Seminars and Colloquia by Series

Wednesday, September 20, 2017 - 13:55 , Location: Skiles 005 , Robert Kesler , Georgia Tech , Organizer: Shahaf Nitzan
 Magyar, Stein, and Wainger proved a discrete variant in Zd of the continuous spherical maximal theorem in Rd for all d ≥ 5. Their argument proceeded via the celebrated “circle method” of Hardy, Littlewood, and Ramanujan and relied on estimates for continuous spherical maximal averages via a general transference principle. In this talk, we introduce a range of sparse bounds for discrete spherical maximal averages and discuss some ideas needed to obtain satisfactory control on the major and minor arcs. No sparse bounds were previously known in this setting.
Wednesday, September 13, 2017 - 13:55 , Location: Skiles 005 , Michael Lacey , Georgia Tech , Organizer: Shahaf Nitzan
 A sparse bound is a novel method to bound a bilinear form. Such a bound gives effortless weighted inequalities, which are also easy to quantify.  The range of forms which admit a sparse bound is broad.  This short survey of the subject will include the case of spherical averages, which has a remarkably easy proof.
Wednesday, September 6, 2017 - 01:55 , Location: Skiles 005 , Shahaf Nitzan , Georgia Tech , Organizer: Shahaf Nitzan
The classical Balian-Low theorem states that if both a function and it's Fourier transform decay too fast then the Gabor system generated by this function (i.e. the system obtained from this function by taking integer translations and integer modulations) cannot be an orthonormal basis or a Riesz basis.Though it provides for an excellent `thumbs--rule' in time-frequency analysis, the Balian--Low theorem is not adaptable to many applications. This is due to the fact that in realistic situations information about a signal is given by a finite dimensional vector rather then by a function over the real line. In this work we obtain an analog of the Balian--Low theorem in the finite dimensional setting, as well as analogs to some of its extensions. Moreover, we will note that the classical Balian--Low theorem can be derived from these finite dimensional analogs.
Wednesday, August 23, 2017 - 14:05 , Location: Skiles 005 , Joey Iverson , University of Maryland , Organizer: Shahaf Nitzan
Abstract: Shift-invariant (SI) spaces play a prominent role in the study of wavelets, Gabor systems, and other group frames. Working in the setting of LCA groups, we use a variant of the Zak transform to classify SI spaces, and to simultaneously describe families of vectors whose shifts form frames for the SI spaces they generate.
Wednesday, June 21, 2017 - 14:00 , Location: Skiles 006 , Michael F. Barnsley , Australian National University , Organizer: Jeff Geronimo
In this seminar I will discuss current work, joint with AndrewVince and Alex Grant. The goal is to tie together several related areas, namelytiling theory, IFS theory, and NCG, in terms most familiar to fractal geometers.Our focus is on the underlying code space structure. Ideas and a conjecture willbe illustrated using the Golden b tilings of Robert Ammann
Wednesday, April 19, 2017 - 14:05 , Location: Skiles 005 , Mishko Mitkovskii , Clemson University , Organizer: Shahaf Nitzan
A well-known elementary linear algebra fact says that any linear independent set of vectors in a finite-dimensional vector space cannot have more elements than any spanning set. One way to obtain an analog of this result in the infinite dimensional setting is by replacing the comparison of cardinalities with a more suitable concept - which is the concept of densities. Basically one needs to compare the cardinalities locally everywhere and then take the appropriate limits. We provide a rigorous way to do this and obtain a universal density theorem that generalizes many classical density results. I will also discuss the connection between this result and the uncertainty principle in harmonic analysis.
Wednesday, April 12, 2017 - 14:05 , Location: Skiles 005 , Eyvi Palsson , Virginia Tech , Organizer: Shahaf Nitzan
Finding and understanding patterns in data sets is of significant importance in many applications. One example of a simple pattern is the distance between data points, which can be thought of as a 2-point configuration. Two classic questions, the Erdos distinct distance problem, which asks about the least number of distinct distances determined by N points in the plane, and its continuous analog, the Falconer distance problem, explore that simple pattern. Questions similar to the Erdos distinct distance problem and the Falconer distance problem can also be posed for more complicated patterns such as triangles, which can be viewed as 3-point configurations. In this talk I will present recent progress on Falconer type problems for simplices. The main techniques used come from analysis and geometric measure theory.
Wednesday, April 5, 2017 - 14:05 , Location: Skiles 005 , Galyna Livshyts , Georgia Tech , Organizer: Shahaf Nitzan
It was shown by Keith Ball that the maximal section of an n-dimensional cube is \sqrt{2}. We show the analogous sharp bound for a maximal marginal of a product measure with bounded density. We also show an optimal bound for all k-codimensional marginals in this setting, conjectured by Rudelson and Vershynin. This bound yields a sharp small ball inequality for the length of a projection of a random vector. This talk is based on the joint work with G. Paouris and P. Pivovarov.
Wednesday, March 29, 2017 - 02:05 , Location: Skiles 005 , Shahaf Nitzan , Georgia Tech , Organizer: Shahaf Nitzan
A Gaussian stationary sequence is a random function f: Z --> R, for which any vector (f(x_1), ..., f(x_n)) has a centered multi-normal distribution and whose distribution is invariant to shifts. Persistence is the event of such a random function to remain positive on a long interval [0,N].  Estimating the probability of this event has important implications in engineering , physics, and probability. However, though active efforts to understand persistence were made in the last 50 years, until recently, only specific examples and very general bounds were obtained. In the last few years, a new point of view simplifies the study of persistence, namely - relating it to the spectral measure of the process. In this talk we will use this point of view to study the persistence in cases where the spectral measure is 'small' or 'big' near zero. This talk is based on Joint work with Naomi Feldheim and Ohad Feldheim.
Wednesday, March 15, 2017 - 14:05 , Location: Skiles 005 , Liran Rotem , University of Minnesota , , Organizer: Galyna Livshyts
In this talk we will discuss several ways to construct new convex bodies out of old ones. We will start by defining various methods of "averaging" convex bodies, both old and new. We will explain the relationships between the various definitions and their connections to basic conjectures in convex geometry. We will then discuss the power operation, and explain for example why every convex body has a square root, but not every convex body has a square. If time permits, we will briefly discuss more complicated constructions such as logarithms. The talk is based on joint work with Vitali Milman.