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Abstracts for Oscillatory integrals in number theory. Number Theory Lunch Seminar jointly with the Hausdorff School

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Oscillatory integrals and stationary phase estimates in analytic number theory

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Speaker: 
Ian Petrow
Zugehörigkeit: 
UCL
Datum: 
Mit, 10/07/2024 - 14:45 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
Oscillatory integrals in number theory. Number Theory Lunch Seminar jointly with the Hausdorff School

I will give an overview of how oscillatory integrals arise in analytic number theory, especially the theory of L-functions and automorphic forms. Usually the integrals we are faced with are multiple-yet-low dimensional, so that they are approachable by repeated one-dimensional stationary phase estimates.

Problems in Fourier restriction theory

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Speaker: 
Dominique Maldague
Zugehörigkeit: 
MPI
Datum: 
Mit, 10/07/2024 - 16:45 - 17:35
Location: 
MPIM Lecture Hall
Parent event: 
Oscillatory integrals in number theory. Number Theory Lunch Seminar jointly with the Hausdorff School

This talk will provide an overview of recent developments in Fourier restriction theory, which one could describe as the study of exponential sums over restricted frequency sets with geometric structure, typically arising in PDE or number theory. Decoupling inequalities measure the square root cancellation behavior of these exponential sums.

 

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