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Colloquia & Seminars

Current Seminars

  1. 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 colloquium-style 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
  2. HA Postdoc Seminar: Variational Methods for a Two-Phase 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 non-variational 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
  3. 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

  1. Harmonic Analysis Seminar: Scalable restriction estimates for the hyperbolic paraboloid in R^3

    Location: MSRI: Baker Board Room
    Speakers: Betsy Stovall (University of Wisconsin-Madison)

    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
  2. 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 wavelet-based theory and outline his main results. Further, we shall discuss an alternative Fourier-based 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
  3. Harmonic Analysis Seminar: On the HRT Conjecture

    Location: MSRI: Baker Board Room
    Speakers: Kasso Okoudjou (University of Maryland)

    Given a non-zero 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 Heil-Ramanathan-Topiwala (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 real-valued function. 

    Updated on Apr 20, 2017 12:24 PM PDT
  4. Harmonic Analysis Seminar: Haar expansions in Sobolev spaces

    Location: MSRI: Simons Auditorium
    Speakers: Andreas Seeger (University of Wisconsin-Madison)

    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
  5. HA Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Updated on Apr 19, 2017 12:31 PM PDT
  6. 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 best-possible, 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, non-tangential 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
  7. MSRI/Pseudorandomness seminar

    Location: MSRI: Simons Auditorium
    Updated on Feb 16, 2017 02:37 PM PST
  8. ANT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Created on Feb 02, 2017 12:03 PM PST
  9. HA Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Created on Feb 02, 2017 12:05 PM PST
  10. Joint ANT & HA Seminar

    Location: MSRI: Simons Auditorium
    Created on Feb 02, 2017 12:01 PM PST

Past Seminars

There are more then 30 past seminars. Please go to Past seminars to see all past seminars.