Difference between revisions of "Analysis Seminar"

From UW-Math Wiki
Jump to: navigation, search
(Abstracts)
(Analysis Seminar Schedule)
 
(525 intermediate revisions by 10 users not shown)
Line 1: Line 1:
'''Analysis Seminar
 
'''
 
  
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.
+
The 2021-2022 Analysis Seminar will be organized by David Beltran and Andreas Seeger.
 +
Some of the talks will be in person (room Van Vleck B139) and some will be online. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).
  
If you wish to invite a speaker please contact  Betsy at stovall(at)math
+
Zoom links will be sent to those who have signed up for the Analysis Seminar List.  If you would like to subscribe to the Analysis seminar list, send a blank email to analysis+join (at) g-groups (dot) wisc (dot) edu. If you are from an institution different than UW-Madison, please send as well as an additional email to David and Andreas (dbeltran, seeger at math (dot) wisc (dot) edu) to notify the request.
  
===[[Previous Analysis seminars]]===
+
If you'd like to suggest speakers for the fall semester please contact David and Andreas.
  
= 2017-2018 Analysis Seminar Schedule =
+
= Analysis Seminar Schedule =
 
{| cellpadding="8"
 
{| cellpadding="8"
 
!align="left" | date   
 
!align="left" | date   
Line 16: Line 15:
 
!align="left" | host(s)
 
!align="left" | host(s)
 
|-
 
|-
|September 8 in B239 (Colloquium)
+
|September 21, VV B139
| Tess Anderson
+
| Dóminique Kemp
| UW Madison
+
| UW-Madison
|[[#linktoabstract A Spherical Maximal Function along the Primes]]
+
|[[#Dóminique Kemp Decoupling by way of approximation ]]
|Tonghai
+
|  
 
|-
 
|-
|September 19
+
|September 28, VV B139
| Brian Street
+
| Jack Burkart
| UW Madison
+
| UW-Madison
|[[#Brian Street Convenient Coordinates ]]
+
|[[#Jack Burkart Transcendental Julia Sets with Fractional Packing Dimension ]]
| Betsy
+
|  
 
|-
 
|-
|September 26
+
|October 5, Online
| Hiroyoshi Mitake
+
| Giuseppe Negro
| Hiroshima University
+
| University of Birmingham
|[[#Hiroyoshi Mitake Derivation of multi-layered interface system and its application ]]
+
|[[#Giuseppe Negro Stability of sharp Fourier restriction to spheres ]]
| Hung
+
|  
 
|-
 
|-
|October 3
+
|October 12, VV B139
| Joris Roos
+
|Rajula Srivastava
| UW Madison
+
|UW Madison
|[[#Joris Roos A polynomial Roth theorem on the real line ]]
+
|[[#Rajula Srivastava Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups ]]
| Betsy
+
|  
 
|-
 
|-
|October 10
+
|October 19, Online
| Michael Greenblatt
+
|Itamar Oliveira
| UI Chicago
+
|Cornell University
|[[#Michael Greenblatt Maximal averages and Radon transforms for two-dimensional hypersurfaces ]]
+
|[[#Itamar Oliveira A new approach to the Fourier extension problem for the paraboloid ]]
| Andreas
+
|  
 
|-
 
|-
|October 17
+
|October 26, VV B139
| David Beltran
+
| Changkeun Oh
| Basque Center of Applied Mathematics
+
| UW Madison
|[[#David Beltran Fefferman-Stein inequalities ]]
+
|[[#Changkeun Oh Decoupling inequalities for quadratic forms and beyond ]]
| Andreas
+
|  
 
|-
 
|-
|Wednesday, October 18, 4:00 p.m.  in B131
+
|October 29, Colloquium
|Jonathan Hickman
+
| Alexandru Ionescu
|University of Chicago
+
| Princeton University
|[[#Jonathan Hickman | Factorising X^n  ]]
+
|[[#Alexandru Ionescu |   Polynomial averages and pointwise ergodic theorems on nilpotent groups]]
|Andreas
 
 
|-
 
|-
|October 24
+
|November 2, VV B139
| Xiaochun Li
+
| Liding Yao
| UIUC
+
| UW Madison
|[[#Xiaochun Li Recent progress on the pointwise convergence problems of Schroedinger equations ]]
+
|[[#Liding Yao An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains ]]
| Betsy
+
|  
 
|-
 
|-
|Thursday, October 26, 4:30 p.m. in B139
+
|November 9, VV B139
| Fedor Nazarov
+
| Lingxiao Zhang
| Kent State University
+
| UW Madison
|[[#Fedor Nazarov | The Lerner-Ombrosi-Perez bound in the Muckenhoupt Wheeden conjecture is sharp  ]]
+
|[[#Lingxiao Zhang |   Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition ]]
| Sergey, Andreas
+
|  
 
