Current Seminars

ANT Postdoc Seminar: Integer partitions and restricted partition functions
Location: MSRI: Simons Auditorium Speakers: Ayla Gafni (University of Rochester)The theory of integer partitions is a rich subject that lives in the intersection of number theory and combinatorics. In this colloquiumstyle talk, I will go through a brief history of partitions and the various tools used to study them, along with connections to Waring's problem and other topics in additive number theory. I will then state some results about counting partitions in which the parts are restricted to various subsets of the integers (e.g., primes, squares, arithmetic progressions).
Updated on Apr 21, 2017 11:26 AM PDT 
HA Postdoc Seminar: Variational Methods for a TwoPhase Free Boundary Problem For Harmonic Measure (Colloquium Talk)
Location: MSRI: Simons Auditorium Speakers: Max Engelstein (Massachusetts Institute of Technology)There are lots of very good techniques for studying the regularity of a minimizer of some functional (think harmonic functions, minimal surfaces etc). But what if you want to study something that doesn't minimize a functional? We will show how GMT and harmonic analysis can help us use shiny tools from the calculus of variations in a nonvariational setting. Some of what we will talk about is joint work with Matthew Badger and Tatiana Toro.
Updated on Apr 19, 2017 12:30 PM PDT 
Joint ANT & HA Seminar: Polynomial congruences: Some light entertainment
Location: MSRI: Simons Auditorium Speakers: James Wright (University of British Columbia)Exponential sums over Z or Z^d are basic objects in Analytic Number Theory and oscillatory integrals over R or R^d are basic objects in Harmonic Analysis. These objects are quite different; for oscillatory integrals over R, a single continuum of scales is often sufficient for the analysis whereas for exponential sums over Z, every prime p gives rise to a family of scales {p^k}, all needed in the analysis. Nevertheless if one fixes the prime p and carries out the analysis at the corresponding scales (e.g. by examining exponential sums over Z/p^k Z, k=1,2,3,...) then the analogy to oscillatory integrals in euclidean settings is uncanny.
We will illustrate this in the simple setting of polynomial congruences and formulate some problems in elementary number theory in a way that harmonic analysts can appreciate and be able to use their prior acquired intuition.
Updated on Apr 20, 2017 12:15 PM PDT
Upcoming Seminars

Harmonic Analysis Seminar: Scalable restriction estimates for the hyperbolic paraboloid in R^3
Location: MSRI: Baker Board Room Speakers: Betsy Stovall (University of WisconsinMadison)We will show how to sharpen to the scaling line known bounds for Fourier restriction to the hyperbolic paraboloid in R^3. As with many "endpoint" estimates, we will need to add together many terms that all seem to be about the same size, and in the talk, we will highlight some techniques that have been useful elsewhere.
Updated on Apr 24, 2017 10:48 AM PDT 
Topics in Partial Differential Equations
Location: Evans Hall 891 Speakers: Tatiana Toro (University of Washington)Created on Feb 02, 2017 12:29 PM PST 
Harmonic Analysis Graduate Student Seminar
Location: MSRI: Baker Board Room Speakers: Weilin Li (University of Maryland)Title: A harmonic analysis perspective on deep learning
Abstract: Deep convolutional neural networks have become one of the most powerful types of machine learning tools, yet there is no adequate theory that explains their remarkable performance. Motivated by this problem, Mallat recently discovered a connection between harmonic analysis and neural networks. In this talk, we illustrate the motivation for his waveletbased theory and outline his main results. Further, we shall discuss an alternative Fourierbased approach to deep learning, potential applications, and directions for further research. This is joint work with Wojciech Czaja.
