University of Haifa – החוג למתמטיקה, אוניברסיטת חיפה
Abstract: I will tell a story of three closely related mathematical problems: the Margulis normal subgroup theorem, the Stuck–Zimmer stabilizer rigidity problem, and Thoma’s character rigidity. I will explain those problems and their history, how each generalizes and extends the…
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Abstract: In this talk, I will present new results on powers of conjugacy classes in higherrank arithmetic groups. I will explain how these results fit into a broader conceptual framework and discuss some of their consequences.
Abstract: We prove that in any dimension n there exists an origin-symmetric ellipsoid of volume c n^2 that contains no points of Z^n other than the origin. Here c > 0 is a universal constant. Equivalently, there exists a lattice…
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Abstract: Classical fractals are self-similar sets, namely sets that “look the same” at different scales. Multifractal sets are geometric objects where different patterns emerge along different sequences of scales. In nature, a snowflake is a fractal while coastlines form a…
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Abstract: Given a finite group G, and a finite dimensional complex representation π: G \to GL(V), the character χπ(g):=tr(π(g)) of π is a function on G which completely determines π. Let G = GL_n(F), where F is the field of…
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The central limit theorem (CLT) and related results for stationary weakly dependent sequences of random variables have been extensively studied in the past century, starting from a pioneering work of Berenstien (1927). However, in many physical phenomena there are external…
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In this talk, we will survey a collection of questions (and partial answers) regarding the role of symmetry in the inequalities of isoperimetric type. We will speculate why symmetry might help with improving isoperimetric properties, recall the B-conjecture, and will…
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We consider the evolutes of plane real-algebraic curves and find lower bounds for the following 4 quantities: (1) the maximal number of times a real line can intersect the evolute of a real-algebraic curve of degree d; (2) the maximal number…
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Abstract: We consider the following dynamics on a connected graph (V,E) with n vertices. Given p>1 and an initial opinion profile f_0: V \to [0,1], at each integer step t >= 1 a uniformly random vertex v=v_t is selected, and the…
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Abstract: The Combinatorial Invariance Conjecture for Kazhdan–Lusztig polynomials posits that the Bruhat graph associated with two elements in a Coxeter group uniquely determines the corresponding Kazhdan–Lusztig polynomial. This conjecture has been a topic of research for over forty years, with…
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