# Analysis Seminar 2018

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

### Spring Quarter, 2019

- April 23,
**M. Ali Asadi-Vasfi** (University of Tehran)

The Cuntz semigroup of the fixed point algebra under a weak Rokhlin action.
- April 30,
**Bill Johnson** (Texas A&M university)

Several 20+ problems about Banach spaces and operators on them
- May 7,
**Martin Hiserote** (UO)

A characterization of anisotropic by smooth homogeneous multipliers
- May 21,
**Darrin Speegle** (Saint Louis University)

The wavelet set existence problem
- May 28,
**Simon Bortz** (University of Washington)

Muckenhoupt Weights and Elliptic Measure
**Abstract**: Initially introduced to study the L^p-boundedness of maximal functions and singular integral operators, Muckenhoupt weights have become ubiquitous in the study of partial differential equations. As a particular example, the solvability of the L^p-Dirichlet problem (in some given domain) for some p > 1 is equivalent to the harmonic measure being a Muckenhoupt weight. We also observe that the probabilistic interpretation of harmonic measure suggests that the geometry of the domain plays an important role in regards to the properties of harmonic measure.

In this talk, we will discuss a “two-phase” free boundary problem,. We show, using the theory of Muckenhoupt weights and an integral identity, that if the harmonic measure for a domain and its exterior are both “optimal” Muckenhoupt weights then the boundary of the domain is “optimally” flat (in the sense of Reifenberg). By way of the work of Kenig and Toro, this gives a characterization of (two-sided) optimally flat domains. This is joint work with M. Engelstein, M. Goering, T. Toro and Z. Zhao.

### Winter Quarter, 2019

- January 8,
**John Jasper** (South Dakota State University)

Diagonals of operators in infinite dimensions

- February 5,
**Qaiser Jahan** (Indian Institute of Technology Mandi)

Wavelets on compact abelian groups
- February 12,
**Baode Li** (Xinjiang University, China)

Ellipsiod cover and quasi-distance
- March 12,
**M. Ali Asadi-Vasfi** (University of Tehran, Iran)

Radius of comparison of fixed point algebras and crossed products of actions of finite groups

### Fall Quarter, 2018

- October 2,
**Marcin Bownik** (UO)

Exponential frames and syndetic frame sequences
- October 9,
**Yuan Xu** (UO)

Intertwining operators associated to dihedral groups
- October 16,
**Chris Phillips** (UO)

Tracially Z-absorbing C*-algebras
- October 23,
**Johann Brauchart** (TU Graz, Austria)

Explicit Construction of Good Point Set Sequences on the Sphere
- October 30,
**Mario Bonk** (UCLA)

Expanding Thurston Maps
- November 6,
**Qingyun Wang** (UO)

A tracially Z-stable C*-algebra which is not Z-stable
- November 13,
**March Boedihardjo** (UCLA)

Similarity of operators on
**Abstract**: I will present some of my recent results about operators on

including

. versions of Voiculescu’s absorption theorem and some results in the Brown-Douglas-Fillmore theory.

- November 20,
**Andrey Blinov** (UO)

Automorphisms of Calkin algebras
- November 27,
**Leonardo Figueroa** (Universidad de Concepción, Chile)

On weighted Sobolev orthogonal polynomials in the ball
**Abstract**: I discuss properties of polynomials orthogonal with respect to weighted Sobolev inner products in the

-dimensional unit ball

. Choosing a special inner product equivalent to the standard

leads to families of orthogonal polynomials satisfying simple Sturm–Liouville problems. I strive to present results in terms of orthogonal polynomial spaces as opposed to particular bases. I discuss approximation theoretical consequences relevant to the analysis of a certain class of Spectral Methods.

- November 29, Analysis/Probability course meeting

**Special Time/Location:** 2pm in 303 Deady
- November 30,
**Maciej Zworski** (Berkeley)

**Special Time:**Friday, 2pm in 209 Deady

Rough control for Schrödinger operators on 2-tori
**Abstract**: I will explain how the results of Bourgain, Burq and the speaker ’13 can be used to obtain control and observability by rough functions and sets on 2-tori. We show that for the time dependent Schrödinger equation, any set of positive measure can be used for observability and controllability.

For non-empty open sets this follows from the results of Haraux ’89 and Jaffard ’90, while for sufficiently long times and rational tori this can be deduced from the results of Jakobson ’97.

Other than tori (of any dimension; cf. Komornik ’91, Anantharaman–Macia ’14) the only compact manifolds for which observability holds for any non-empty open sets are hyperbolic surfaces. That follows from results of Bourgain–Dyatlov ’16 and Dyatlov–Jin ’17 and I will discuss the difficulty of passing to rougher rougher sets in that case. Joint work with N Burq.

- December 4,
**Dawn Archey** (University of Detroit Mercy) and **Julian Buck** (Francis Marion University)

Structure Properties for Certain Non

-Stable Crossed Product C*-Algebras
**Abstract**: Crossed product C*-algebras of the form

, where X is a compact metric space, D is an infinite-dimensional C*-algebra, and h is an automorphism induced by a minimal homeomorphism of X, have been studied extensively by the speakers and Chris Phillips in the case where D is stable under tensoring with the Jiang-Su algebra

. Very little is previously known when this is not assumed to be the case, such as when D is

, the free group C*-algebra on 2 or more generators. In fact not only are such algebras not Jiang-Su stable, they are not even nuclear. As a result, in order to obtain results on the structure of the crossed product, additional assumptions need to be made on the underlying space X. We will show that in the case where X is the Cantor Set, we can obtain stable rank one and real rank zero in the crossed product for examples using such algebras as D, the fiber term, in C(X,D).

**Previous years:**

2017-18

2016-17

2015-16

2014-15

2013-14