### Kasso Okoudjou, Tufts University, On the HRT Conjecture

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Given a non-zero square-integrable function $g$ and $\Lambda=\{(a_k, b_k)\}_{k=1}^N \subset \mathbb{R}^2$ let $\mathcal{G}(g, \Lambda)=\{e^{2\pi i b_k \cdot}g(\cdot - a_k)\}_{k=1}^N.$ The Heil-Ramanathan-Topiwala (HRT) Conjecture is the question of whether $\mathcal{G}(g, \Lambda)$ is linearly independent. For the last two decades, very little progress has been made in settling the conjecture. In the first part of the talk,…

### Christoph Thäle, Ruhr-Universität Bochum, Germany, Random Cones

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Let $U_1,\ldots,U_n$ be independent random vectors which are uniformly distributed on the unit sphere. The random hyperplanes $U_1^\perp,\ldots,U_n^\perp$ dissect the space into a collection of random cones. A uniform random cone $S_n$ from this collection is called the Schläfli random cone. In a classical paper of Cover and Efron (1967) it was proved that the…

### Mariusz Mirek, Rutgers University, Dimension free estimates for the discrete Hardy–Littlewood maximal functions

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I will discuss recent progress on dimension-free estimates for the Hardy--Littlewood maximal functions in the continuous and discrete settings. Website: https://sites.google.com/view/paw-seminar Host: Paata Ivanisvili  pivanis@ncsu.edu

### Bobby Wilson, University of Washington, Marstrand’s Theorem in general Banach spaces

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We will discuss Marstrand's classical theorem concerning the interplay between density of a measure and the Hausdorff dimension of the measure's support in the context of finite-dimensional Banach spaces. This is joint work with David Bate and Tatiana Toro. Website: https://sites.google.com/view/paw-seminar Host: Paata Ivanisvili  pivanis@ncsu.edu

### Renan Gross, Weizmann Institute of Science, Israel, Stochastic processes for Boolean profit

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Not even influence inequalities for Boolean functions can escape the long arm of stochastic processes. I will present a (relatively) natural stochastic process which turns Boolean functions and their derivatives into jump-process martingales. There is much to profit from analyzing the individual paths of these processes: Using stopping times and level inequalities, we will reprove…

### Alexander Volberg, Michigan State University, Multi-parameter Poincaré inequality, multi-parameter Carleson embedding: Box condition versus Chang–Fefferman condition.

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Carleson embedding theorem is a building block for many singular integral operators and the main instrument in proving Leibniz rule" for fractional derivatives (Kato--Ponce, Kenig). It is also an essential step in all known corona theorems’’. Multi-parameter embedding is a tool to prove more complicated Leibniz rules that are also widely used in well-posedness questions…

### ‪Sudan Xing, University of Alberta, On Lp-Brunn-Minkowski type and Lp-isoperimetric type inequalities for measures

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In 2011, Lutwak, Yang and Zhang extended the definition of the Lp-Minkowski convex combination (p ≥ 1) from convex bodies containing the origin in their interiors to all measurable subsets in R n , and as a consequence, extended the Lp-Brunn-Minkowski inequality to the setting of all measurable sets. In this talk, I will present…

### Ohad Klein, Bar-Ilan University, Israel, On the distribution of Randomly Signed Sums and Tomaszewski’s Conjecture

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A Rademacher sum X is a random variable characterized by real numbers a_1, ..., a_n, and is equal to X = a_1 x_1 + ... + a_n x_n, where x_1, ..., x_n are independent signs (uniformly selected from {-1, 1}). A conjecture by Bogusław Tomaszewski, 1986: all Rademacher sums X satisfy Pr >= 1/2. We…

### Galyna Livshyts, Georgia Institute of Technology, On an inequality somewhat related to the Log-Brunn-Minkowski conjecture

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I shall prove a neat inequality concerning convex bodies and semi-norms, and show that cylinders (i.e. direct products of intervals with convex bodies of lower dimension) give equality cases for it. I shall explain its connections to the Log-Brunn-Minkowski conjecture. If time permits, I will discuss related results and surrounding questions. Based on a joint…