|-
 
|-
|Friday, October 27, 4:00 p.m.  in B239
+
|November 12, Colloquium
| Stefanie Petermichl
+
| Kasso Okoudjou
| University of Toulouse
+
| Tufts University
|[[#Stefanie Petermichl | Higher order Journé commutators   ]]
+
|[[#Kasso Okoudjou An exploration in analysis on fractals ]]
| Betsy, Andreas
 
 
|-
 
|-
|Wednesday, November 1, 4:00 p.m. in B239 (Colloquium)
+
|November 16, VV B139
| Shaoming Guo
+
| Rahul Parhi
| Indiana University
+
| UW Madison (EE)
|[[#Shaoming Guo |   Parsell-Vinogradov systems in higher dimensions ]]
+
|[[#Rahul Parhi |   On BV Spaces, Splines, and Neural Networks ]]
| Andreas
+
|  
 
|-
 
|-
|November 14
+
|November 30, VV B139
| Naser Talebizadeh Sardari
+
| Alexei Poltoratski
 
| UW Madison
 
| UW Madison
|[[#Naser Talebizadeh Sardari |   Quadratic forms and the semiclassical eigenfunction hypothesis ]]
+
|[[#Alexei Poltoratski | Pointwise convergence for the scattering data and non-linear Fourier transform. ]]
| Betsy
+
|  
 
|-
 
|-
|November 28
+
|December 7, Online
| Xianghong Chen
+
| John Green
| UW Milwaukee
+
| The University of Edinburgh
|[[#Xianghong Chen |   Some transfer operators on the circle with trigonometric weights ]]
+
|[[#John Green | Estimates for oscillatory integrals via sublevel set estimates ]]
| Betsy
+
|  
 
|-
 
|-
|Monday, December 4, 4:00, B139
+
|December 14, VV B139
| Bartosz Langowski and Tomasz Szarek
+
| Tao Mei
| Institute of Mathematics, Polish Academy of Sciences
+
| Baylor University
|[[#Bartosz Langowski and Tomasz Szarek Discrete Harmonic Analysis in the Non-Commutative Setting ]]
+
|[[#Tao Mei Fourier Multipliers on free groups ]]
| Betsy
+
|  
 
|-
 
|-
|Wednesday, December 13, 4:00, B239 (Colloquium)
+
|February 8
|Bobby Wilson
+
| Person
|MIT
+
| Institution
|[[#Bobby Wilson | Projections in Banach Spaces and Harmonic Analysis ]]
+
|[[#linktoabstract  |   Title ]]
| Andreas
+
|
 +
|-
 +
|February 15
 +
| Sebastian Bechtel
 +
| Institut de Mathématiques de Bordeaux
 +
|[[#linktoabstract  |  Title ]]
 +
|  
 
|-
 
|-
| Monday, February 5, 3:00-3:50, B341  (PDE-GA seminar)
+
|February 22
| Andreas Seeger
+
|Betsy Stovall
| UW
+
|UW Madison
|[[#Andreas Seeger | Singular integrals and a problem on mixing flows]]  
+
|[[#linktoabstract  |   Title ]]
|
+
|  
 
|-
 
|-
|February 6
+
|March 1
| Dong Dong
+
| Person
| UIUC
+
| Institution
| [[#Dong Dong | Hibert transforms in a 3 by 3 matrix and applications in number theory]]
+
|[[#linktoabstract  |   Title ]]
|Betsy
+
|  
 
|-
 
|-
|February 13
+
|March 8
| Sergey  Denisov
+
| Brian Street
 
| UW Madison
 
| UW Madison
| [[#Sergey Denisov | Spectral Szegő theorem on the real line]]
+
|[[#linktoabstract  |   Title ]]
 
|  
 
|  
 
|-
 
|-
|February 20
+
|March 15: No Seminar
| Ruixiang Zhang
+
| Person
| IAS (Princeton)
+
| Institution
| [[#Ruixiang Zhang | The (Euclidean) Fractal Uncertainty Principle]]
+
|[[#linktoabstract  |   Title ]]
| Betsy, Jordan, Andreas
+
|
 +
|-
 +
|March 23
 +
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 +
|  
 
|-
 
|-
|February 27
+
|March 30
|Detlef Müller
+
| Person
|University of Kiel
+
| Institution
| [[#Detlef Müller | On Fourier restriction for a non-quadratic hyperbolic surface]]
+
|[[#linktoabstract  |   Title ]]
|Betsy, Andreas
+
|  
 
|-
 
|-
|Wednesday, March 7, 4:00 p.m.
+
|April 5
| Winfried Sickel
+
| Person
|Friedrich-Schiller-Universität Jena
+
| Institution
| [[#Winfried Sickel | On the regularity of compositions of functions]]
+
|[[#linktoabstract  |   Title ]]
|Andreas
+
|  
 
