Related papers: A pamphlet on motivic cohomology
This is an informal and mostly expository note describing some asymptotic behavior and qualitative properties of the q-binomial coefficients. The results are mostly not new, but the overall story we present does not seem to be well known --…
This paper aims to answer the following question: Given an adjunction between two categories, how is Quillen (co)homology in one category related to that in the other? We identify the induced comparison diagram, giving necessary and…
An expository hitchhikers guide to some theorems in mathematics.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath…
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.
This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.
We propose an action of a certain motivic cohomology group on the coherent cohomology of Hilbert modular varieties, extending conjectures of Venkatesh, Prasanna, and Harris. The action is described in two ways: on cohomology modulo $p$ and…
We give an elementary description of the space of formal periods of a mixed motive. This allows for a simplified reformulation of the period conjectures of Grothendieck and Kontsevich-Zagier. Furthermore, we develop a machinery which in…
The purpose of this sophomore-level textbook is twofold: to introduce the student to classical electrodynamics and, at the same time, explain in simple terms the quantum theory of conducting substances (in particular, the solid ones). The…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
In quantum mechanics, not everything that can be observed can be observed simultaneously. Observational data exhibits \emph{contextuality} -- a generalisation of nonlocality -- if the result of an observation is necessarily dependent on…
These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent developments in the field of reciprocity sheaves.
We generalize some classical results on Chow group of an abelian variety to semiabelian varieties and to motivic (co)homology, using a result of Ancona--Enright-Ward--Huber on a decomposition of the motive of a semiabelian variety in the…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
This text consists on a series of introductory lectures on cosmology for mathematicians and physicists who are not specialized on the subject.
We develop the theory of motivic integration for formal schemes
We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.