The seminar meets on Thursdays, 11:10-12:00, in -101

## This Week

Place: Online

### Random walks on finite partite simplicial complexes

Random walks on graphs (and their spectral analysis) is an extensively explored topic with many applications in pure math and computer science. Recently, there has been much interest (by both the math and the CS communities) in the study of random walks on simplicial complexes as a high dimensional generalization on random walks on graphs. In this talk, we consider the spectrum of random walks on finite partite simplicial complexes and show how with a general decomposition theorem on Hilbert spaces we can improve previous works. All the definitions will be given. This is a joint work with Izhar Oppenheim.

## 2020–21–B meetings

### Upcoming Meetings

Date
Title
Speaker
Abstract
Apr 22, In Online Random walks on finite partite simplicial complexesOnline Zohar Reizis (Ben-Gurion University)

Random walks on graphs (and their spectral analysis) is an extensively explored topic with many applications in pure math and computer science. Recently, there has been much interest (by both the math and the CS communities) in the study of random walks on simplicial complexes as a high dimensional generalization on random walks on graphs. In this talk, we consider the spectrum of random walks on finite partite simplicial complexes and show how with a general decomposition theorem on Hilbert spaces we can improve previous works. All the definitions will be given. This is a joint work with Izhar Oppenheim.

Apr 29, In Online TBAOnline Nishant Chandgotia (The Hebrew University)
May 6, In Online TBAOnline Tsachik Gelander (Weizmann Institute)
May 13, In Online TBAOnline Faustin Adiceam (The University of Manchester)
May 20, In Online TBAOnline Doron Puder (Tel-Aviv University)
May 27, In Online TBAOnline Yiftach Dayan (Tel-Aviv University)
Jun 3, In Online Slow entropy of higher rank abelian unipotent actionsOnline Daren Wei (The Hebrew University)

We study slow entropy invariants for abelian unipotent actions U on any finite volume homogeneous space $G/\Gamma$. For every such action we show that the topological complexity can be computed directly from the dimension of a special decomposition of Lie(G) induced by Lie(U). Moreover, we are able to show that the metric complexity of the action coincides with its topological complexity, which provides a classification of these actions in isomorphic class. As a corollary, we obtain that the complexity of any abelian horocyclic action is only related to the dimension of G. This generalizes our previous rank one results from to higher rank abelian actions. This is a joint work with Adam Kanigowski, Philipp Kunde and Kurt Vinhage.

Jun 10, In Online TBAOnline Henna Koivusalo (University of Bristol)
Jun 17, In Online TBAOnline

### Past Meetings

Date
Title
Speaker
Abstract
Mar 4, In Online TBAOnline
Mar 11, 16:00–17:00, In Online Effective equidistribution of horospherical flows in infinite volumeOnline Nattalie Tamam (University of California, San Diego)

Horospherical flows in homogeneous spaces have been studied intensively over the last several decades and have many surprising applications in various fields. Many basic results are under the assumption that the volume of the space is finite, which is crucial as many basic ergodic theorems fail in the setting of an infinite measure space. In the talk we will discuss the infinite volume setting, and specifically, when can we expect horospherical orbits to equidistribute. Our goal will be to provide an effective equidistribution result, with polynomial rate, for horospherical orbits in the frame bundle of certain infinite volume hyperbolic manifolds. This is a joint work with Jacqueline Warren.

Mar 18, In Online A multiplicative ergodic theorem for von Neumann algebra valued cocyclesOnline Yuqing Frank Lin (Ben-Gurion University)

Oseledets’ multiplicative ergodic theorem (MET) is an important tool in smooth ergodic theory. It may be viewed as a generalization of Birkhoff’s pointwise ergodic theorem where numbers are replaced by matrices and arithmetic means are replaced by geometric means. Starting from Ruelle in 1982, many infinite-dimensional generalizations of the MET have been produced; however, these results assume quasi-compactness conditions and so do not deal with continuous spectrum. In a different direction Karlsson-Margulis obtained a geometric generalization of the MET, which we apply in our work to obtain an MET with operators in von Neumann algebras with semi-finite trace. We do not assume any compactness conditions on the operators. Joint work with Lewis Bowen and Ben Hayes.

Mar 25 Passover break
Apr 1 Passover break
Apr 8 Holocaust Memorial Day
Apr 15 Memorial day for Israel’s fallen