|-
 
|-
|March 13
+
|April 12
|
+
| Person
 +
| Institution
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|March 20
+
|April 19
| Betsy Stovall
+
| No seminar
| UW
+
|  
| [[#linkofabstract | Two endpoint bounds via inverse problems]]
 
 
|
 
|
 +
|
 
|-
 
|-
|April 3
+
|April 22, Colloquium
 +
|Detlef Müller
 +
|University of Kiel
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
|
 
| [[#linkofabstract | Title]]
 
|
 
 
|-
 
|-
|April 10
+
|April 25, 4:00 p.m., Distinguished Lecture Series
| Martina Neuman
+
|Larry Guth
| UC Berkeley
+
|MIT
| [[#Martina Neuman | Gowers-Host-Kra norms and Gowers structure on Euclidean spaces]]
+
|[[#linktoabstract  |   Title ]]
| Betsy
 
 
|-
 
|-
|Friday, April 13, 4:00 p.m. (Colloquium)
+
|April 26, 4:00 p.m., Distinguished Lecture Series
|Jill Pipher
+
|Larry Guth
|Brown
+
|MIT
| [[#Jill Pipher | Mathematical ideas in cryptography]]
+
|[[#linktoabstract  |   Title ]]
|WIMAW
 
 
|-
 
|-
|April 17
+
|April 27, 4:00 p.m., Distinguished Lecture Series
 +
|Larry Guth
 +
|MIT
 +
|[[#linktoabstract  |  Title ]]
 
|  
 
|  
|  
+
|-
| [[#linkofabstract | Title]]
+
|
 
|
 
|
|-
 
|April 24
 
| Lenka Slavíková
 
| University of Missouri
 
| [[#Lenka Slavíková | <math>L^2 \times L^2 \to L^1</math> boundedness criteria]]
 
|Betsy, Andreas
 
|-
 
|May 1
 
| Xianghong Gong
 
| UW
 
| [[#linkofabstract | Title]]
 
 
|
 
|
|-
 
|May 15
 
|Gennady Uraltsev
 
|Cornell University
 
| [[#linkofabstract | TBA]]
 
|Betsy, Andreas
 
|-
 
| May 16-18, [http://www.math.wisc.edu/~stovall/FA2018/ Workshop in Fourier Analysis]
 
 
|
 
|
 
|
 
|
 
|
 
|
|Betsy, Andreas
 
 
|-
 
|-
 +
|Talks in the Fall semester 2022:
 +
|-
 +
|September 20,  PDE and Analysis Seminar
 +
|Andrej Zlatoš
 +
|UCSD
 +
|[[#linktoabstract  |  Title ]]
 +
| Hung Tran
 +
|-
 +
 +
 
|}
 
|}
  
 
=Abstracts=
 
=Abstracts=
===Brian Street===
+
===Dóminique Kemp===
  
Title:  Convenient Coordinates
+
Decoupling by way of approximation
  
Abstract:  We discuss the method of picking a convenient coordinate system adapted to vector fields. Let X_1,...,X_q be either real or complex C^1 vector fields.  We discuss the question of when there is a coordinate system in which the vector fields are smoother (e.g., C^m, or C^\infty, or real analytic).  By answering this in a quantitative way, we obtain coordinate charts which can be used as generalized scaling maps. When the vector fields are real this is joint work with Stovall, and continues in the line of quantitative sub-Riemannian geometry initiated by Nagel, Stein, and Wainger.  When the vector fields are complex one obtains a geometry with more structure which can be thought of as "sub-Hermitian".
+
Since Bourgain and Demeter's seminal 2017 decoupling result for nondegenerate hypersurfaces, several attempts have been made to extend the theory to degenerate hypersurfaces $M$. In this talk, we will discuss using surfaces derived from the local Taylor expansions of $M$ in order to obtain "approximate" decoupling results. By themselves, these approximate decouplings do not avail much. However, upon considerate iteration, for a specifically chosen $M$, they culminate in a decoupling partition of $M$ into caps small enough either as originally desired or otherwise genuinely nondegenerate at the local scale. A key feature that will be discussed is the notion of approximating a non-convex hypersurface $M$ by convex hypersurfaces at various scales. In this manner, contrary to initial intuition, non-trivial $\ell^2$ decoupling results will be obtained for $M$.
  
===Hiroyoshi Mitake===
+
===Jack Burkart===
  
Title:  Derivation of multi-layered interface system and its application
+
Transcendental Julia Sets with Fractional Packing Dimension
  
Abstract:  In this talk, I will propose a multi-layered interface system which can
+
If f is an entire function, the Julia set of f is the set of all points such that f and its iterates locally do not form a normal family; nearby points have very different orbits under iteration by f. A topic of interest in complex dynamics is studying the fractal geometry of the Julia set.
be formally derived by the singular limit of the weakly coupled system of  
 
the Allen-Cahn equation.  By using the level set approach, this system can be
 
written as a quasi-monotone degenerate parabolic system.  
 
