Related papers: Lectures on Seiberg-Witten Invariants
In this note we elaborate on a recent counter-example to the Nelson-Seiberg theorem and to its generalizations. We provide sufficient conditions for the existence of such counter-examples, finding new ones. We claim that these…
This survey on flexible Weinstein manifolds is, essentially, an extract from our recent joint book.
This paper is a contribution to Vinberg's theory of $\theta$-groups, or in other words, to Invariant Theory of periodically graded semisimple Lie algebras. One of our main tools is Springer's theory of regular elements of finite reflection…
Recently the Fermi GBM and LAT Collaborations reported their new observational data disfavoring quite a number of the quantum gravity theories, including the one suggesting the nonlinear (logarithmic) modification of a quantum wave…
These are lecture notes on string theory at Fudan University.
A topological gauge invariant lagrangian for Seiberg-Witten monopole equations is constructed. The action is invariant under a huge class of gauge transformations which after BRST fixing leads to the BRST invariant action associated to…
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…
This note proposes a new notion of a gradient-like vector field and discusses its implications for the theory of Stein and Weinstein structures.
This is an English translation of the expository article written by the author in Japanese for publication in {\em Sugaku}. The author will explain Milnor invariants from the viewpoint of his research.
We study moduli spaces of Seiberg-Witten monopoles over spin^c Riemannian 4-manifolds with long necks and/or tubular ends. This first part discusses compactness, exponential decay, and transversality. As applications we prove two vanishing…
These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this…
This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December~20--23, 2004, at the Indian Statistical Institute, Kolkata. The lecture…
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.
Lecture notes for an introductory course in elementary particles.
A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.
These notes are based on a lecture course by L. Chekhov held at the University of Manchester in May 2006 and February-March 2007. They are divulgative in character, and instead of containing rigorous mathematical proofs, they illustrate…
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in…
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating…
In this paper we define the basic concepts for left or right Leibniz algebras and prove some of the main results. Our proofs are often variations of the known proofs and several results seem to be new.