Adeel Khan | Sheaf-theoretic Fourier transforms
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2020-11-19

Seminar on A1-topology, motives and K-theory, November 19, 2020
Adeel Khan (IHES)
Sheaf-theoretic Fourier transforms

In the 70's, Sato and Deligne introduced sheaf-theoretic versions of the Fourier transform, which interchange sheaves on a vector bundle with sheaves on its dual.  The Fourier-Sato transform has proven to be a vital tool in microlocal analysis on manifolds, and the Fourier-Deligne transform is similarly important in the theory of l-adic sheaves.  I will talk about a version for motivic sheaves, developed jointly with Cisinski and Zargar, which unifies the Fourier-Sato transform and Laumon's homogeneous variant of the Fourier-Deligne transform.  This leads to a motivic theory of microlocalization which is currently under development.  In another direction, I will describe an extension of the Fourier-Sato transform to perfect complexes and, time-permitting, applications of this in Donaldson-Thomas theory.