We give results of the well-posedness of viscosity solutions, and study the  
 
singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.
 
  
===Joris Roos===
+
In this talk, we will discuss my thesis result where I construct non-polynomial (transcendental) entire functions whose Julia set has packing dimension strictly between (1,2). We will introduce various notions of dimension and basic objects in complex dynamics, and discuss a history of dimension results in complex dynamics. We will discuss some key aspects of the proof, which include a use of Whitney decompositions of domains as a tool to calculate the packing dimension, and some open questions I am thinking about.
  
Title: A polynomial Roth theorem on the real line
+
===Giuseppe Negro===
  
Abstract: For a polynomial P of degree greater than one, we show the existence of patterns of the form (x,x+t,x+P(t)) with a gap estimate on t in positive density subsets of the reals. This is an extension of an earlier result of Bourgain. Our proof is a combination of Bourgain’s approach and more recent methods that were originally developed for the study of the bilinear Hilbert transform along curves. This talk is based on a joint work with Polona Durcik and Shaoming Guo.
+
Stability of sharp Fourier restriction to spheres
  
===Michael Greenblatt===
+
In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate.
  
Title:  Maximal averages and Radon transforms for two-dimensional hypersurfaces
+
Joint work with E.Carneiro and D.Oliveira e Silva.
  
Abstract:  A general local result concerning L^p boundedness of maximal averages over 2D hypersurfaces is described, where p > 2. The surfaces are allowed to have either the traditional smooth density function or a singularity growing as |(x,y)|^{-t} for some 0 < t < 2. This result is a generalization of a theorem of Ikromov, Kempe, and Mueller. Similar methods can be used to show sharp L^p to L^p_a Sobolev estimates for associated Radon transform operators when p is in a certain interval containing 2.
+
===Rajula Srivastava===
  
===David Beltran===
+
Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups
  
Title:  Fefferman Stein Inequalities
+
We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.
  
Abstract:  Given an operator T, we focus on obtaining two-weighted inequalities in which the weights are related via certain maximal function. These inequalites, which originated in work of Fefferman and Stein, have been established in an optimal way for different classical operators in Harmonic Analysis. In this talk, we survey some classical results and we present some recent Fefferman-Stein inequalities for pseudodifferential operators and for the solution operators to dispersive equations.
+
===Itamar Oliveira===
  
===Jonathan Hickman===
+
A new approach to the Fourier extension problem for the paraboloid
  
Title: Factorising X^n.
+
An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $  of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.
  
Question: how many ways can the polynomial $X^n$ be factorised as a product of linear factors? Answer: it depends on the ring... In this talk I will describe joint work with Jim Wright investigating certain exponential sum estimates over rings of integers modulo N. This theory serves as a discrete analogue of the (euclidean) Fourier restriction problem, a central question in contemporary harmonic analysis. In particular, as part of this study, the question of counting the number of factorisations of polynomials over such rings naturally arises. I will describe how these number-theoretic considerations can themselves be approached via methods from harmonic analysis.
+
===Changkeun Oh===
  
===Xiaochun Li ===
+
Decoupling inequalities for quadratic forms and beyond
  
Title:  Recent progress on the pointwise convergence problems of Schrodinger equations
+
In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.
  
Abstract:  Recently, Guth, Du and I solved the pointwise convergence problem of Schrodinger equations in two-dimensional case. We proved that the solution to free Schrodinger equation in R^2 converges to its initial data, provided the initial data belongs to H^s for s larger than 1/3.  This result is sharp, up to the end point, due to Bourgain's example. The proof relies on the polynomial partitioning method and  the decoupling method. In addition, the pointwise convergence problem is closely related to Fourier restriction conjecture.
+
===Alexandru Ionescu===
  
===Fedor Nazarov=== 
+
Polynomial averages and pointwise ergodic theorems on nilpotent groups
  
Title: The Lerner-Ombrosi-Perez bound in the Muckenhoupt-Wheeden
+
I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.
conjecture is sharp.
 
  
Abstract: We show that the upper bound $[w]_{A_1}\log (e+[w]_{A_1})$ for
+
===Liding Yao===
the norm of the Hilbert transform on the line as an operator from $L^1(w)$
 
to $L^{1,\infty}(w)$ cannot be improved in general. This is a joint work
 
with Andrei Lerner and Sheldy Ombrosi.
 
  
===Stefanie Petermichl===
+
An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains
Title: Higher order Journé commutators
 
  
Abstract: We consider questions that stem from operator theory via Hankel and
+
Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.
Toeplitz forms and target (weak) factorisation of Hardy spaces. In
 
more basic terms, let us consider a function on the unit circle in its
 
Fourier representation. Let P_+ denote the projection onto
 
non-negative and P_- onto negative frequencies. Let b denote
 
multiplication by the symbol function b. It is a classical theorem by
 
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and
 
only if b is in an appropriate space of functions of bounded mean
 
oscillation. The necessity makes use of a classical factorisation
 
theorem of complex function theory on the disk. This type of question
 
can be reformulated in terms of commutators [b,H]=bH-Hb with the
 
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such
 
as in the real variable setting, in the multi-parameter setting or
 
other, these classifications can be very difficult.
 
