Monday, April 16

PROBABILITY SEMINAR (note different time and location)

TIME: 1010 a. m. - 11:00 a.m.
ROOM: Buehler 472
SPEAKER: Fedor Nazarov, Michigan State University/University of Wisconsin
TITLE: "Probabilities of moderate and large deviations for the number of zeroes of a Gaussian entire function in a large disk."
ABSTRACT: Let $\xi_k$ be i.i.d. standard complex Gaussian random variables. Let $F(z)=\sum_{k\ge 0}\xi_k z^k/\sqrt{k!}$. Let $N(R)$ be the number of its zeroes in the disk of large radius $R$. It is not hard to show that $E N(R)=R^2$ and that $Var N(R)$ is comparable to $R$. We shall show that, for $a>1/2$, the probability $P\{|N(R)-R^2|>R^a\}$ is about $\exp[-R^{b(a)}]$ where $b(a)$ is some explicit piecewise linear function of $a$. This is a joint work with Mikhail Sodin and Alexander Volberg.

DE/COMPUTATIONAL AND APPLIED MATH SEMINAR
TIME: 3:35 p.m. - 4:25 p.m.
ROOM: Ayres Hall 309A
SPEAKER: Nick Gewecke
TITLE: "Minimization of the principal eigenvalue with indefinite weight and applications to population dynamics"
SPEAKER: Despina Stavri
TITLE: "Solving differential equations by asymptotic methods"

ORAL SPECIALITY EXAMINATION

FOR: Mr. George Butler
ROOM: Ayres 309B
COMMITTEE: Dr. Mulay; Dr. Anderson; Dr. Finotti and Dr. Tzermias

Tuesday, April 17

ANALYSIS SEMINAR (note different time and location)

TIME: 3:35 p.m.-4:25p.m.
ROOM: Ayres Hall 209A
SPEAKER: Fedor Nazarov, Michigan State University/University of Wisconsin
TITLE: "On the average length of the projections of the $n$-th generation $1/4$-Cantor square.
ABSTRACT: Let $F_n$ be the average length of the projections of the $n$-th generation $1/4$-Cantor square to lines in $R^2$. It is still an unsolved problem to determine the rate of decay of $F_n$ as $n$ tends to infinity. The best known lower estimate (due to Mattila) is $1/n$. Until 2002 no non-trivial explicit upper bound had been known. In 2002 Peres and Solomyak proved the upper bound $\exp[-\log_* n]$ where $\log_* n$ is the number of times one needs to take natural logarithm to get a number less than $1$ starting from $n$. We will derive a much better upper bound using Fourier analytic techniques. This is a joint work with Yuval Peres and Alexander Volberg.

Thursday, April 19

Probability Seminar

TIME: 10:10 a.m – 11:00 a.m.
ROOM: 309B Ayres Hall
SPEAKER: Kirill Yakovlev
TITLE: Bear Population Control

Friday, April 20

COLLOQUIUM

TIME: 3:35 - 4:25 p.m.
ROOM: 214 Ayres Hall
SPEAKER: Prof. Vassilios Dougalis (Univ of Athens, Greece) and Institute of Applied and Computational Mathematics, FORTH
TITLE: "Theory and Numerical Analysis of Boussinesq systems in two space dimensions
ABSTRACT: We consider a family of Boussinesq systems in two space dimensions. These systems approximate the three-dimensional Euler equations of hydrodynamics, and consist of three coupled nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids. For some of these systems it is possible to prove that their initial-value problem is well-posed in suitable Sobolev spaces; we also consider the well-posedness of some simple initial-boundary value problems in bounded domains. The systems are solved numerically by fully discrete Galerkin-finite element methods. Error estimates and numerical experiments are presented.

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