# Mathematical Sciences Research Institute

Home > Scientific > Colloquia & 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

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. # Topics in Partial Differential Equations

Location: Evans Hall 891
Speakers: Tatiana Toro (University of Washington)
Created on Feb 02, 2017 12:29 PM PST
3. # 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
4. # 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
5. # Topics in Partial Differential Equations

Location: Evans Hall 891
Speakers: Tatiana Toro (University of Washington)
Created on Feb 02, 2017 12:29 PM PST
6. # 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
7. # HA Postdoc Seminar

Location: MSRI: Simons Auditorium
Updated on Apr 19, 2017 12:31 PM PDT
8. # Analytic Number Theory Seminar

Location: MSRI: Simons Auditorium
Created on Feb 02, 2017 12:27 PM PST
9. # Harmonic Analysis Graduate Student Seminar

Location: MSRI: Baker Board Room
Created on Feb 23, 2017 03:51 PM PST
10. # 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
11. # Analytic Number Theory Seminar

Location: MSRI: Simons Auditorium
Created on Feb 02, 2017 12:27 PM PST
12. # MSRI/Pseudorandomness seminar

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

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

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

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

seminar
1. # SeminarMSRI/Pseudorandomness seminar: Local central limit theorems for combinatorial problems

Updated on Apr 27, 2017 08:45 AM PDT
2. # SeminarAnalytic Number Theory Seminar: Trace Inequalities and Non-vanishing of L-functions

Updated on Apr 20, 2017 12:17 PM PDT
3. # SeminarTopics in Partial Differential Equations

Updated on Feb 02, 2017 12:16 PM PST
4. # SeminarHarmonic Analysis Seminar: The pointwise convergence of Fourier Series near L^1

Updated on Apr 20, 2017 02:29 PM PDT
5. # SeminarHarmonic Analysis Graduate Student Seminar: Rough path theory and Harmonic Analysis

Updated on Apr 20, 2017 02:40 PM PDT
6. # SeminarAnalytic Number Theory Graduate Student Seminar

Updated on Apr 20, 2017 12:13 PM PDT
7. # SeminarTopics in Partial Differential Equations

Updated on Feb 02, 2017 12:16 PM PST
8. # SeminarHarmonic Analysis Seminar: On boundary value problems for parabolic equations with time-dependent measurable coefficients

Updated on Apr 19, 2017 01:24 PM PDT
9. # SeminarJoint ANT & HA Seminar: Concatenating cubic structures

Updated on Apr 13, 2017 01:15 PM PDT
10. # SeminarHA Postdoc Seminar: Poincare inequality 3/2 on the Hamming cube

Updated on Apr 13, 2017 08:54 AM PDT
11. # SeminarANT Postdoc Seminar: Sums of Kloosterman sums of half-integral weight

Updated on Apr 13, 2017 01:47 PM PDT
12. # SeminarMSRI/Pseudorandomness seminar: Rigidity theorems for multiplicative functions and applications

Updated on Apr 13, 2017 04:17 PM PDT
13. # SeminarAnalytic Number Theory Seminar: The distribution of zeros of polynomials

Updated on Apr 13, 2017 01:44 PM PDT
14. # SeminarThesis Defense: On Some Variants of the Gauss Circle Problem

Created on Apr 13, 2017 09:58 AM PDT
15. # SeminarTopics in Partial Differential Equations

Updated on Feb 02, 2017 12:10 PM PST
16. # SeminarHarmonic Analysis Seminar: Convenient Coordinates

Updated on Apr 10, 2017 08:53 AM PDT
17. # SeminarHarmonic Analysis Graduate Student Seminar

Created on Feb 23, 2017 03:51 PM PST
18. # SeminarTopics in Partial Differential Equations

Updated on Feb 02, 2017 12:10 PM PST
19. # SeminarHarmonic Analysis Seminar: A multilinear extension identity on $L^2(\mathbb{R}^n)$

Updated on Apr 04, 2017 11:14 AM PDT
20. # SeminarJoint ANT & HA Seminar: Fourier optimization with constraints, bounds for zeta and related stories

Updated on Apr 06, 2017 11:10 AM PDT
21. # SeminarHA Postdoc Seminar: Sparse domination of singular integral operators (Colloquium)

Updated on Apr 06, 2017 10:48 AM PDT
22. # SeminarANT Postdoc Seminar: Complexity of strong approximation on the sphere

Updated on Apr 06, 2017 02:27 PM PDT
23. # SeminarLogic and Literature: The Magic of Charles S. Peirce

Updated on Apr 12, 2017 09:26 AM PDT
24. # SeminarHermann Weyl’s Philosophy of Mathematics: What and Why

Updated on Apr 12, 2017 03:18 PM PDT
25. # SeminarAnalytic Number Theory Seminar: The long and the short of character sums

Updated on Apr 07, 2017 08:50 AM PDT
26. # SeminarTopics in Partial Differential Equations

Updated on Feb 02, 2017 12:16 PM PST
27. # SeminarHarmonic Analysis Seminar: The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions

Updated on Mar 31, 2017 01:34 PM PDT
28. # SeminarHarmonic Analysis Graduate Student Seminar

Updated on Apr 07, 2017 01:39 PM PDT
29. # SeminarAnalytic Number Theory Graduate Student Seminar

Created on Feb 23, 2017 03:52 PM PST
30. # SeminarAnalytic Number Theory Seminar: Averages of central $L$-values using the relative trace formula

Updated on Apr 07, 2017 10:50 AM PDT
There are more then 30 past seminars. Please go to Past seminars to see all past seminars.