  
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and
+
===Lingxiao Zhang===
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of
 
spaces of bounded mean oscillation via L^p boundedness of commutators.
 
We present here an endpoint to this theory, bringing all such
 
characterisation results under one roof.
 
  
The tools used go deep into modern advances in dyadic harmonic
+
Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition
analysis, while preserving the Ansatz from classical operator theory.
 
  
===Shaoming Guo ===
+
We study operators of the form
Title: Parsell-Vinogradov systems in higher dimensions
+
$Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$
 +
where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.
  
Abstract:
+
===Kasso Okoudjou===
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.
 
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.
 
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.
 
  
===Naser Talebizadeh Sardari===
+
An exploration in analysis on fractals
  
Title: Quadratic forms and the semiclassical eigenfunction hypothesis
+
Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.
  
Abstract:  Let <math>Q(X)</math> be any integral primitive positive definite quadratic form in <math>k</math> variables, where <math>k\geq4</math>,  and discriminant <math>D</math>. For any integer <math>n</math>, we give an upper bound on the number of integral solutions of <math>Q(X)=n</math>  in terms of <math>n</math>, <math>k</math>, and <math>D</math>. As a corollary, we prove  a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given  eigenspace of the Laplacian on the flat torus <math>\mathbb{T}^d</math> for <math>d\geq 5</math>. This conjecture is motivated by the work of Berry\cite{Berry, Michael} on semiclassical eigenfunction hypothesis.
+
===Rahul Parhi===
  
===Xianghong Chen===
+
On BV Spaces, Splines, and Neural Networks
  
Title:  Some transfer operators on the circle with trigonometric weights
+
Many problems in science and engineering can be phrased as the problem
 +
of reconstructing a function from a finite number of possibly noisy
 +
measurements. The reconstruction problem is inherently ill-posed when
 +
the allowable functions belong to an infinite set. Classical techniques
 +
to solve this problem assume, a priori, that the underlying function has
 +
some kind of regularity, typically Sobolev, Besov, or BV regularity. The
 +
field of applied harmonic analysis is interested in studying efficient
 +
decompositions and representations for functions with certain
 +
regularity. Common representation systems are based on splines and
 +
wavelets. These are well understood mathematically and have been
 +
successfully applied in a variety of signal processing and statistical
 +
tasks. Neural networks are another type of representation system that is
 +
useful in practice, but poorly understood mathematically.
  
Abstract:  A transfer operator is an averaging operator over the preimages of a given map. Certain dynamical properties of the map can be studied through its associated transfer operator. In this talk we will introduce a class of weighted transfer operators associated to the Bernoulli maps on the circle (i.e. multiplication by a given integer, mod 1). We will illustrate how the spectral properties of these operators may depend on the specific weight chosen and demonstrate multiple phase transitions. We also present some results on evaluating the spectral radii and corresponding eigenfunctions of these operators, as well as their connections to Fourier analysis. This is joint work with Hans Volkmer.  
+
In this talk, I will discuss my research which aims to rectify this
 +
issue by understanding the regularity properties of neural networks in a
 +
similar vein to classical methods based on splines and wavelets. In
 +
particular, we will show that neural networks are optimal solutions to
 +
variational problems over BV-type function spaces defined via the Radon
 +
transform. These spaces are non-reflexive Banach spaces, generally
 +
distinct from classical spaces studied in analysis. However, in the
 +
univariate setting, neural networks reduce to splines and these function
 +
spaces reduce to classical univariate BV spaces. If time permits, I will
 +
also discuss approximation properties of these spaces, showing that they
 +
are, in some sense, "small" compared to classical multivariate spaces
 +
such as Sobolev or Besov spaces.
  
===Bobby Wilson===
+
This is joint work with Robert Nowak.
  
Title: Projections in Banach Spaces and Harmonic Analysis
+
===Alexei Poltoratski===
  
Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.
+
Title: Pointwise convergence for the scattering data and non-linear Fourier transform.
  
===Andreas Seeger===
+
Abstract: This talk is about applications of complex and harmonic analysis in spectral and scattering theory
 +
for differential operators. The scattering transform for the Dirac system of differential equations
 +
can be viewed as the non-linear version of the classical Fourier transform. This connection raises many natural
 +
problems on extensions of classical results of Fourier analysis to non-linear settings. In this talk
 +
I will discuss one of such problems, an extension of Carleson's theorem on pointwise convergence of Fourier series to the non-linear case.
  
