Ilya Shkredov: Higher Sumsets and Energies in Additive Combinatorics and Number Theory (NTWS 222) 

Abstract: We provide an overview of the results obtained by the method of higher sumsets and higher energies to some problems of additive combinatorics (the sum-product phenomenon and incidence geometry, universality, additive decomposition, etc.), number theory (exponential sums over subgroups and Gauss sums, sums with multiplicative characters, the square-root barrier), Fourier analysis (uncertainty principle) and others. We will also discuss some perspectives for this approach.
Link to slides: drive.google.c...
Number Theory Web Seminar: www.ntwebsemin...
Original air date:
Thursday, October 3, 2024 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, October 4, 2024 (1am AEDT, 4am NZDT)