Seminars and Colloquia by Series

On some extremal problems for polynomials

Series
Analysis Seminar
Time
Wednesday, April 3, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex StokolosGeorgia Southern

In this talk we will discuss some some extremal problems for polynomials. Applications to the problems in discrete dynamical systems as well as in the geometric complex analysis will be suggested.

Energy minimization on the sphere.

Series
Analysis Seminar
Time
Wednesday, March 27, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dmitry BilykUniversity of Minnesota

Many problems of spherical discrete and metric geometry may be reformulated as energy minimization problems and require techniques that stem from harmonic analysis, potential theory, optimization etc. We shall discuss several such problems as well of applications of these ideas to combinatorial geometry, discrepancy theory, signal processing etc.

The Bishop-Phelps-Bolloba ́s Property for Numerical Radius in the space of summable sequnces

Series
Analysis Seminar
Time
Wednesday, March 13, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Olena KozhushkinaUrsinus college
The Bishop-Phelps-Bolloba ́s property for numerical radius says that if we have a point in the Banach space and an operator that almost attains its numerical radius at this point, then there exist another point close to the original point and another operator close to the original operator, such that the new operator attains its numerical radius at this new point. We will show that the set of bounded linear operators from a Banach space X to X has a Bishop-Phelps-Bolloba ́s property for numerical radius whenever X is l1 or c0. We will also discuss some constructive versions of the Bishop-Phelps- Bolloba ́s theorem for l1(C), which are an essential tool for the proof of this result.

A restriction estimate in $\mathbb{R}^3$

Series
Analysis Seminar
Time
Wednesday, March 6, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hong WangMIT

If $f$ is a function supported on a truncated paraboloid, what can we say about $Ef$, the Fourier transform of f? Stein conjectured in the 1960s that for any $p>3$, $\|Ef\|_{L^p(R^3)} \lesssim \|f\|_{L^{\infty}}$.

We make a small progress toward this conjecture and show that it holds for $p> 3+3/13\approx 3.23$. In the proof, we combine polynomial partitioning techniques introduced by Guth and the two ends argument introduced by Wolff and Tao.

Schur multipliers in perturbation theory

Series
Analysis Seminar
Time
Wednesday, February 27, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Anna SkripkaUniversity of New Mexico
Linear Schur multipliers, which act on matrices by entrywisemultiplications, as well as their generalizations have been studiedfor over a century and successfully applied in perturbation theory. Inthis talk, we will discuss extensions of Schur multipliers tomultilinear infinite dimensional transformations and then look intoapplications of the latter to approximation of operator functions.

The symmetric Gaussian isoperimetric inequality

Series
Analysis Seminar
Time
Wednesday, February 20, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Steven HeilmanUSC
It is well known that a Euclidean set of fixed Euclidean volume with least Euclidean surface area is a ball. For applications to theoretical computer science and social choice, an analogue of this statement for the Gaussian density is most relevant. In such a setting, a Euclidean set with fixed Gaussian volume and least Gaussian surface area is a half space, i.e. the set of points lying on one side of a hyperplane. This statement is called the Gaussian Isoperimetric Inequality. In the Gaussian Isoperimetric Inequality, if we restrict to sets that are symmetric (A= -A), then the half space is eliminated from consideration. It was conjectured by Barthe in 2001 that round cylinders (or their complements) have smallest Gaussian surface area among symmetric sets of fixed Gaussian volume. We discuss our result that says this conjecture is true if an integral of the curvature of the boundary of the set is not close to 1. https://arxiv.org/abs/1705.06643 http://arxiv.org/abs/1901.03934

Some results for functionals of Aharanov-Bohm type

Series
Analysis Seminar
Time
Wednesday, February 13, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael LossGeorgia Tech
In this talk I present some variational problems of Aharanov-Bohm type, i.e., they include a magnetic flux that is entirely concentrated at a point. This is maybe the simplest example of a variational problems for systems, the wave function being necessarily complex. The functional is rotationally invariant and the issue to be discussed is whether the optimizer have this symmetry or whether it is broken.

Sparse bounds for discrete spherical maximal functions

Series
Analysis Seminar
Time
Wednesday, February 6, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dario Alberto MenaUniversity of Costa Rica
We prove sparse bounds for the spherical maximal operator of Magyar,Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint esti-mate. The new method of proof is inspired by ones by Bourgain and Ionescu, is veryefficient, and has not been used in the proof of sparse bounds before. The Hardy-Littlewood Circle method is used to decompose the multiplier into major and minor arccomponents. The efficiency arises as one only needs a single estimate on each elementof the decomposition.

Distance sets, lattice points, and decoupling estimates

Series
Analysis Seminar
Time
Wednesday, January 30, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex IosevichUniversity of Rochester
We are going to discuss some recent results pertaining to the Falconer distance conjecture, including the joint paper with Guth, Ou and Wang establishing the $\frac{5}{4}$ threshold in the plane. We are also going to discuss the extent to which the sharpness of our method and similar results is tied to the distribution of lattice points on convex curves and surfaces.

Valuations on convex sets and integral geometry

Series
Analysis Seminar
Time
Wednesday, January 23, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Semyon AleskerTel Aviv University
Valuations are finitely additive measures on convex compact subsets of a finite dimensional vector space. The theory of valuations originates in convex geometry. Valuations continuous in the Hausdorff metric play a special role, and we will concentrate in the talk on this class of valuations. In recent years there was a considerable progress in the theory and its applications. We will describe some of the progress with particular focus on the multiplicative structure on valuations and its applications to kinematic formulas of integral geometry.

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