# Analysis Seminar

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

### Winter Quarter, 2018

- February 6,
**Qingyun Wang** (UO)

Classification of Rokhlin actions on classifiable C*-algebras
- February 13,
**Yuan Xu** (UO)

Minimal cubature rules and common zeros of polynomials
- February 20,
**Chris Phillips** (UO)

Isometric inner automorphisms of operator algebras
**Abstract**: Consider an isometric automorphism of a unital Banach algebra. Suppose it is inner. Can the implementing invertible element be taken to be an isometry in the algebra?

For C*-algebras, the answer is yes, by polar decomposition. For nonselfadjoint Hilbert space operator algebras, in general the answer is no. We give several examples of operator algebras for which the answer is yes (in one case, modulo verification of some details). The results suggest that a positive answer is (weak) evidence for the algebra in question to be “C*-like”.

This is joint work with Andrey Blinov.

- February 27,
**Fu** (UO)
- March 6,
**Jianchao Wu** (Penn State)
- March 13,
**David Cruz-Uribe** (Alabama)

### Spring Quarter, 2018

- April 17,
**John Jasper** (South Dakota State U)
- April 24,
**Huaxin Lin** (UO)
- May 8,
**Dimitar Dimitrov** (State University of São Paulo, Brazil)
- May 22,
**Daniel Wang** (South Houston State U)

### Fall Quarter, 2017

- October 3,
**Qingyun Wang** (UO)

Stability of the rotation relations of three unitaries
- October 10,
**Marcin Bownik** (UO)

Lyapunov’s theorem for continuous frames
- October 17,
**Saeid Jamali**

Tracially Z-absorbing C*-algebras
- October 24,
**Ning Zhang** (Berkeley)

**Special Time/Location:** 1pm in 303 Deady

Analysis : Generalizations of Grunbaum’s Inequality
- October 24,
**Itay Londner** (Tel Aviv University)

Interpolation sets and arithmetic progressions
**Abstract**: Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data {c(k)} in l^2(K) there exists a function f in L^2(S) such that its Fourier coefficients satisfy f^(k)=c(k) for all k in K.

In the talk I will discuss the relationship between the concept of IS and the existence of arbitrarily long arithmetic progressions with specified lengths and step sizes in K.

Multidimensional analogue and recent developments will also be considered.

Based on joint work with A. Olevskii.

- October 31,
**Mark Rudelson** (University of Michigan and MSRI)

Density of a projection of a random vector
- November 7,
**Hyun Ho Lee** (University of Ulsan, South Korea)

An extension of Phillip’s theorem to inclusions of unital C*-algebras
**Abstract**: N.C. Phillips extended M. Izumi’s works on the Rokhlin property of a finite group action and established tracial analogs of many results. Among them, there is a beautiful result which says that a finite abelian group action has the tracial Rokhlin property if and only if its dual group action is tracially approximately representable. We can formulate such notions in the setting of inclusions of unital C*-algebras and provide a duality between them. We also provide an evidence why this notion is an extension of Phillip’s definition.

- November 14,
**Huaxin Lin** (UO)

Classification of stably projectionless simple C*-algebras
- November 21,
**Chris Phillips** (UO)

L^p operator algebras with contractive approximate identities
- November 28,
**Rafał Latała** (University of Warsaw & MSRI)

Dimension-free bounds for nonhomogenous random matrices
**Abstract**: What does the spectrum of a random matrix look like when the entries can have an arbitrary variance pattern? Such questions, which are of interest in several areas of pure and applied mathematics, are largely orthogonal to problems of classical random matrix theory. For example, one might ask the following basic question: when does an infinite matrix with independent Gaussian entries define a bounded operator on l_2? In this talk, I will describe recent work with Ramon Van Handel and Pierre Youssef in which we completely answer this question, settling an old conjecture of Latała. More generally, we provide optimal estimates on the Schatten norms of random matrices with independent Gaussian entries. These results not only answer some basic questions in this area, but also provide significant insight on what such matrices look like and how they behave.

**Previous years:**

2016-17

2015-16

2014-15

2013-14