Updated on Apr 27, 2017 09:34 AM PDT 
Harmonic Analysis Seminar: On the HRT Conjecture
Location: MSRI: Baker Board Room Speakers: Kasso Okoudjou (University of Maryland)Given a nonzero square integrable function $g$ and a subset $\Lambda=\{(a_k, b_k)\}_{k=1}^N \subset \R^2$, let $$\mathcal{G}(g, \Lambda)=\{e^{2\pi i b_k \cdot}g(\cdot  a_k)\}_{k=1}^N.$$ The HeilRamanathanTopiwala (HRT) Conjecture asks 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, I will give an overview of the state of the conjecture. I will then describe a small variation of the conjecture that asks the following question: Suppose that the HRT conjecture holds for a given $g\in L^{2}(\R)$ and a given set $\Lambda=\{(a_k, b_k)\}_{k=1}^N \subset \R^2$. Give a characterization of all points $(a, b)\in \R^2\setminus \Lambda$ such that the conjecture remains true for the same function $g$ and the new set of point $\Lambda_1=\Lambda\cup\{(a, b)\}$. If time permits I will illustrate this approach for the cases $N=4$, and $5$ and when $g$ is a realvalued function.
Updated on Apr 20, 2017 12:24 PM PDT 
Topics in Partial Differential Equations
Location: Evans Hall 891 Speakers: Tatiana Toro (University of Washington)Created on Feb 02, 2017 12:29 PM PST 
Harmonic Analysis Seminar: Haar expansions in Sobolev spaces
Location: MSRI: Simons Auditorium Speakers: Andreas Seeger (University of WisconsinMadison)Consider expansions with respect to the Haar system on the real line, for functions in Sobolev spaces with small smoothness parameter. We report on work with Gustavo Garrig\'os and with Tino Ullrich and answer the following questions: Is the Haar system a Schauder basis? Is it an unconditional basis? We discuss the boundedness of multiplier transformations and other quantitative versions of these questions.
Updated on Apr 21, 2017 11:28 AM PDT 
HA Postdoc Seminar
Location: MSRI: Simons AuditoriumUpdated on Apr 19, 2017 12:31 PM PDT 
Analytic Number Theory Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 02, 2017 12:27 PM PST 
Harmonic Analysis Graduate Student Seminar
Location: MSRI: Baker Board RoomCreated on Feb 23, 2017 03:51 PM PST 
Harmonic Analysis Seminar: A Sharp Divergence Theorem in Rough Domains and Applications
Location: MSRI: Simons Auditorium Speakers: Marius Mitrea (University of Missouri)Arguably, one of the most basic results in analysis is Gauss' Divergence Theorem. Its original formulation involves mildly regular domains and sufficiently smooth vector fields (typically both of class C^1), though applications to rougher settings have prompted various generalizations. One famous extension, due to De Giorgi and Federer, lowers the regularity assumptions on the underlying domain to a mere local finite perimeter condition. While geometrically this is in the nature of bestpossible, the De Giorgi Federer theorem still asks that the intervening vector field has Lipschitz components. The latter assumption is, however, unreasonably strong, both from the point of view of the very formulation of the Divergence Formula, and its applications to PDE's which often involve much less regular functions. In my talk I will discuss a refinement which addresses this crucial issue, through the use of tools and techniques from Harmonic Analysis (Whitney decompositions, weighted isoperimetric inequalities, nontangential maximal operators). In particular, this sharpened form of the Divergence Theorem yields a variety of refined results, from the nature of the Green function, to the behavior of singular integral operators in very general domains.
