GAPS: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
VisualWikitext
No edit summary
 
(42 intermediate revisions by 5 users not shown)
Line 5: Line 5:
To join the mailing list, send an email to: gaps+subscribe@g-groups.wisc.edu.  
To join the mailing list, send an email to: gaps+subscribe@g-groups.wisc.edu.  


=== Fall 2024 Schedule ===
We also loosely coordinate with the graduate analysis seminar (and many students go to both). The graduate analysis seminar meets on Fridays 1:20pm-2:10pm, in Van Vleck B219. For questions on the graduate analysis seminar, please email the organizers: Betsy Stovall (stovall (at) math.wisc.edu) and Lars Niedorf (niedorf (at) wisc.edu).
 
=== Spring 2025 Schedule for GAPS (Wednesdays in 901) and Graduate Analysis Seminar (Fridays in B219) ===
{| class="wikitable"
{| class="wikitable"
|+
|'''Date'''
!Date
|'''Presenter'''
!Speaker
|'''Title'''
!Title
|'''Comments'''
!Comments
|-
|-
|September 4
|January 22
|Summer & Allison
|Summer Al Hamdani and Allison Byars
|Planning / Social!
|Organizing!
|
|
|-
|-
|September 11
|January 29
|Jake Fiedler
|Gautam Neelakantan
|Projection theorems in geometric measure theory
|On Almgren’s frequency function
|A continuation of this talk, "Universal sets for projections," will happen on September 13th in the Graduate Analysis Seminar (Fridays @ 1:20pm-2:10pm in VV B235).
|
|-
|-
|September 18
|January 31
|Sam Craig
|Sam Craig
|Structural properties of sticky Kakeya sets
|The p-adic Kakeya problem
|A continuation of this talk will happen on September 20th in the Graduate Analysis Seminar.
|
|-
|-
|September 25
|February 5
|Kaiyi Huang
|Kaiyi Huang
|A fast algorithm to solve the discrete integrable NLS
|Brascamp-Lieb Inequalities
|
|-
|February 7
|Dimas de Albuquerque
|Sign uncertainty principle for the Fourier transform
|
|-
|February 12
|Sam Craig
|An introduction to the Kakeya problem.
|
|-
|February 14
|Gautam Neelakantan
|Different Perspectives on Pseudodifferential Operators
|
|-
|February 19
|Mingfeng Chen
|Rational points near manifold
|
|
|-
|-
|October 2
|February 21
|Kaiwen Jin
|Mingfeng Chen
|$L^2$ Schrödinger maximal function estimate via fractal extension estimate
|Rational points near planar curves
|A continuation of this talk (title TBA) will happen on October 4th in the Graduate Analysis Seminar.
|
|-
|-
|October 9
|February 26
|Chiara Paulsen
|Chiara Paulsen
|Norm convergence of ergodic averages
|Some basics about orthogonal polynomials on the unit circle
|
|
|-
|-
|October 16
|February 28
|CANCELLED
|Chiara Paulsen
|good luck with grading midterms!
|A proof of Szegő’s theorem
|
|
|-
|-
|October 23
|March 5
|Amelia Stokolosa & Allison Byars
|Canceled
|TBA
|
|
|
|-
|-
|October 30
|March 7
|Multiple
|Jia Hao Tan
|''Elevator Pitches''
|Uniqueness of Signal Recovery: Uncertainty Principles, Randomness and Restriction
|
|
|-
|-
|November 6
|March 12
|Amelia Stokolosa
|Reading groups!
|TBA
|
|
|
|-
|-
|November 13
|March 14
|Yupeng Zhang
|Discrete uniqueness pairs of Fourier transform on the real line
|
|
|-
|March 19
|Elevator Pitches
|
|
|
|
|-
|-
|November 20
|March 26
|Adrian Calderon
|SPRING BREAK
|TBA
|CANCELLED
|:)
|-
|April 2
|Jiankun Li
|
|
|-
|April 4
|Jiankun Li
|
|
|
|-
|-
|November 27
|April 9
|CANCELLED
|Gustavo Flores
|CANCELLED
|
|Day before Thanksgiving!
|
|-
|-
|December 4
|April 11
|Gustavo Flores
|Gustavo Flores
|TBA
|
|
|-
|April 16
|Kaiwen Jin
|
|
|-
|April 18
|Kaiwen Jin
|
|
|
|-
|-
|December 11
|April 23
|Dimas de Albuquerque
|Dimas de Albuquerque
|TBA
|
|
|-
|April 25
|Summer Al Hamdani
|
|
|-
|April 30
|Raj Vasu
|
|
|-
|(May 2)
|TBD
|
|
|
|}
|}


