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**Title**

**Speaker**

**Time**

**Place**

On minimal Haar covering of \(d\)-dimensional spaces, Part II

Boris Shekhtman

4:00pm-5:00pm

CMC 130

Thanksgiving holiday — no seminar this week.

**Title**

**Speaker**

**Time**

**Place**

On minimal Haar covering of \(d\)-dimensional spaces

Boris Shekhtman

4:00pm-5:00pm

CMC 130

**Abstract**

An \(n\)-dimensional subspace \(H\) of \(C(K)\) is called Haar if every non-zero function in \(H\) has at most \((n-1)\) zeroes. Space of polynomials of degree \(n\) is the prime example of a Haar space.

It is well-known that Haar spaces of functions of several (more than 1) variables do not exist. To compensate for this “loss of Haar” we introduce a notion of “Haar covering” and discuss some questions associated with this notion. In addition to approximation theory these questions are relevant to algebraic geometry (in the complex case) and algebraic topology (in the real case).

**Title**

**Speaker**

**Time**

**Place**

Radial interpolation in the unit disc and related questions

Arthur Danielyan

4:00pm-5:00pm

CMC 130

**Abstract**

The talk will present a new approach for the peak-interpolation theorem of E. Bishop. We also discuss further interpolation problems and present new results in particular on the radial interpolation in the unit disc which are related to the Rudin-Carleson theorem.

**Title**

**Speaker**

**Time**

**Place**

Stahl's theorem on convergence of Padé approximants and various attempts to generalize it for Hermite-Padé approximants, Part III

E. A. Rakhmanov

4:00pm-5:00pm

CMC 130

**Title**

**Speaker**

**Time**

**Place**

Groups \(\mathrm{SL}(2,R)\) and its symmetric spaces

Igor Chitikov

4:00pm-5:00pm

CMC 130

**Abstract**

TBA

**Title**

**Speaker**

**Time**

**Place**

Stahl's theorem on convergence of Padé approximants and various attempts to generalize it for Hermite-Padé approximants, Part II

E. A. Rakhmanov

4:00pm-5:00pm

CMC 130

**Title**

**Speaker**

**Time**

**Place**

Two dimensional orthogonal polynomials \(=\) orthogonal polynomials on complex contours

Seung-Yeop Lee

4:00pm-5:00pm

CMC 130

**Abstract**

Motivated by the normal matrix ensemble with the external potential given by \(Q(z)=|z|^2+(\text{harmonic})\), we study the special case where the corresponding orthogonal polynomials are equivalent to the orthogonal polynomials that are orthogonal with respect to certain contour integrals.

**Title**

**Speaker**

**Time**

**Place**

Stahl's theorem on convergence of Padé approximants and various attempts to generalize it for Hermite-Padé approximants

E. A. Rakhmanov

4:00pm-5:00pm

CMC 130

**Abstract**

Generalizations did not go too far yet. I am going to discuss some very recent progress in spirit of classical orthogonal polynomials based on DE for first kind Hermite-Padé polynomials for a special class of analytic function.

**Title**

**Speaker**

**Time**

**Place**

Sharpness of connectivity bounds for quadrature domains, Part III

Seung-Yeop Lee

4:00pm-5:00pm

CMC 130

**Title**

**Speaker**

**Time**

**Place**

Sharpness of connectivity bounds for quadrature domains, Part II

Seung-Yeop Lee

4:00pm-5:00pm

CMC 130

**Title**

**Speaker**

**Time**

**Place**

Sharpness of connectivity bounds for quadrature domains

Seung-Yeop Lee

4:00pm-5:00pm

CMC 130

**Abstract**

Given the degree of a rational function, the “possible” topology of the associated quadrature domain can be identified (http://arxiv.org/pdf/1307.0487.pdf). We further claim that there exists a quadrature domain for each possible topology. This is a joint work with Nikolai Makarov.