# Research

## Analysis

### Friday, November 18, 2016

Title: A convergence result for harmonic measures and applications, III
Speaker: Myrto Manolaki
Time: 4:00pm–5:00pm
Place: CMC 130

### Friday, November 4, 2016

Title: A convergence result for harmonic measures and applications, II
Speaker: Myrto Manolaki
Time: 4:00pm–5:00pm
Place: CMC 130

### Friday, October 28, 2016

Title: A convergence result for harmonic measures and applications
Speaker: Myrto Manolaki
Time: 4:00pm–5:00pm
Place: CMC 130

#### Abstract

In this talk we will present a recent convergence theorem for harmonic measures which was originally motivated by the study of universal Taylor series. We will discuss certain potential theoretic notions that lie behind this result (such as minimal thinness) and we will see how it can be used as a tool to “glue” the boundary behaviour of a Taylor series with the behaviour of its partial sums on the circle of convergence. This finds applications to various classes of universal series and improves previous results. (Joint work with Stephen Gardiner.)

### Friday, October 21, 2016

Title: Weak regularization of singularities in dynamical systems: the divisibility criterion, II
Speaker: Razvan Teodorescu
Time: 4:00pm–5:00pm
Place: CMC 130

### Friday, October 14, 2016

Title: Weak regularization of singularities in dynamical systems: the divisibility criterion
Speaker: Razvan Teodorescu
Time: 4:00pm–5:00pm
Place: CMC 130

#### Abstract

I will discuss a method for regularization of singularities in dynamical systems which are reducible to evolution of equilibrium measures in the plane. This approach allows to construct certain weak solutions and to apply duality methods to an extended functional space.

### Friday, October 7, 2016

Title: Asymptotics for orthogonal polynomials on the real axis, III
Speaker: E. A. Rakhmanov
Time: 4:00pm–5:00pm
Place: CMC 130

### Friday, September 30, 2016

Title: Asymptotics for orthogonal polynomials on the real axis, II
Speaker: E. A. Rakhmanov
Time: 4:00pm–5:00pm
Place: CMC 130

### Friday, September 23, 2016

Title: Asymptotics for orthogonal polynomials on the real axis
Speaker: E. A. Rakhmanov
Time: 4:00pm–5:00pm
Place: CMC 130

#### Abstract

There is an extended theory related to the problem. For its two centuries history it had several ups and downs. I will try to review some key moments in history. I think I can do that. I will also try to predict the future (where it is going). I think I can not do that, but I will try anyway.

### Friday, September 16, 2016

Title: Searching for singularities for solutions of partial differential equations, III
Speaker: Dima Khavinson
Time: 4:00pm–5:00pm
Place: CMC 130

### Friday, September 9, 2016

Title: Searching for singularities for solutions of partial differential equations, II
Speaker: Dima Khavinson
Time: 4:00pm–5:00pm
Place: CMC 130

### Friday, September 2, 2016

University closed — no seminar this week.

### Friday, August 26, 2016

Title: Searching for singularities for solutions of partial differential equations
Speaker: Dima Khavinson
Time: 4:00pm–5:00pm
Place: CMC 130

#### Abstract

Where should we look for singularities of electrostatic potentials (a/k/a harmonic functions), or solutions of the heat equation, where do the waves break down? We all know the mean value theorem for harmonic functions in balls in
$$R^n$$, the mean value is the value at the center. What about ellipsoids, or other algebraic surfaces? How can we predict the nature of a singularity (ramified, unbounded, etc.) of a solution to a PDE without “going there” and being destroyed? We shall indicate a general scheme to these and many other questions. The talk will be accessible to graduate students and seniors in mathematics, physics and engineering.