronted with non-class functions and unstructured subsets.

In this talk, we bypass this barrier by replacing classical representation theory with discrete analysis. By decomposing functions as f = \sum f_\rho and bounding the L_2 norm \|f_\rho\|_2 \le \chi_\rho(1)^\alpha for each representation \rho, we develop a robust theory of Fourier anti-concentration. We will demonstrate how this resolves the Liebeck–Nikolov–Shalev (LNS) conjecture—proving a group can be expressed optimally as the product of conjugates of an arbitrary subset A—and discuss how applying Boolean function analysis tools like hypercontractivity pushes this philosophy even further.

Data for paper "Different cadaver astigmatan mites (Arthropoda: Acari) are designed to bite flesh differently" by C E Bowman in Experimental and Applied Acarology
Bowman, C
Thu, 23 Apr 2026
17:00
L4

Conjugacy of trivial autohomeomorphisms of $\beta N\setminus N$.

Ilijas Farah
(York University, Toronto)
Abstract
An autohomeomorphism of the Čech--Stone remainder $\beta N\setminus N$ is called trivial if it has a continuous extension to a map from $\beta N$ into itself. Such map is determined by an almost permutation, which is a bijection between cofinite subsets of $N$. By results of W. Rudin and S. Shelah, the question whether nontrivial autohomeomorphisms of $\beta N\setminus N$ exist is independent from ZFC. We will be considering the so-called rotary autohomeomorphisms. An autohomeomorphism is called rotary if it corresponds to a permutation of $N$ all of whose cycles are finite. If all autohomeomorphisms are trivial, then the problem of their conjugacy is also trivial (in the usual sense of the word). However the Continuum Hypothesis makes the conjugacy relation nontrivial. While our results are somewhat incomplete, they suffice to decide whether for example the rotary autohomeomorphisms whose cycles have lengths $2^{2n}$, for $n\in N$, and $2^{2n+1}$, for $n\in N$, are conjugate. This is a joint work with Will Brian.
Numerical studies of the power-sharing during MAST L-mode discharges
Xia, Q Militello, F Moulton, D Omotani, J Nuclear Fusion volume 66 issue 4 (01 Apr 2026)
Preface
Fowler, A Ng, F Springer Textbooks in Earth Sciences Geography and Environment volume Part F10283 xi-xiii (01 Jan 2021)
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