Related papers: Motivic L-Functions
In 2006, the course "Modeling of Organizations" is taught for the third time. This third time will be the second time we will use the new lecture notes "Work Systems Modelling" from the DA VINCI series. These lecture notes, however, will be…
This is an expanded set of notes based on two lectures given by the author at the 2022 IHES summer school on the Langlands program, on explicit techniques for the construction of automorphic representations.
This is a short summary of main results of our paper arXiv:0811.2435 where the concept of motivic Donaldson-Thomas invariant was introduced. It also contains a discussion of some open questions from the loc.cit., in particular, the geometry…
We prove a motivic enhancement of the classical Picard--Lefschetz formula. Our proof is completely motivic, and yields a description of the motivic nearby cycles at a quasi-homogeneous singularity, as well as its monodromy, in terms of an…
Public lecture given at The Fields Institute, June 2, 2005.
The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.
We develop a "motivic integration" version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and obtain…
These are the notes of a lecture held by Michael Hopkins in march 2007, at the Talbot workshop.
The first part of a set of notes based on lectures given at the IHES in May 2015 on Feynman amplitudes and motivic periods.
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
Personal recollections about Alexandre Grothendieck and early days of his theory of motives
The motivic Hilbert zeta function of a variety is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points of the variety. In this paper, the motivic Hilbert zeta function of a reduced curve is…
We define motivic analogues of Igusa's local zeta functions. These functions take their values in a Grothendieck group of Chow motives. They specialize to p-adic Igusa local zeta functions and to the topological zeta functions we introduced…
This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.
We develop notions of integrable functions within the theory of schemic motivic integration.
In this paper, we present a general approach to establish motivic cohomology and build part of its six operations formalism. Applying this together with symplectic orientation on MW-motivic cohomology, we discuss the embedding theorem of…
Given two smooth projective varieties X and Y over a field, we say that X motivates Y if the (suitably defined) motive of Y is contained in the category generated from X by taking sums, summands and products. This notion has appeared…
Mixed Tate motives are central objects in the study of cohomology groups of algebraic varieties and their arithmetic invariants. They also play a crucial role in a wide variety of questions related to multiple zeta values and…
This article is a summary of four introductory lectures on ``Neutrino Experiments,'' given at the 2006 TASI summer school. The purposes were to sketch out the present questions in neutrino physics and to discuss the experimental challenges…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…