Related papers: Lectures on Factorization of Birational Maps
We construct a factorization theorem that allows to systematically include QCD corrections to the contribution of the electromagnetic dipole operator in the effective weak Hamiltonian to the $\bar B_s \to \mu^+\mu^-$ decay amplitude. We…
We develop a method of quantization for free field theories on manifolds with boundary where the bulk theory is topological in the direction normal to the boundary and a local boundary condition is imposed. Our approach is within the…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
This is the second of a series of papers studying real algebraic threefolds using the minimal model program. The main result is the following. Let $X$ be a smooth projective real algebraic 3-fold. Assume that the set of real points is an…
A brief overview of publications in approximation theory of functions known to the author and connected with scientific publications by V.~K.~Dzyadyk (1919--1998).
We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using…
In this article we use existing machinery to define connective $K$-theory spectra associated to topological ringoids. Algebraic $K$-theory of discrete ringoids, and the analytic $K$-theory of Banach categories are obtained as special cases.…
These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…
We extend Pisier's abstract version of Grothendieck's theorem to general non-locally convex quasi-Banach spaces. We also prove a related result on factoring operators through a Banach space and apply our results to the study of…
We study the (so-called bilinear) factorization problem answered by a weak wreath product (of monads and, more specifically, of algebras over a commutative ring) in the works by Street and by Caenepeel and De Groot. A bilinear factorization…
This thesis comes within the scope of algebraic combinatorics and studies problems related to three orders on permutations: the two said weak orders (right and left) and the strong order or Bruhat order. The first part deals with bases of…
Awfully idiosyncratic lecture notes from CMI summer school in arithmetic geometry July 31-August 4, 2006. Does not include: rationality problems, techniques of the minimal model problem and much of the rest. Includes: Lecture 0: geometry…
An embedding theorem for algebraic systems is presented, basing on a certain old ultrafilter construction. As an application, we outline alternative proofs of some results from the theory of PI algebras, and establish some properties of…
We give a simple quantitative condition, involving the "mapping content" of Azzam--Schul, that implies that a Lipschitz map from a Euclidean space to a metric space must be close to factoring through a tree. Using results of Azzam--Schul…
We give a complete factorization of the invariant factors of resultant matrices built from birational parameterizations of rational plane curves in terms of the singular points of the curve and their multiplicity graph. This allows us to…
This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…
We report on the construction of a factorization theorem for the contribution of the electromagnetic dipole operator ${\cal O}_7$ to the $\bar B_s \to \mu^+\mu^-$ decay amplitude. The leading-order contribution from a QED box diagram…
We exhibit how the Rasiowa-Sikorski Lemma simplifies, in a sense, proofs of results that make use of the technique known as back-and-forth, often resulting in not very illustrative arguments. The first two sections seek to show one simple…
These are lecture notes of a C.I.M.E. course I gave at Cetraro, June 6-11 2005. The theory described is the version of Chen-Ruan's Gromov-Witten theory of orbifolds developed by Graber, Vistoli and me in the algebraic setting, but with…