Time and location
Aug. 21. to Aug. 25. 2022
Madison, WI
Classrooms
Monday and Friday: B135 Van Vleck (math building)
Tuesday, Wednesday and Thursday: B107 Van Vleck (math building)
(B135 is reserved for summer school use for the entire week. Feel free to use it at any time. )
Organizers
Semyon Dyatlov, Shaoming Guo, Ruixiang Zhang
Participants
Graduate students and recent PhD graduates
Topic
Fractal uncertainty principles
Modes
Participants will report pre-selected papers. Each participant will need to select one paper, read, write notes and present during the week of the summer school.
Financial support
Hotels for non-local participants will be covered. Check-in on Sunday, check-out on Saturday.
Papers to discuss
J. Bourgain and S. Dyatlov, “Spectral gaps without the pressure condition,”
Ann. Math. (2) 187, 825–867 (2018).
by Zhongkai Tao and Mengxuan Yang
Mashreghi, J., Nazarov, F., Havin, V.: Beurling–Malliavin multiplier theorem: the seventh proof.
St. Petersb. Math. J. 17, 699–744 (2006)
By Dimas de Albuquerque
Jin, Zhang: Fractal uncertainty principle with explicit exponent.
Math Ann. 2020
by Shengwen Gan
R. Han and W. Schlag, “A higher dimensional Bourgain-Dyatlov fractal uncertainty principle,”
Anal. PDE. 2020
By Alex Cohen
Cohen: Fractal uncertainty for discrete 2D Cantor sets
arXiv, 2022
Dyatlov-Jin: Resonances for open quantum maps and a fractal uncertainty principle
CMP, 2017.
By Aidan Backus
J. Bourgain and S. Dyatlov, “Fourier dimension and spectral gaps for hyperbolic surfaces,”
Geom. Funct. Anal. 27, 744–771 (2017).
By Olivine Silier
S. Dyatlov and L. Jin, “Dolgopyat’s method and the fractal uncertainty principle,”
Anal. PDE 11, 1457–1485 (2018).
By Gautam Neelakantan
S. Dyatlov and J. Zahl, “Spectral gaps, additive energy, and a fractal uncertainty principle,”
Geom. Funct. Anal. 26, 1011–1094 (2016).
By Terry Harris
Cladek, Tao: Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle
arXiv, 2020
By Jake Fiedler and Sarah Tammen
S. Dyatlov and L. Jin, “Semiclassical measures on hyperbolic surfaces have full support,”
Acta Math. 220, 297–339 (2018).
By Elena Kim
Cohen: Fractal uncertainty in higher dimensions,
arXiv, 2023
By Alejo Salvatore
Acknowledgement
The summer school is supported by Shaoming's NSF grant, Ruixiang's NSF grant, and by the NSF RTG grant Analysis and PDEs at Wisconsin.
A few places to see near Madison
Boating. Please google for boat rentals. I heard this website has reasonably priced ones.
Hiking. Devil's lake is what many people would recommend. I personally also like Parfrey's Glen State natural area.
Cycling. Rent a bike (BCycle, which is electronic, is quite popular) and cycle around the city and lake Monona.