Title: Singular integrals and a problem on mixing flows
 
  
Abstract: The talk will be about  results related to Bressan's mixing problem. We present  an inequality for the change of a  Bianchini semi-norm of characteristic functions under the  flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator  for which one proves bounds  on Hardy spaces. This is joint work with Mahir Hadžić,  Charles Smart and    Brian Street.
 
  
===Dong Dong===
+
===John Green===
  
Title: Hibert transforms in a 3 by 3 matrix and applications in number theory
+
Estimates for oscillatory integrals via sublevel set estimates.
  
Abstract:  This talk could interest both analysts and number theorists. I will first present 35 variants of Hilbert transforms, with a focus on their connections with ergodic theory, number theory, and combinatorics. Then I will show how to use Fourier analysis tools to reduce a number theory problem (Roth theorem) to an algebraic geometry problem: this joint work Li and Sawin fully answers a question of Bourgain and Chang about three-term polynomial progressions in subsets of finite fields. I guarantee that a second-year graduate student can understand at least 50% of the talk.
+
In many situations, oscillatory integral estimates are known to imply sublevel set estimates in a stable manner. Reversing this implication is much more difficult, but understanding when this is true is helpful for understanding scalar oscillatory integral estimates. We shall motivate a line of investigation in which we seek to reverse the implication in the presence of a qualitative structural assumption. After considering some one-dimensional results, we turn to the setting of convex functions in higher dimensions.
  
===Sergey Denisov===
+
===Tao Mei===
  
Title:  Spectral Szegő  theorem on the real line
+
Fourier Multipliers on free groups.
  
Abstract: For even measures on the real line, we give the criterion for the logarithmic integral to converge in terms of the corresponding De-Branges system (or Krein's string). The applications to probability (linear prediction for stationary Gaussian processes) will be explained. This is the joint result with R. Bessonov.
+
In this introductory talk, I will try to explain what is the noncommutative Lp spaces associated with the free groups, and what are the to be answered questions on  the corresponding Fourier multiplier operators. At the end, I will explain a recent work on an analogue of Mikhlin’s Lp Fourier multiplier theory on free groups (joint with Eric Ricard and Quanhua Xu).
  
===Ruixiang Zhang===
+
=[[Previous_Analysis_seminars]]=
  
Title: The (Euclidean) Fractal Uncertainty Principle
+
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars
  
Abstract:  On the real line, a  version of the uncertainty principle says: If a nonzero function f has its Fourier support lying in B and |A||B| is much smaller than 1, then the L^2 norm of f on A cannot be close to the whole L^2 norm of f. Recently, Bourgain and Dyatlov proved a Fractal Uncertainty Principle (FUP) which has a similar statement. The difference is that in FUP the product of |A| and |B| can be much bigger, but A and B both have to be porous at many scales. We will introduce the theorem and then discuss some unusual features of its proof, most notably the application of the Beurling-Malliavin Theorem. In the original work  the dependence on the dimensions of both fractals was ineffective. We will also discuss why we can overcome this ineffectivity (joint work with Long Jin).
+
=Extras=
  
===Detlef Müller===
+
[[Blank Analysis Seminar Template]]
  
Title: On Fourier restriction for a non-quadratic hyperbolic surface
 
  
Abstract: In contrast to what is known about Fourier restriction for elliptic surfaces, rather little is known about  hyperbolic surfaces. Hitherto, basically only the quadric $z=xy$ had been studied successfully. In my talk, after giving some background on Fourier restriction, I shall report on recent joint work with S. Buschenhenke and A. Vargas on a cubic perturbation of this quadric. Our analysis reveals that the geometry of the problem changes drastically  in the presence of a perturbation term,  and that new techniques, compared to the elliptic case, are required to handle more general hyperbolic surfaces.
+
Graduate Student Seminar:
  
===Winfried Sickel===
+
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html
 
 
Title: On the regularity of compositions of functions
 
 
 
Abstract: Let <math>E</math> denote a Banach space of locally integrable functions on <math>\mathbb{R}</math>. To each continuous function <math>f:\mathbb{R} \to \mathbb{R}</math>
 
we associate the composition operator
 
<math>T_f(g):= f\circ g</math>, <math>g\in E</math>.
 
The properties of <math>T_f</math> strongly depend on the chosen function space <math>E</math>.
 
In my talk I will concentrate on Sobolev spaces <math>W^m_p</math> and  Slobodeckij spaces <math>W^s_p</math>.
 
The main aim will consist in giving a survey on necessary and sufficient conditions on <math>f</math>
 
such that the composition operator maps such a space <math>E</math> into itself.
 
 
 
===Martina Neuman===
 
 
 
Title:  Gowers-Host-Kra norms and Gowers structure on Euclidean spaces
 
 
 
Abstract:  The investigation on Brascamp-Lieb data - their structure, their extremizability, their stability and regularity of their constants - has been an active one in Harmonic Analysis. In this talk, I'll present an example of a Brascamp-Lieb structure: a so-called Gowers structure on Euclidean spaces, together with the related Gowers-Host-Kra norms - these were originally tools in additive combinatorics context. I'll dissertate on what happens when a function nearly achieves its Gowers-Host-Kra norm in a Euclidean context - this can be seen as continuation of the work of Eisner-Tao - and a related stability result of the Gowers structure on Euclidean spaces.
 
