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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
|Universal sets for projections
|On Almgren’s frequency function
|
|
|-
|-
|September 18
|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
|
|
|-
|-
|September 25
|February 12
|Kaiyi Huang
|Sam Craig
|An introduction to the Kakeya problem.
|
|
|-
|February 14
|Gautam Neelakantan
|Different Perspectives on Pseudodifferential Operators
|
|
|-
|-
|October 2
|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
|
|
|-
|-
|October 9
|February 28
|Chiara Paulsen
|A proof of Szegő’s theorem
|
|
|-
|March 5
|Canceled
|
|
|
|
|-
|-
|October 16
|March 7
|Jia Hao Tan
|Uniqueness of Signal Recovery: Uncertainty Principles, Randomness and Restriction
|
|
|-
|March 12
|Reading groups!
|
|
|
|
|-
|-
|October 23
|March 14
|Yupeng Zhang
|Discrete uniqueness pairs of Fourier transform on the real line
|
|
|-
|March 19
|Elevator Pitches
|
|
|
|
|-
|-
|October 30
|March 26
|SPRING BREAK
|CANCELLED
|:)
|-
|April 2
|Jiankun Li
|
|
|
|-
|April 4
|Jiankun Li
|
|
|
|
|-
|-
|November 6
|April 9
|Gustavo Flores
|
|
|
|-
|April 11
|Gustavo Flores
|
|
|
|
|-
|-
|November 13
|April 16
|Kaiwen Jin
|
|
|
|-
|April 18
|Kaiwen Jin
|
|
|
|
|-
|-
|November 20
|April 23
|
|Dimas de Albuquerque
|
|
|
|
|-
|-
|November 27
|April 25
|Summer Al Hamdani
|
|
|
|
|Day before Thanksgiving
|-
|-
|December 4
|April 30
|
|Raj Vasu
|
|
|
|
|-
|-
|December 11
|(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 ===
=== 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.

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