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Mathematics & Statistics

(Leader: Prof. Dmitry Khavinson )

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**Speaker**

**Time**

**Place**

Lubinsky’s approach to Universality for General Measures

Marty Findley

4:00pm-5:00pm

PHY 108

**Abstract**

Recently D. S. Lubinsky discovered a simple relationship between reproducing kernels and Christoffel functions for general measures supported on the interval \([-1,1]\). With it, he establishes universality for measures whose weights are positive and continuous. We will discuss his approach and an extension of his result to regular measures with locally Szegö weights as well as an application to the asymptotic spacing of zeros of orthogonal polynomials.

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**Speaker**

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On equilibrium problems for the logarithmic potential, Part III

E. A. Rakhmanov

3:00pm-4:00pm

PHY 108

**Title**

**Speaker**

**Time**

**Place**

Geometry of the unit ball of \(L_p\) and minimal projections

Lesław Skrzypek

3:00pm-4:00pm

PHY 108

**Title**

**Speaker**

**Time**

**Place**

On equilibrium problems for the logarithmic potential, Part II

E. A. Rakhmanov

3:00pm-4:00pm

PHY 108

**Title**

**Speaker**

**Time**

**Place**

On equilibrium problems for the logarithmic potential, Part I

E. A. Rakhmanov

3:00pm-4:00pm

PHY 108

**Abstract**

We will start with a historic introduction related to two things: (a) Equilibrium (Robin) measure of a compact in complex plane and its applications to investigation of asymptotics for extremal polynomials. (b) Fekete points and their connections (in particular to classical orthogonal polynomials).

The main concept here is an equilibrium measure as minimizing a logarithmic energy functional (typical result: “discrete equilibrium is close to the continuous one”). More recently some approximation problems were investigated by a reduction to a new kind of equilibrium distributions — saddle points of the energy functional (equilibriums are unstable). In turn, there are important connections of these new equilibrium problems and the classical problems and tools of geometric function theory (moduli problems, quadratic differentials and so on).

This week's seminar has been replaced by a colloquium.

**Title**

**Speaker**

**Time**

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Limits of Lagrange Projections

Boris Shekhtman

3:00pm-4:00pm

PHY 108

**Abstract**

This is a joint work with Carl de Boor. The fact that every ideal projector in two variables is a limit of Lagrange projectors was proved using non-trivial facts from algebraic geometry. Recently we found a completely elementary proof of this result using nothing more than some elementary facts from linear algebra. I am hoping to present this proof with all the necessary details.