 
 
===Jill Pipher===
 
 
 
Title:  Mathematical ideas in cryptography
 
 
 
Abstract:  This talk does not assume prior knowledge of public key crypto (PKC). I'll talk about the history of the subject and some current areas of research,
 
including homomorphic encryption.
 
 
 
===Lenka Slavíková===
 
 
 
Title:  <math>L^2 \times L^2 \to L^1</math> boundedness criteria
 
 
 
Abstract:  It is a consequence of Plancherel's identity that a linear multiplier operator associated with a function <math>m</math> is bounded from <math>L^2</math> to itself if and only if <math>m</math> belongs to the space <math>L^\infty</math>. In this talk we will investigate the <math>L^2 \times L^2 \to L^1</math> boundedness of bilinear multiplier operators which is as central in the bilinear theory as the </math> boundedness is in the linear multiplier theory. We will present a sharp <math>L^2 \times L^2 \to L^1</math> boundedness criterion for a class of bilinear operators associated with a multiplier given by a signed sum of dyadic dilations of a given function, in terms of the <math>L^q</math> integrability of this function; precisely we will show that boundedness holds if and only if <math>q<4</math>. We will then discuss applications of this result concerning bilinear rough singular integrals and bilinear dyadic spherical maximal functions. This is a joint work with L. Grafakos and D. He.
 
 
 
=Extras=
 
[[Blank Analysis Seminar Template]]
 

Latest revision as of 13:33, 2 December 2021

The 2021-2022 Analysis Seminar will be organized by David Beltran and Andreas Seeger. Some of the talks will be in person (room Van Vleck B139) and some will be online. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).

Zoom links will be sent to those who have signed up for the Analysis Seminar List. If you would like to subscribe to the Analysis seminar list, send a blank email to analysis+join (at) g-groups (dot) wisc (dot) edu. If you are from an institution different than UW-Madison, please send as well as an additional email to David and Andreas (dbeltran, seeger at math (dot) wisc (dot) edu) to notify the request.

If you'd like to suggest speakers for the fall semester please contact David and Andreas.

Analysis Seminar Schedule

date speaker institution title host(s)
September 21, VV B139 Dóminique Kemp UW-Madison Decoupling by way of approximation
September 28, VV B139 Jack Burkart UW-Madison Transcendental Julia Sets with Fractional Packing Dimension
October 5, Online Giuseppe Negro University of Birmingham Stability of sharp Fourier restriction to spheres
October 12, VV B139 Rajula Srivastava UW Madison Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups
October 19, Online Itamar Oliveira Cornell University A new approach to the Fourier extension problem for the paraboloid
October 26, VV B139 Changkeun Oh UW Madison Decoupling inequalities for quadratic forms and beyond
October 29, Colloquium Alexandru Ionescu Princeton University Polynomial averages and pointwise ergodic theorems on nilpotent groups
November 2, VV B139 Liding Yao UW Madison An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains
November 9, VV B139 Lingxiao Zhang UW Madison Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition
November 12, Colloquium Kasso Okoudjou Tufts University An exploration in analysis on fractals
November 16, VV B139 Rahul Parhi UW Madison (EE) On BV Spaces, Splines, and Neural Networks
November 30, VV B139 Alexei Poltoratski UW Madison Pointwise convergence for the scattering data and non-linear Fourier transform.
December 7, Online John Green The University of Edinburgh Estimates for oscillatory integrals via sublevel set estimates
December 14, VV B139 Tao Mei Baylor University Fourier Multipliers on free groups
February 8 Person Institution Title
February 15 Sebastian Bechtel Institut de Mathématiques de Bordeaux Title
February 22 Betsy Stovall UW Madison Title
March 1 Person Institution Title
March 8 Brian Street UW Madison Title
March 15: No Seminar Person Institution Title
March 23 Person Institution Title
March 30 Person Institution Title
April 5 Person Institution Title
April 12 Person Institution Title
April 19 No seminar
April 22, Colloquium Detlef Müller University of Kiel Title
April 25, 4:00 p.m., Distinguished Lecture Series Larry Guth MIT Title
April 26, 4:00 p.m., Distinguished Lecture Series Larry Guth MIT Title
April 27, 4:00 p.m., Distinguished Lecture Series Larry Guth MIT Title
Talks in the Fall semester 2022:
September 20, PDE and Analysis Seminar Andrej Zlatoš UCSD Title Hung Tran

Abstracts

Dóminique Kemp

Decoupling by way of approximation

Since Bourgain and Demeter's seminal 2017 decoupling result for nondegenerate hypersurfaces, several attempts have been made to extend the theory to degenerate hypersurfaces $M$. In this talk, we will discuss using surfaces derived from the local Taylor expansions of $M$ in order to obtain "approximate" decoupling results. By themselves, these approximate decouplings do not avail much. However, upon considerate iteration, for a specifically chosen $M$, they culminate in a decoupling partition of $M$ into caps small enough either as originally desired or otherwise genuinely nondegenerate at the local scale. A key feature that will be discussed is the notion of approximating a non-convex hypersurface $M$ by convex hypersurfaces at various scales. In this manner, contrary to initial intuition, non-trivial $\ell^2$ decoupling results will be obtained for $M$.

