Dear colleagues,
This email is to remind everyone that Alex Lubotzky, the Maurice and Clara Weil Chair of Mathematics at Hebrew University, will be delivering this year’s Distinguished Lectures next week.
Alex has made major contributions to group theory, representation theory, and theoretical computer science, and is a winner of the Rothschild Prize and the Ferran Sunyer i Balaguer Prize. He also gives a superb lecture, as we will all see next
week!
I include in this email a small request. If anyone who is handy in this way were willing to make a quick webpage announcing these lectures, I would be *extremely grateful* — I will link to that to publicize the talks, especially the first talk,
beyond our department.
If you want to meet with Alex to talk math, he will be in office 805 — or you can contact me if you want to make a specific appointment. Alex will be going straight to the airport after his second talk, so Tuesday morning or Monday is best.
Best,
Jordan
MONDAY, FEB 5, 4pm, Van Vleck 911:
High dimensional expanders: From Ramanujan graphs to Ramanujan complexes
Abstract: Expander graphs in general, and Ramanujan graphs , in particular, have played a major role in computer science in the last 5 decades and more recently also in pure math. The first explicit construction of bounded degree expanding
graphs was given by Margulis in the early 70's. In mid 80' Margulis and Lubotzky-Phillips-Sarnak provided Ramanujan graphs which are optimal such expanders.
In recent years a high dimensional theory of expanders is emerging. A notion of topological expanders was defined by Gromov in 2010 who proved that the complete d-dimensional simplical complexes are such. He raised the basic question of existence
of such bounded degree complexes of dimension d>1.
This question was answered recently affirmatively (by T. Kaufman, D. Kazdhan and A. Lubotzky for d=2 and by S. Evra and T. Kaufman for general d) by showing that the d-skeleton of (d+1)-dimensional Ramanujan complexes provide such topological
expanders. We will describe these developments and the general area of high dimensional expanders.
(This talk will be suitable for a general audience — please invite friends!)
TUESDAY, FEB 6, 2pm (note early time!) Van Vleck 911:
Groups' approximation, stability and high dimensional expanders
Several well-known open questions, such as: are all groups sofic or hyperlinear?, have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric
groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms.
We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2) norm.
The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using high dimensional expanders, it is shown that
some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated.
All notions will be explained. (Joint work with M, De Chiffre, L. Glebsky and A. Thom.)
(This talk is a math colloquium.)
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