Activities This Week
Logic, Set Theory and Topology
On Vietoris hyperspaces for some Boolean algebras
Dec 19, 12:15—13:30, 2017, Math -101
Speaker
Robert Bonnet (CNRS) (Université de Savoie-Mont Blanc, France)
Colloquium
Approximations of convex bodies by measure-generated sets
Dec 19, 13:00—14:00, 2017, Math -101
Speaker
Boaz Slomka (University of Michigan)
Abstract
Problems pertaining to approximation and their applications have been extensively studied in the theory of convex bodies. In this talk we discuss several such problems, and focus on their extension to the realm of measures. In particular, we discuss variations of problems concerning the approximation of convex bodies by polytopes with a given number of vertices. This is done by introducing a natural construction of convex sets from Borel measures. We provide several estimates concerning these problems, and describe an application to bounding certain average norms.
Based on joint work with Han Huang
Algebraic Geometry and Number Theory
Poles of the Standard L-function and Functorial Lifts for G2
Dec 20, 15:10—16:30, 2017, Math -101
Speaker
Avner Segal (UBC)
Abstract
The functoriality conjecture is a key ingredient in the theory of automorphic forms and the Langlands program. Given two reductive groups G and H, the principle of functoriality asserts that a map r:G^->H^ between their dual complex groups should naturally give rise to a map r*:Rep(G)->Rep(H) between their automorphic representations. In this talk, I will describe the idea of functoriality, its connection to L-functions and recent work on weak functorial lifts to the exceptional group of type G_2.
Geometry and Group Theory
Equations in permutations and group theoretic local testability
Dec 24, 14:30—15:30, 2017, -101
Speaker
Oren Becker (HUJI)
Abstract
Given two permutations A and B which “almost” commute, are they “close” to permutations A’ and B’ which really commute? Arzhantseva and Paunescu (2015) formalized this question and answered affirmatively. This can be viewed as a property of the equation $XY=YX$, and turns out to be equivalent to the following property of the group $Z^2 = \langle X,Y \vert XY=YX \rangle$ Every “almost-everywhere locally-defined” action of $X^2$ is close to a genuine action of $Z^2$. This leads to the notion of locally testable groups (aka “stable groups”).
We will take the opportunity to say something about “local testability” in general, which is an important subject in computer science. We will then describe some results and methods to decide whether various groups are locally testable. This will bring in some important notions in group theory, such as amenability, Kazhdan’s Property (T) and sofic groups.
Based on joint work with Alex Lubotzky.
Operator Algebras and Operator Theory
Representations of Toeplitz-Cuntz-Krieger algebras
Dec 25, 16:00—17:00, 2017, -101
Speaker
Adam Dor-On (Technion)
Abstract
By a result of Glimm, we know that classifying representations of non-type-I $C^*$-algebras up to unitary equivalence is essentially impossible (at least with countable structures). Instead of this, one either restricts to a tractable subclass or weakens the invariant.
In the theory of free semigroup algebras, the latter is done for Toeplitz-Cuntz algebras, and is achieved via two key results in the theory: the first is a theorem of Davidson, Katsoulis and Pitts on the $2\times 2$ structure of free semigroup algebras, and the second, a Lebesuge-von Neumann-Wold decomposition theorem of Kennedy.
This talk is about joint work with Ken Davidson and Boyu Li, where we generalize this theory to representations of Toeplitz-Cuntz-Krieger algebras associated to a directed graph $G.$ We prove a structure theorem akin to that of Davidson, Katsoulis and Pitts, and provide a Lebesuge-von Neumann Wold decomposition using Kennedy’s theorem. We discuss some of the difficulties and similarities when passing to the more general context of operator algebras associated to directed graphs.
אשנב למתמטיקה
תורת ההצגות, הילוכים על גרפים ומספרי קטלן
Dec 25, 18:30—20:00, 2017, אולם 101-
Speaker
אינה אנטובה-אייזנבוד
Abstract
תורת ההצגות היא תורה אשר חוקרת ייצוגים של חבורות כאוסף “סימטריות” של אובייקט כלשהו. למשל, ניתן להציג חבורה מסוימת כאוסף מטריצות (כלומר, אוסף טרנספורמציות לינאריות על מרחב ווקטורי נתון, אשר סגור תחת כפל והופכי). ייצוג כזה נקרא הצגה של חבורה. נדבר קצת על מבנה ההצגות של חבורות סופיות ולא סופיות, ונראה כיצד מופיעים בתורה זו הילוכים על גרפים ומספרי קטלן.