Jack Burkart

Transcendental Julia Sets with Fractional Packing Dimension

If f is an entire function, the Julia set of f is the set of all points such that f and its iterates locally do not form a normal family; nearby points have very different orbits under iteration by f. A topic of interest in complex dynamics is studying the fractal geometry of the Julia set.

In this talk, we will discuss my thesis result where I construct non-polynomial (transcendental) entire functions whose Julia set has packing dimension strictly between (1,2). We will introduce various notions of dimension and basic objects in complex dynamics, and discuss a history of dimension results in complex dynamics. We will discuss some key aspects of the proof, which include a use of Whitney decompositions of domains as a tool to calculate the packing dimension, and some open questions I am thinking about.

Giuseppe Negro

Stability of sharp Fourier restriction to spheres

In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate.

Joint work with E.Carneiro and D.Oliveira e Silva.

Rajula Srivastava

Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups

We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.

Itamar Oliveira

A new approach to the Fourier extension problem for the paraboloid

An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $ of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.

Changkeun Oh

Decoupling inequalities for quadratic forms and beyond

In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.

Alexandru Ionescu

Polynomial averages and pointwise ergodic theorems on nilpotent groups

I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.

Liding Yao

An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains

Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.

Lingxiao Zhang

Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition

We study operators of the form $Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$ where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.

Kasso Okoudjou

An exploration in analysis on fractals

Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.

Rahul Parhi

On BV Spaces, Splines, and Neural Networks

Many problems in science and engineering can be phrased as the problem of reconstructing a function from a finite number of possibly noisy measurements. The reconstruction problem is inherently ill-posed when the allowable functions belong to an infinite set. Classical techniques to solve this problem assume, a priori, that the underlying function has some kind of regularity, typically Sobolev, Besov, or BV regularity. The field of applied harmonic analysis is interested in studying efficient decompositions and representations for functions with certain regularity. Common representation systems are based on splines and wavelets. These are well understood mathematically and have been successfully applied in a variety of signal processing and statistical tasks. Neural networks are another type of representation system that is useful in practice, but poorly understood mathematically.

In this talk, I will discuss my research which aims to rectify this issue by understanding the regularity properties of neural networks in a similar vein to classical methods based on splines and wavelets. In particular, we will show that neural networks are optimal solutions to variational problems over BV-type function spaces defined via the Radon transform. These spaces are non-reflexive Banach spaces, generally distinct from classical spaces studied in analysis. However, in the univariate setting, neural networks reduce to splines and these function spaces reduce to classical univariate BV spaces. If time permits, I will also discuss approximation properties of these spaces, showing that they are, in some sense, "small" compared to classical multivariate spaces such as Sobolev or Besov spaces.

This is joint work with Robert Nowak.

Alexei Poltoratski

Title: Pointwise convergence for the scattering data and non-linear Fourier transform.

Abstract: This talk is about applications of complex and harmonic analysis in spectral and scattering theory for differential operators. The scattering transform for the Dirac system of differential equations can be viewed as the non-linear version of the classical Fourier transform. This connection raises many natural problems on extensions of classical results of Fourier analysis to non-linear settings. In this talk I will discuss one of such problems, an extension of Carleson's theorem on pointwise convergence of Fourier series to the non-linear case.


John Green

Estimates for oscillatory integrals via sublevel set estimates.

In many situations, oscillatory integral estimates are known to imply sublevel set estimates in a stable manner. Reversing this implication is much more difficult, but understanding when this is true is helpful for understanding scalar oscillatory integral estimates. We shall motivate a line of investigation in which we seek to reverse the implication in the presence of a qualitative structural assumption. After considering some one-dimensional results, we turn to the setting of convex functions in higher dimensions.

Tao Mei

Fourier Multipliers on free groups.

In this introductory talk, I will try to explain what is the noncommutative Lp spaces associated with the free groups, and what are the to be answered questions on the corresponding Fourier multiplier operators. At the end, I will explain a recent work on an analogue of Mikhlin’s Lp Fourier multiplier theory on free groups (joint with Eric Ricard and Quanhua Xu).

Previous_Analysis_seminars

https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars

Extras

Blank Analysis Seminar Template


Graduate Student Seminar:

https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html