# Mathematical Sciences Research Institute

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1. # Harmonic Analysis Seminar: On boundary value problems for parabolic equations with time-dependent measurable coefficients

Location: MSRI: Simons Auditorium
Speakers: Pascal Auscher (Université de Paris XI)

We will explain the proof of a Carleson measure estimate on solutions of parabolic equations with real measurable time-dependent coefficients that implies that the parabolic measure is an $A_\infty$ weight.
This corresponds to the parabolic analog of a recent result by Hofmann, Kenig, Mayboroda and Pipher for elliptic equations. Our proof even simplifies theirs. As is well known, the $A_\infty$ property implies that   $L^p$ Dirichlet problem is well-posed. An important ingredient of the proof is a Kato square root property for parabolic operators on the boundary, which can be seen as a consequence of certain square function estimates applicable to Neumann and regularity problems.  All this is  joint work with Moritz Egert and Kaj Nyström.

Updated on Apr 19, 2017 01:24 PM PDT

1. # Topics in Partial Differential Equations

Location: Evans Hall 891
Speakers: Tatiana Toro (University of Washington)
Updated on Feb 02, 2017 12:16 PM PST
2. # Analytic Number Theory Graduate Student Seminar

Location: MSRI: Baker Board Room
Speakers: Corina Panda (California Institute of Technology), Vinay Viswanathan (University of Bristol)

4:00pm: Vinay Kumaraswamy

Title: On correlations between class numbers of imaginary quadratic fields

Abstract: Let h(-d) denote the class number of the imaginary quadratic field Q(\sqrt{-d}).  Moments of class numbers​ have been studied in the past, and are well understood. In this talk, I will speak about obtaining an asymptotic formula for the shifted sum \sum_{d \leq X} h(-d)h(-d-l), where l is a positive integer; the proof makes use of the smooth delta-symbol.

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4:30pm: Corina Panda

Title:
​
A generalization of a theorem of Hecke for SL_2(F_p) to fundamental discriminants

Abstract:
​ ​
Let p > 3 be an odd prime, p ≡ 3 mod 4 and let π+, π− be the pair of cuspidal representations of SL2(Fp). It is well known by Hecke that the difference mπ+ − mπ− in the multiplicities of these two irreducible representations occurring in the space of weight 2 cusps forms with respect to the principal congruence subgroup Γ(p), equals the class number h(−p) of the imaginary quadratic field Q(\sqrt(−p)). We extend this result to all fundamental discriminants −D of imaginary quadratic fields Q( \sqrt(−D)). The proof uses the holomorphic Lefschetz number.

Updated on Apr 20, 2017 12:13 PM PDT
3. # Harmonic Analysis Graduate Student Seminar: Rough path theory and Harmonic Analysis

Location: MSRI: Baker Board Room
Speakers: Gennady Uraltsev (Rheinische Friedrich-Wilhelms-Universität Bonn)

In this talk we will cover the basics of Rough Path theory. We will make several examples of how these results can be used in harmonic analysis problems (e.g. proving a variational non-linear Hausdorff Young inequality) and, maybe we will see how harmonic analysis results come into the theory of rough paths.

Updated on Apr 20, 2017 02:40 PM PDT
4. # Harmonic Analysis Seminar: The pointwise convergence of Fourier Series near L^1

Location: MSRI: Simons Auditorium
Speakers: Victor Lie (Purdue University)

Abstract

Updated on Apr 20, 2017 02:29 PM PDT
5. # Topics in Partial Differential Equations

Location: Evans Hall 891
Speakers: Tatiana Toro (University of Washington)
Updated on Feb 02, 2017 12:16 PM PST
6. # Analytic Number Theory Seminar: Trace Inequalities and Non-vanishing of L-functions

Location: MSRI: Simons Auditorium
Speakers: Dinakar Ramakrishnan (California Institute of Technology)
Let f be a holomorphic newform of prime level N, weight 2 and trivial character, for example one associated to a elliptic curve E over Q. For any imaginary quadratic field K of discriminant -D in which N is inert, and an ideal class character \chi of K, one is led to the ubiquitous Rankin-Selberg L-function L(s, f x g_\chi), where g_\chi is the modular form of level D associated to \chi by Hecke. It is well known that the central value L(1/2, f x g_\chi) is non-zero for "many" (D, \chi), which is a consequence of equidistribution of special points. The object of this talk is to indicate how to derive a strengthening of this, namely that if we fix an f as above together with a finite number of even Dirichlet characters \eta_1, ..., \eta_r, then one can find many (D,\chi) for which one has the simultaneous non-vanishing of L(1/2, (f.\eta_j) x g_\chi) for all j. The additional ingredient used here is an inequality of traces for tori relative to a non-abelian twist.

The talk will hopefully be accessible to a variety of mathematicians.
Updated on Apr 20, 2017 12:17 PM PDT
7. # MSRI/Pseudorandomness seminar

Location: Simons Institute
Updated on Feb 16, 2017 02:37 PM PST
8. # 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
9. # 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
10. # 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
11. # 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
12. # Topics in Partial Differential Equations

Location: Evans Hall 891
Speakers: Tatiana Toro (University of Washington)
Created on Feb 02, 2017 12:29 PM PST
13. # Harmonic Analysis Graduate Student Seminar

Location: MSRI: Baker Board Room
Created on Feb 23, 2017 03:51 PM PST
14. # 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
15. # Topics in Partial Differential Equations

Location: Evans Hall 891
Speakers: Tatiana Toro (University of Washington)
Created on Feb 02, 2017 12:29 PM PST
16. # 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
17. # HA Postdoc Seminar

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

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

Location: MSRI: Baker Board Room
Created on Feb 23, 2017 03:51 PM PST
20. # 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
21. # Analytic Number Theory Seminar

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

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

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

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

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

seminar
1. # SeminarJoint ANT & HA Seminar: Concatenating cubic structures

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Updated on Feb 02, 2017 12:16 PM PST
19. # 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
20. # SeminarHarmonic Analysis Graduate Student Seminar

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

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

Updated on Apr 07, 2017 10:50 AM PDT
23. # SeminarTopics in Partial Differential Equations

Updated on Feb 02, 2017 12:16 PM PST
24. # SeminarHarmonic Analysis Seminar: Critical perturbations of Dirac Hamiltonians: selfadjointness and spectrum

Updated on Apr 07, 2017 01:43 PM PDT
25. # SeminarJoint ANT & HA Seminar: Additive structure of sets of Fourier coefficients

Updated on Apr 05, 2017 12:09 PM PDT
26. # SeminarHA Postdoc Seminar: Muckenhoupt Weights and their dynamical counterpart (Colloquium talk)

Updated on Mar 30, 2017 12:14 PM PDT
27. # SeminarANT Postdoc Seminar: Gaps between zeros of the Riemann zeta-function

Updated on Mar 30, 2017 12:25 PM PDT
28. # SeminarMSRI/Pseudorandomness seminar: Lonely runners in function fields

Updated on Mar 31, 2017 08:40 AM PDT
29. # SeminarTopics in Partial Differential Equations

Updated on Feb 02, 2017 12:10 PM PST
30. # SeminarHarmonic Analysis Seminar: Lipschitz maps, Littlewood-Paley, and directional operators

Updated on Mar 20, 2017 08:47 AM PDT
There are more then 30 past seminars. Please go to Past seminars to see all past seminars.