5 papers
Jacobian graphs
Arthur Forey, Javier Fresán, Emmanuel Kowalski +1
We introduce jacobian graphs, which are explicit families of regular graphs that are spectrally indistinguishable from random graphs, but whose local structure is very different fr…
A motivic Fundamental Lemma
Arthur Forey, François Loeser, François Loeser +1
In this paper we prove motivic versions of the Langlands-Shelstad Fundamental Lemma and Ngô's Geometric Stabilization. To achieve this, we follow the strategy from the recent proof…
Spectrally indistinguishable pseudorandom graphs
Arthur Forey, Javier Fresán, Emmanuel Kowalski +1
We construct explicit families of graphs whose eigenvalues are asymptotically distributed according to Wigner's semicircle law; in other words, that are spectrally indistinguishabl…
Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution
Arthur Forey, Javier Fresán, Emmanuel Kowalski
We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of…
Fixed-point statistics from spectral measures on tensor envelope categories
Arthur Forey, Javier Fresán, Emmanuel Kowalski
We prove some old and new convergence statements for fixed-points statistics using tensor envelope categories, such as the Deligne--Knop category of representations of the "symmetr…