==== September 11. [https://sites.google.com/view/jakefiedler Jake Fiedler], ''Projection theorems in geometric measure theory.'' ====
=== Abstracts ===
Abstract: Geometric measure theory (GMT) investigates how certain geometric properties of sets or operations on sets affect their size. Orthogonal projections are one such operation, and have been closely studied in this context for many years. Marstrand's projection theorem is the most prominent result of this type and states that for any (reasonable) set, the projections of that set in almost every direction have maximal Hausdorff dimension. We will introduce some of the main ideas of GMT, discuss Marstrand's projection theorem and other projection results, and begin to explore some new tools that have enabled recent progress in this area. This is the first of two talks.
 
The second talk will happen on September 13th, at 1:20pm-2:10pm in VV B235 during the Graduate Analysis Seminar:
 
Title: Universal sets for projections


Abstract: In this talk, we will consider certain variants of Marstrand's projection theorem that hold for ''classes'' of sets in the plane. In particular, we will examine the class of sets with optimal oracles, the class of weakly regular sets, and the class of Ahlfors-David regular sets. This is the second of two talks and is based on joint work with Don Stull.
====== '''January 29. Gautam Neelakantan, ''On Almgren’s frequency function.''''' ======
'''Abstract:''' I will introduce Almgren’s frequency function and discuss its monotonicity property and application to unique continuation problems. If time permits I will also talk about other Almgren type frequency functions and some open problems related to the same.


==== September 18. [https://people.math.wisc.edu/~secraig2/ Sam Craig], ''Structural properties of sticky Kakeya sets.'' ====
====== '''January 31. Sam Craig, ''The p-adic Kakeya problem''.''' ======
Abstract: We heard last week about the Kakeya set conjecture, that a set in $\mathbb{R}^n$ with a line segment in every direction has Hausdorff dimension $n$. A 2022 paper by Hong Wang and Josh Zahl proves this in $\mathbb{R}^3$ for ''sticky Kakeya sets'', which have an additional structural property called stickiness. I will outline how sticky Kakeya sets with near-minimal dimension must have additional structural properties Wang and Zahl call ''local and global grains'' and how these properties, along with previously known sum-product estimates, lead to a contradiction. This talk will be followed by a talk on Friday giving more details on how Wang and Zahl prove the existence of local and global grains.
'''Abstract:''' The Kakeya conjecture over the p-adic field $Q_p$ is that the Hausdorff dimension of a set in $Q_p^n$ with a line segment in every direction is always $n$. This was proven in 2021 by Bodan Arsovski. I will present proof.


==== September 25. Kaiyi Huang, ''A fast algorithm to solve the discrete integrable NLS.'' ====
==== '''February 5. Kaiyi Huang, ''Brascamp-Lieb Inequalities.''''' ====
Abstract: We study the discrete integrable nonlinear Schrödinger equation (aka. Ablowitz—Ladik equation) on the integer lattice with l^2 initial data. Thanks to the stability results of Schur’s algorithm and nonlinear Fourier transform properties, there is a fast algorithm to solve the equation of high accuracy.
'''Abstract:''' I will sketch the proof of this classical of inequalities done by Bennett, et al (2008).


==== October 2. Kaiwen Jin, ''L^2 Schrödinger maximal function estimate via fractal extension estimate.'' ====
==== '''February 12. Sam Craig, ''An introduction to the Kakeya problem.''''' ====
Abstract: I plan to present the paper '''''Sharp $L^2$ estimate of Schrödinger maximal function in higher dimensions''''' by Xiumin Du and Ruixiang Zhang (2019) in two consecutive talks. In the GAPS seminar, the main focus will be how we can deduce the Schrödinger maximal function estimate, which in turn will imply pointwise convergence of the free Schrödinger equation, from the fractal extension estimate using a localization argument, parabolic rescaling, and locally constant property. If time permits, I will also give a proof sketch of the main theorem in the paper about fractal extension estimate. In the second talk on Friday, I will give a more detailed sketch of the proof of the fractal extension estimate.
'''Abstract:''' I will introduce the Kakeya and Kakeya maximal conjecture, prove that L^p bounds for the Kakeya maximal function imply lower bounds on the dimension of Kakeya sets, and use Wolff’s brush method to prove the dimension of Kakeya sets in R^d is at least (d+2)/2.


