# Analysis Seminar 2016

The analysis seminar is held on Tuesdays at 2:00-2:50 in 210 Deady Hall unless otherwise noted.

### Winter Quarter, 2017

- February 7,
**Eusebio Gardella** (Westfaelische Wilhelmsuniversitaet Muenster)

### Fall Quarter, 2016

- September 21,
**Ilan Hirshberg** (Ben Gurion University of the Negev)

*Rokhlin actions and Z-absorption*

(Special time: Wednesday at 4:00 pm).
**Abstract:** Suppose A is a C*-algebra, and \alpha is an automorphism. One would like to find conditions which guarantee that the crossed product absorbs the Jiang-Su algebra Z tensorially. Previous work on the topic (by Winter and myself, Winter, Zacharias and myself and by Matui and Sato) focused on permanence results: if A is already assumed to be Z-absorbing, and \alpha satisfies an appropriate generalization of the Rokhlin property, then the crossed product is Z-absorbing as well. I’ll discuss some work in progress which addresses the case in which A is not assumed to be Z-absorbing. Here the Rohklin property in its own is not sufficient to imply that the crossed product is Z-absorbing, however, I will show that it is if we furthermore require that the action satisfies a weak form of approximate innerness.

- October 4,
**Stefan Steinerberger** (Yale University)

*New Interactions between Analysis and Number Theory*
**Abstract:** I will discuss three different topic that connect classical analysis with number theory in an unexpected way. (1) A new Poincare inequality on the Torus that is optimal in all sort of ways; extensions to different geometries would be nice to have! (2a) If the Hardy-Littlewood maximal function of f(x) is easy to compute, the function is f(x) = sin(x) or, equivalently, (2b) if f(x) is periodic and the trapezoidal rule is sharp on all intervals of length 1, then the function is trigonometric. The precise statement is very elementary and the proof is not, I don’t know why. (3) Mysterious pattern that appear in an old integer sequence of Stanislaw Ulam from the 1960s [Prize Money: $200 dollars for an explanation/proof].

- October 11,
**Qingyun Wang** (UO)

*A self-absorbing action on the Jiang-Su algebra*
**Abstract:** Let $G$ be a finite abelian group, we shall construct a self-absorbing action $\alpha$ of $G$ on the Jiang-Su algebra with the weak tracial Rokhlin property. Let $A$ be a simple, unital, separable $C^*$-algebra with a mild condition on the trace space. We shall show that this action $\alpha$ is absorbed by any action of $G$ on $A$ with the weak tracial Rokhlin property. Thus this action is the analogue of the Jiang-Su algebra in the equivariant setting. This is a joint work with Chris Phillips.

- October 18,
**Hannah Feng** (UO)

*Riesz transforms and fractional integration for orthogonal expansions on spheres, balls and simplices*
**Abstract:** I am going to talk something about weighted orthogonal polynomial expansions (WOPEs) on some domains-spheres, unit balls and simplices. The weights involved are invariant under a general finite reflection group. In particular, such WOPEs are named as spherical h-harmonics underlying the unit sphere. For the fractional integration associated to WOPEs on these domains, we estab- lish the Hardy-LittlewoodSobolev inequality. Then the Riesz transforms are introduced and studied, which are motivated by discovering a new decomposi- tion of the Dunkl-Laplace-Beltrami operator and are proved to process analogue properties with the classical ones. This is a joint work with Feng Dai.

- October 25,
**Jiajie Hua** (Jiaxing University)

*Rotation algebras and the Exel trace formula*
- November 1,
**Andrey Blinev** (Oregon State University)

*Holomorphically Finitely Generated Algebras*
**Abstract:** The general idea behind noncommutative geometry is based on the notion that we can replace geometric objects with corresponding commutative algebras of functions. For example, Hilbert’s Nullstellensatz shows that affine algebraic varieties are anti-equivalent to finitely generated commutative unital algebras without nilpotents, while the Gelfand-Naimark theorem makes a similar statement about locally compact topological spaces and commutative C*-algebras. Considering that correspondence, we expand our view to noncommutative algebras and treat them as “algebras of functions on noncommutative spaces”. This approach works well with algebraic geometry and topology, but the situation is different in complex analytic geometry: The “right” noncommutative version of a complex space is still unclear. One possible approach is to use holomorphically finitely generated algebras, introduced by A. Pirkovskii. In my talk, I will speak about that class of algebras, show some explicit examples such as quantum affine spaces and quantum holomorphic tori, and discuss some of their properties. In particular, I will show that quantum holomorphic tori share the same criteria of

simplicity with their algebraic and continuous counterparts.

- November 8
- November 15,
**Vincent Genest** (MIT)

*49 minutes to Bannai-Ito algebras*
**Abstract:** This talk will be an overview of Bannai-Ito algebras. Using concrete examples, I will explain the role played by these algebras in Schur-Weyl dualities, how they arise in super integrable quantum systems, and their relation to orthogonal polynomials.

- November 22
- November 28,
**Jianchao Wu** (Pennsylvania State University)

**Previous years:**

2015-16

2014-15

2013-14