Department of Mathematics Calendar

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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

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Mathematics Department colloquium

Event Type
Mathematics Department
314 Altgeld
Oct 14, 2022   4:00 - 5:00 pm  
Ciprian Demeter
Kevin Ford

Title:  Restriction of exponential sums to hypersurfaces

Abstract: The last decade has witnessed a revolution in the circle of problems concerned with proving sharp moment inequalities  for exponential sums on tori. This has in turn led to a better understanding of pointwise estimates, but this topic remains extremely challenging. One way to bridge the gap between global and pointwise behavior is to study the restriction of exponential sums to submanifolds of the torus.

In my talk I will explore the behavior of lower dimensional Weyl sums and toral Laplace eigenfunctions, restricted to hypersurfaces. The proofs will involve decoupling, a Fourier analytic tool that has recently found a broad range of applications in many areas of mathematics.

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