==== October 9. Chiara Paulsen, ''Norm convergence of ergodic averages.'' ====
==== '''February 19. Mingfeng Chen, ''Rational points near manifold.''''' ====
Abstract: We will look at the norm convergence of ergodic averages of the form $\frac{1}{N}\sum_{n=0}^{N-1}T^nf_1T^{2n}f_2...T^{kn}f_k$ where $T$ is the dynamic of an ergodic system and $f_1,...,f_k\in L^\infty$ using the method of characteristic factors..
'''Abstract:''' How many rational points are near a compact manifold? This natural problem is closed related to many problems in number theory. In the first talk, I will survey the state of art and give some applications.


==== October 16. CANCELLED. ====
==== '''February 26. Chiara Paulsen, ''Some basics about orthogonal polynomials on the unit circle.''''' ====
Abstract: good luck with grading! :)
'''Abstract:''' In this talk I will introduce some concepts about orthogonal polynomials associated to a probability measure $\mu$ on the unit circle $\mathbb{T}$. We will look at objects like its Verblunsky coefficients, the Schur parameters of the Schur function associated to $\mu$ or the Toeplitz determinant of $\mu$ and connect all these objects in various ways.


==== October 23. Amelia Stokolosa & Allison Byars, ''TBA.'' ====
==== '''March 12. Everyone, ''Reading groups.''''' ====
Abstract: TBA.
'''Abstract:''' This week we will be forming reading groups. We all have a few papers we've been wanting to read but find it hard to motivate ourselves to actually take the time to read them.  Reading groups can be a great way to hold each other accountable.  Please bring ideas of any materials (papers, books, notes, etc) you've been wanting to read, or just a general topics you've been wanting to learn about.  We can discuss different materials to read on these topics and we'll take this time to form groups!


==== October 30. Multiple, ''Elevator Pitches.'' ====
==== '''March 19. Multiple, ''Elevator pitches.''''' ====
Abstract: TBA.
'''Abstract:''' Elevator pitches from several members of the analysis and PDEs groups as a part of the prospective students' visit day.


==== November 6. Amelia Stokolosa, ''TBA.'' ====
==== '''April 2. Jiankun Li, ''TBD.''''' ====
Abstract: TBA.
'''Abstract:''' TBA.


==== November 13. TBA, ''TBA.'' ====
==== '''April 9. Gustavo Flores, ''TBD.''''' ====
Abstract: TBA.
'''Abstract:''' TBA.


==== November 20. Adrian Calderon, ''TBA.'' ====
==== '''April 16. Kaiwen Jin, ''TBD.''''' ====
Abstract: TBA.
'''Abstract:''' TBA.


==== December 4. Gustavo Flores, ''TBA.'' ====
==== '''April 23. Dimas de Albuquerque, ''TBD.''''' ====
Abstract: TBA.
'''Abstract:''' TBA.


==== December 11. Dimas de Albuquerque, ''TBA.'' ====
==== '''April 30. Raj Vasu, ''TBD.''''' ====
Abstract: TBA.
'''Abstract:''' TBA.


=== Previous Semesters ===
=== Previous Semesters ===
[[GAPS Previous Semesters|Click here]] to view of all previous semesters' speakers and abstracts.
[[GAPS Previous Semesters|Click here]] to view of all previous semesters' speakers and abstracts.

Latest revision as of 23:21, 7 March 2025

The Graduate Analysis and PDEs Seminar (GAPS) is intended to build community for graduate students in the different subfields of analysis and PDEs. The goal is to give accessible talks about your current research projects, papers you found interesting on the arXiv, or even just a theorem/result that you use and think is really cool!

We currently meet Wednesdays, 1:20pm-2:10pm, in Van Vleck 901. Cookies are provided. If you have any questions, please email the organizers: Summer Al Hamdani (alhamdani (at) wisc.edu) and Allison Byars (abyars (at) wisc.edu).

To join the mailing list, send an email to: gaps+subscribe@g-groups.wisc.edu.

We also loosely coordinate with the graduate analysis seminar (and many students go to both). The graduate analysis seminar meets on Fridays 1:20pm-2:10pm, in Van Vleck B219. For questions on the graduate analysis seminar, please email the organizers: Betsy Stovall (stovall (at) math.wisc.edu) and Lars Niedorf (niedorf (at) wisc.edu).

