Time and Location

Department of Mathematics, University of Pennsylvania

Aug. 14 to Aug. 18, 2023

Participants

Graduate students and recent PhD graduates. 

Application and Deadline

To receive full consideration of your application, please submit the application form by the end of May 15. To complete the application, please make sure to also email a copy of your CV to us at studyguideworkshop2023@gmail.com. Please use the subject name "Application-CV-Your full name" in your email.

Topics

Literature in Harmonic analysis and related fields. The main topic areas include Decoupling, Fourier restriction, Oscillatory integrals, Kakeya problem, and Projection theory. 

Modes

The purpose of this workshop is to have graduate students and recent PhD graduates carefully read an important paper from harmonic analysis, and write a study guide in groups that will help others understand the result. The goal is that students will gain a deeper understanding of results and techniques relevant to their research, and that the study guide they produce will be a valuable pedagogical contribution to the field.

The exact format and content of the study guides may vary by groups, and may contain explanation of technical details, added examples, alternative arguments, extension of the theory, or tips on how to read the paper. Participants are expected to start studying the assigned paper and design the study guide before the August workshop, under the guidance of the organizers. During the workshop, there will be dedicated collaboration sessions where participants will work in groups to compare notes, edit drafts, and work on extension of the theory or related follow-up projects. In addition, participants will have the opportunity to learn about other papers by attending presentations given by each group and cross-group discussion sessions. There will also be career development panels and networking events at the workshop. After the workshop, the completed study guides will be made available to the whole community and submitted for publication if applicable.

Financial support

Hotels for non-local participants will be covered and support for travel expenses will be provided. The exact amount of travel support will be need based, but we expect to be able to reimburse up to about $600 for travel for each participant. Participants with concerns about reimbursement levels should reach out to the organizers at studyguideworkshop2023@gmail.com.

Completed study guides (to be updated)

• A study guide for the ℓ2 decoupling theorem for the paraboloid (Ataleshvara Bhargava, Tiklung Chan, Zi Li Lim, Yixuan Pang) arXiv

• Study guide for "On restriction projections to planes in $\mathbb{R}^3$" (Tainara Borges, Siddharth Mulherkar, Tongou Yang) arXiv 

• A Study Guide to "Kaufman and Falconer estimates for radial projections" (Paige Bright, Ryan Bushling, Caleb Marshall, Alex Ortiz) arXiv

• A Study Guide for "A Restriction Estimate using Polynomial Partitioning" (John Green, Terry Harris, Kaiyi Huang, Arian Nadjimzadah) arXiv

• A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" (Martin Hsu, Fred Yu-Hsiang Lin, Amelia Stokolosa) arXiv

• A study guide for "On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" after T. Orponen and P. Shmerkin (Jacob B. Fiedler, Guo-Dong Hong, Donggeun Ryou, Shukun Wu) arXiv

Organizers

Philip Gressman, University of Pennsylvania

Yumeng Ou, University of Pennsylvania

Hong Wang, University of California, Los Angeles

Josh Zahl, University of British Columbia

Contact

If you have any questions regarding the program or the application process, please reach out to the organizers at studyguideworkshop2023@gmail.com.

Acknowledgement

This event is sponsored by the NSF grant DMS 2142221 and the Department of Mathematics, University of Pennsylvania.