Updated on Apr 18, 2017 11:01 AM PDT 
Analytic Number Theory Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 02, 2017 12:27 PM PST 
MSRI/Pseudorandomness seminar
Location: MSRI: Simons AuditoriumUpdated on Feb 16, 2017 02:37 PM PST 
ANT Postdoc Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 02, 2017 12:03 PM PST 
HA Postdoc Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 02, 2017 12:05 PM PST 
Joint ANT & HA Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 02, 2017 12:01 PM PST
Past Seminars

Seminar MSRI/Pseudorandomness seminar: Local central limit theorems for combinatorial problems
Updated on Apr 27, 2017 08:45 AM PDT 
Seminar Analytic Number Theory Seminar: Trace Inequalities and Nonvanishing of Lfunctions
Updated on Apr 20, 2017 12:17 PM PDT 
Seminar Topics in Partial Differential Equations
Updated on Feb 02, 2017 12:16 PM PST 
Seminar Harmonic Analysis Seminar: The pointwise convergence of Fourier Series near L^1
Updated on Apr 20, 2017 02:29 PM PDT 
Seminar Harmonic Analysis Graduate Student Seminar: Rough path theory and Harmonic Analysis
Updated on Apr 20, 2017 02:40 PM PDT 
Seminar Analytic Number Theory Graduate Student Seminar
Updated on Apr 20, 2017 12:13 PM PDT 
Seminar Topics in Partial Differential Equations
Updated on Feb 02, 2017 12:16 PM PST 
Seminar Harmonic Analysis Seminar: On boundary value problems for parabolic equations with timedependent measurable coefficients
Updated on Apr 19, 2017 01:24 PM PDT 
Seminar Joint ANT & HA Seminar: Concatenating cubic structures
Updated on Apr 13, 2017 01:15 PM PDT 
Seminar HA Postdoc Seminar: Poincare inequality 3/2 on the Hamming cube
Updated on Apr 13, 2017 08:54 AM PDT 
Seminar ANT Postdoc Seminar: Sums of Kloosterman sums of halfintegral weight
Updated on Apr 13, 2017 01:47 PM PDT 
Seminar MSRI/Pseudorandomness seminar: Rigidity theorems for multiplicative functions and applications
Updated on Apr 13, 2017 04:17 PM PDT 
Seminar Analytic Number Theory Seminar: The distribution of zeros of polynomials
Updated on Apr 13, 2017 01:44 PM PDT 
Seminar Thesis Defense: On Some Variants of the Gauss Circle Problem
Created on Apr 13, 2017 09:58 AM PDT 
Seminar Topics in Partial Differential Equations
Updated on Feb 02, 2017 12:10 PM PST 
Seminar Harmonic Analysis Seminar: Convenient Coordinates
Updated on Apr 10, 2017 08:53 AM PDT 
Seminar Harmonic Analysis Graduate Student Seminar
Created on Feb 23, 2017 03:51 PM PST 
Seminar Topics in Partial Differential Equations
Updated on Feb 02, 2017 12:10 PM PST 
Seminar Harmonic Analysis Seminar: A multilinear extension identity on $L^2(\mathbb{R}^n)$
Updated on Apr 04, 2017 11:14 AM PDT 
Seminar Joint ANT & HA Seminar: Fourier optimization with constraints, bounds for zeta and related stories
Updated on Apr 06, 2017 11:10 AM PDT 
Seminar HA Postdoc Seminar: Sparse domination of singular integral operators (Colloquium)
Updated on Apr 06, 2017 10:48 AM PDT 
Seminar ANT Postdoc Seminar: Complexity of strong approximation on the sphere
Updated on Apr 06, 2017 02:27 PM PDT 
Seminar Logic and Literature: The Magic of Charles S. Peirce
Updated on Apr 12, 2017 09:26 AM PDT 
Seminar Hermann Weylâ€™s Philosophy of Mathematics: What and Why
Updated on Apr 12, 2017 03:18 PM PDT 
Seminar Analytic Number Theory Seminar: The long and the short of character sums
Updated on Apr 07, 2017 08:50 AM PDT 
Seminar Topics in Partial Differential Equations
Updated on Feb 02, 2017 12:16 PM PST 
Seminar Harmonic Analysis Seminar: The Cauchy problem for the LandauLifshitzGilbert equation in BMO and selfsimilar solutions
Updated on Mar 31, 2017 01:34 PM PDT 
Seminar Harmonic Analysis Graduate Student Seminar
Updated on Apr 07, 2017 01:39 PM PDT 
Seminar Analytic Number Theory Graduate Student Seminar
Created on Feb 23, 2017 03:52 PM PST 
Seminar Analytic Number Theory Seminar: Averages of central $L$values using the relative trace formula
Updated on Apr 07, 2017 10:50 AM PDT