### ‪Rupert Frank, Caltech, Lieb-Thirring bounds and other inequalities for orthonormal functions

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We discuss extensions of several inequalities in harmonic analysis to the setting of families of orthonormal functions. While the case of Sobolev-type inequalities is classical, newer results concern the Strichartz inequality, the Stein-Tomas inequality and Sogge’s spectral cluster estimates, among others. Of particular interest is the dependence of the constants in the resulting bounds on…

### Nicholas Cook, Duke University, Universality for the minimum modulus of random trigonometric polynomials

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We consider the restriction to the unit circle of random degree-n polynomials with iid coefficients (Kac polynomials). Recent work of Yakir and Zeitouni shows that for Gaussian coefficients, the minimum modulus (suitably rescaled) follows a limiting exponential distribution. We show this is a universal phenomenon, extending their result to arbitrary sub-Gaussian coefficients, such as Rademacher…

### Mateusz Kwaśnicki, Wrocław University of Science and Technology, Poland

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Zoom ID: 939 3643 7199 (opens 15 min prior to the meeting) Passcode: 9917

### ‪Steven Heilman, University of Southern California, Three Candidate Plurality is Stablest for Small Correlations

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Suppose we model n votes in an election between two candidates as n i.i.d. uniform random variables in {-1,1}, so that 1 represents a vote for the first candidate, and -1 represents a vote for the other candidate. Then, for each vote, we flip a biased coin (with fixed probability larger than 1/2 of landing…

### ‪Theresa Anderson, Purdue University, Dyadic analysis (virtually) meets number theory

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In this talk we discuss two ways in which dyadic analysis and number theory share a rich interaction. The first involves a complete classification of "distinct dyadic systems". These are sets of grids which allow one to compare any Euclidean ball nicely with any dyadic cube, and allow for showing that a large number of…

### ‪Peter Pivovarov, University of Missouri, Stochastic functional inequalities and shadow systems

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I will discuss stochastic geometry of random concave functions. In particular, I will explain how a "local" stochastic dominance underlies several functional inequalities. Emphasis will be on a notion of shadow systems for s-concave functions and their interplay with functional inequalities. Based on joint works with J. Rebollo Bueno.

### Stanislaw Szarek, Case Western Reserve University/Sorbonne Université

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Zoom ID: 936 5420 1948 Password: the last four digits of the Zoom ID in reverse order

### Vishesh Jain, Stanford University, On the real Davies’ conjecture

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We show that every $n \times n$ real matrix $A$ is within distance $\delta \|A\|$ in the operator norm of an $n\times n$ real matrix $A'$ whose eigenvectors have condition number $\tilde{O}(\text{poly}(n)/\delta)$. In fact, we show that with high probability, an additive i.i.d. sub-Gaussian perturbation of $A$ has this property. Up to log factors, this…

### Sarah Peluse, Princeton University/IAS, On the polynomial Szemer\’edi theorem and related results

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In this talk, I'll survey recent progress on problems in additive combinatorics, harmonic analysis, and ergodic theory related to Bergelson and Leibman's polynomial generalization of Szemer\'edi's theorem.   Zoom ID: 980 3116 7550 Passcode: last 4 digits of the Zoom ID in reverse order

### Oliver Dragičević, University of Ljubljana, Slovenia, Trilinear embedding theorem for elliptic partial differential operators in divergence form with complex coefficients

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We introduce the notion of p-ellipticity of a complex matrix function and discuss basic examples where it plays a major role, as well as the techniques that led to the introduction of the notion. In the second part of the talk we focus on a so-called trilinear embedding theorem for complex elliptic operators and its…

### ‪Joris Roos, University of Massachusetts Lowell, Discrete analogues of maximally modulated singular integrals of Stein-Wainger type

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Stein and Wainger introduced an interesting class of maximal oscillatory integral operators related to Carleson's theorem. The talk will be about joint work with Ben Krause on discrete analogues of some of these operators. These discrete analogues feature a number of substantial difficulties that are absent in the real-variable setting and involve themes from number theory and analysis.   Zoom…