Activities This Week

In this talk we will discuss two central problems in multivariable operator theory: (1) joint invariant subspaces of the tuple of shift operators on the Hardy space over the unit polydisc, and (2) a commutant lifting theorem of the tuple of shift operator on certain analytic reproducing kernel Hilbert spaces over the unit ball. If time permits, we will also talk about Nevanlinna-Pick interpolation theorem and a relevant factorization result for multipliers on reproducing kernel Hilbert spaces over the unit ball.

Benjamini-Schramm convergence is a probabilistic notion useful in studying the asymptotic behavior of sequences of metric spaces. The goal of this talk is to discuss this notion and some of its applications from various perspectives, e.g. for groups, graphs, hyperbolic manifolds and locally symmetric spaces, emphasizing the distinction between the hyperbolic rank-one case and the rigid high-rank case. Understanding the “sofic” part of the Benjamini-Schramm space, i.e. all limit points of “finitary” objects, will play an important role. From the group-theoretic perspective, I will talk about sofic groups, i.e. groups which admit a probabilistic finitary approximation, as well as a companion notion of permutation stability. Several results and open problems will be discussed.

לפירות שמקיימים את המשוואה בתמונה יש לפחות 80 ספרות. נראה איך ניתן למצוא אותם - באמצעות פונקציות מרוכבות על מרחב כל השריגים, וגיאומטריה של עקומים מעוקבים.

Differential graded algebras(DGAs) are one of the most important objects of study in homological algebra. These are chain complexes with an associative and unital multiplication. Examples of DGAs include cochain complexes of topological spaces equipped with the cup product.

In this talk, I present our recent classification results on DGAs with polynomial homology. These results are obtained by exploiting interesting interactions between DGAs and stable homotopy theory. I am going to start my talk by stating these classification results. For the rest of the talk, I am going to present how stable homotopy theory comes into play for the classification of DGAs. This presentation is going to be accessible to a general audience.

I’ll show the invalidity of finitary counterparts for three theorems in classification theory: The preservation of being a Bernoulli shift through factors, Sinai’s factor theorem, and the weak Pinsker property. This gives a negative answer to an old conjecture and to a recent open problem.