Spring 2025 Schedule for GAPS (Wednesdays in 901) and Graduate Analysis Seminar (Fridays in B219)

Date Presenter Title Comments
January 22 Summer Al Hamdani and Allison Byars Organizing!
January 29 Gautam Neelakantan On Almgren’s frequency function
January 31 Sam Craig The p-adic Kakeya problem
February 5 Kaiyi Huang Brascamp-Lieb Inequalities
February 7 Dimas de Albuquerque Sign uncertainty principle for the Fourier transform
February 12 Sam Craig An introduction to the Kakeya problem.
February 14 Gautam Neelakantan Different Perspectives on Pseudodifferential Operators
February 19 Mingfeng Chen Rational points near manifold
February 21 Mingfeng Chen Rational points near planar curves
February 26 Chiara Paulsen Some basics about orthogonal polynomials on the unit circle
February 28 Chiara Paulsen A proof of Szegő’s theorem
March 5 Canceled
March 7 Jia Hao Tan Uniqueness of Signal Recovery: Uncertainty Principles, Randomness and Restriction
March 12 Reading groups!
March 14 Yupeng Zhang Discrete uniqueness pairs of Fourier transform on the real line
March 19 Elevator Pitches
March 26 SPRING BREAK CANCELLED :)
April 2 Jiankun Li
April 4 Jiankun Li
April 9 Gustavo Flores
April 11 Gustavo Flores
April 16 Kaiwen Jin
April 18 Kaiwen Jin
April 23 Dimas de Albuquerque
April 25 Summer Al Hamdani
April 30 Raj Vasu
(May 2) TBD

Abstracts

January 29. Gautam Neelakantan, On Almgren’s frequency function.

Abstract: I will introduce Almgren’s frequency function and discuss its monotonicity property and application to unique continuation problems. If time permits I will also talk about other Almgren type frequency functions and some open problems related to the same.

January 31. Sam Craig, The p-adic Kakeya problem.

Abstract: The Kakeya conjecture over the p-adic field $Q_p$ is that the Hausdorff dimension of a set in $Q_p^n$ with a line segment in every direction is always $n$. This was proven in 2021 by Bodan Arsovski. I will present proof.

February 5. Kaiyi Huang, Brascamp-Lieb Inequalities.

Abstract: I will sketch the proof of this classical of inequalities done by Bennett, et al (2008).

February 12. Sam Craig, An introduction to the Kakeya problem.

Abstract: I will introduce the Kakeya and Kakeya maximal conjecture, prove that L^p bounds for the Kakeya maximal function imply lower bounds on the dimension of Kakeya sets, and use Wolff’s brush method to prove the dimension of Kakeya sets in R^d is at least (d+2)/2.

February 19. Mingfeng Chen, Rational points near manifold.

Abstract: How many rational points are near a compact manifold? This natural problem is closed related to many problems in number theory. In the first talk, I will survey the state of art and give some applications.

February 26. Chiara Paulsen, Some basics about orthogonal polynomials on the unit circle.

Abstract: In this talk I will introduce some concepts about orthogonal polynomials associated to a probability measure $\mu$ on the unit circle $\mathbb{T}$. We will look at objects like its Verblunsky coefficients, the Schur parameters of the Schur function associated to $\mu$ or the Toeplitz determinant of $\mu$ and connect all these objects in various ways.

March 12. Everyone, Reading groups.

Abstract: This week we will be forming reading groups. We all have a few papers we've been wanting to read but find it hard to motivate ourselves to actually take the time to read them. Reading groups can be a great way to hold each other accountable. Please bring ideas of any materials (papers, books, notes, etc) you've been wanting to read, or just a general topics you've been wanting to learn about. We can discuss different materials to read on these topics and we'll take this time to form groups!

March 19. Multiple, Elevator pitches.

Abstract: Elevator pitches from several members of the analysis and PDEs groups as a part of the prospective students' visit day.

April 2. Jiankun Li, TBD.

Abstract: TBA.

April 9. Gustavo Flores, TBD.

Abstract: TBA.

April 16. Kaiwen Jin, TBD.

Abstract: TBA.

April 23. Dimas de Albuquerque, TBD.

Abstract: TBA.

April 30. Raj Vasu, TBD.

Abstract: TBA.

Previous Semesters

Click here to view of all previous semesters' speakers and abstracts.

Retrieved from "https://wiki.math.wisc.edu/index.php?title=GAPS&oldid=28263"