Characteristic functions and functional models on noncommutative varieties

Operator Theory on Noncommutative Varieties

We develop a dilation theory for row contractions T := [T1, . . . , Tn] subject to constraints such as p(T1, . . . , Tn) = 0, p ∈ P , where P is a set of noncommutative polynomials. The model n-tuple is the universal row contraction [B1, . . . , Bn] satisfying the same constraints as T , which turns out to be, in a certain sense, the maximal constrained piece of the n-tuple [S1, . . . , Sn] of ...

Models of Shimura varieties in mixed characteristic

FUNCTIONAL CALCULUS AND SQUARE FUNCTIONS ON NONCOMMUTATIVE L p - SPACES

In this work we investigate semigroups of operators acting on noncommutative L-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H∞ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, q-Ornstein-Uhlenbeck semigroups, and the noncommutative Poiss...

Minimal Noncommutative Varieties and Power Varieties

A variety of finite monoids is a class of finite monoids closed under taking submonoids, quotients and finite direct products. A language L is a subset of a finitely generated free monoid. The variety theorem of Eilenberg sets up a one to one correspondence between varieties of finite monoids and classes of languages called, appropriately, varieties of languages. Recent work in variety theory h...

Noncommutative L-functions for for varieties over finite fields

In this article we prove a Grothendieck trace formula for L-functions of not necessarily commutative adic sheaves.