## Seminars and Colloquia by Series

### Means and powers of convex bodies

Series
Analysis Seminar
Time
Wednesday, March 15, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Liran RotemUniversity of Minnesota
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.

### Sparse operators and the sparse T1 Theorem

Series
Analysis Seminar
Time
Wednesday, March 8, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dario MenaGeorgia Tech
We impose standard $T1$-type assumptions on a Calderón-Zygmund operator $T$, and deduce that for bounded compactly supported functions $f,g$ there is a sparse bilinear form $\Lambda$ so that $$|\langle T f, g \rangle | \lesssim \Lambda (f,g).$$ The proof is short and elementary. The sparse bound quickly implies all the standard mapping properties of a Calderón-Zygmund on a (weighted) $L^p$ space.

### Do Minkowski averages get progressively more convex?

Series
Analysis Seminar
Time
Wednesday, March 1, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Artem ZvavitchKent State University
For a compact subset $A$ of $R^n$ , let $A(k)$ be the Minkowski sum of $k$ copies of $A$, scaled by $1/k$. It is well known that $A(k)$ approaches the convex hull of $A$ in Hausdorff distance as $k$ goes to infinity. A few years ago, Bobkov, Madiman and Wang conjectured that the volume of $A(k)$ is non-decreasing in $k$, or in other words, that when the volume deficit between the convex hull of $A$ and $A(k)$ goes to $0$, it actually does so monotonically. While this conjecture holds true in dimension $1$, we show that it fails in dimension $12$ or greater. Then we consider whether one can have monotonicity of convergence of $A(k)$ when its non-convexity is measured in alternate ways. Our main positive result is that Schneider’s index of non-convexity of $A(k)$ converges monotonically to $0$ as $k$ increases; even the convergence does not seem to have been known before. We also obtain some results for the Hausdorff distance to the convex hull, along the way clarifying various properties of these notions of non-convexity that may be of independent interest.Joint work with Mokshay Madiman, Matthieu Fradelizi and Arnaud Marsiglietti.

### Interpolation sets and arithmetic progressions

Series
Analysis Seminar
Time
Wednesday, February 8, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Itay LondnerTel-Aviv University
Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data {c(k)} in l^2(K) there exists a function f in L^2(S) such that its Fourier coefficients satisfy f^(k)=c(k) for all k in K. In the talk I will discuss the relationship between the concept of IS and the existence of arbitrarily long arithmetic progressions with specified lengths and step sizes in K. Multidimensional analogues of this subject will also be considered.This talk is based on joint work with Alexander Olevskii.

### Results on two variable orthogonal polynomials associated with Bernstein-Szego measures on the circle and square.

Series
Analysis Seminar
Time
Wednesday, February 1, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeff GeronimoGeorgia Tech
The theory of two variable orthogonal polynomials is not very well developed. I will discuss some recent results on two variable orthogonal polynomials on the bicircle and time permitting on the square associate with orthogonality measures that are one over a trigonometric polynomial. Such measures have come to be called Bernstein-Szego measures. This is joint work with Plamen Iliev and Greg Knese.

### Sparse Domination of Multilinear Dyadic Operators and Their Commutators

Series
Analysis Seminar
Time
Wednesday, January 25, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ishwari KunwarGeorgia Tech
We show that multilinear dyadic paraproducts and Haar multipliers, as well as their commutators with locally integrable functions, can be pointwise dominated by multilinear sparse operators. These results lead to various quantitative weighted norm inequalities for these operators. In particular, we introduce multilinear analog of Bloom's inequality, and prove it for the commutators of the multilinear Haar multipliers.

### The HRT Conjecture

Series
Analysis Seminar
Time
Wednesday, January 18, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chris HeilGeorgia Tech
The Linear Independence of Time-Frequency Translates Conjecture, also known as the HRT conjecture, states that any finite set of time-frequency translates of a given $L^2$ function must be linearly independent. This conjecture, which was first stated in print in 1996, remains open today. We will discuss this conjecture, its relation to the Zero Divisor Conjecture in abstract algebra, and the (frustratingly few) partial results that are currently available.

### Alpert multiwavelets and Legendre-Angelesco multiple orthogonal polynomials

Series
Analysis Seminar
Time
Wednesday, January 11, 2017 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Walter Van AsscheKatholieke University Lueven
We show that the multiwavelets, introduced by Alpert in 1993, are related to type I Legendre-Angelesco multiple orthogonal polynomials. We give explicit formulas for these Legendre-Angelesco polynomials and for the Alpert multiwavelets. The multiresolution analysis can be done entirely using Legendre polynomials, and we give an algorithm, using Cholesky factorization, to compute the multiwavelets and a method, using the Jacobi matrix for Legendre polynomials, to compute the matrices in the scaling relation for any size of the multiplicity of the multiwavelets.Based on joint work with J.S. Geronimo and P. Iliev

### Multiple q-Meixner polynomials of the first kind

Series
Analysis Seminar
Time
Friday, December 16, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Jorge Arvesu Carballo Universida Carlos III de Madrid
I will present a discrete family of multiple orthogonal polynomials defined by a set of orthogonality conditions over a non-uniform lattice with respect to different q-analogues of Pascal distributions. I will obtain some algebraic properties for these polynomials (q-difference equation and recurrence relation, among others) aimed to discuss a connection with an infinite Lie algebra realized in terms of the creation and annihilation operators for a collection of independent ascillators. Moreover, if time allows, some vector equilibrium problem with constraint for the nth root asymptotics of these multiple orthogonal polynomials will be discussed.

### TBA by Scott Spencer

Series
Analysis Seminar
Time
Wednesday, November 30, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Scott SpencerGeorgia Tech