Related papers: Lectures on Seiberg-Witten Invariants
This in an introduction to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. The material is mainly based on the two books of the lecturer, one…
We present a review of the results on the associativity algebras and WDVV equations associated with the Seiberg-Witten solutions of N=2 SUSY gauge theories. It is mostly based on the integrable treatment of these solutions. We consider…
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…
The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants. They may be indicative of some deep phenomena in symplectic topology that in full generality are outside…
A derivation of the Bohm model, and some general comments about it, are given. A modification of the model which is formally local and Lorentz-invariant is introduced, and its properties studied for a simple experiment.
This is an expanded version of the talk I gave at Oberwolfach, MIT and several other universities.
We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a $\star$-product via an abelian twist (e.g. the Groenewold-Moyal twist). The Seiberg-Witten map between…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
Since their introduction in 1994, the Seiberg-Witten invariants have become one of the main tools used in 4-manifold theory. In this thesis, we will use these invariants to identify sufficient conditions for a 3-manifold to fibre over a…
This is the written version of my five lectures at the Banach Center mini-school on "Schubert Varieties", in Warsaw, May 18-22, 2003.
A new diffeomorphism invariant of integral homology 3-spheres is defined using a non-abelian 'quaternionic' version of the Seiberg-Witten equations.
This is an exposition of some recent developments related to the object in the title, particularly the combinatorial computation of the (genus 0) Gromov-Witten invariants of the flag manifold and the quadratic algebra approach. The notes…
These lecture notes provide an elementary introduction, within the framework of finite quantum systems, to recent developments in the theory of entropic fluctuations.
This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…
We present a selection of known as well as new variants of the Sensitivity Conjecture and point out some weaker versions that are also open.
We construct the Seiberg-Witten theory on 3-manifolds with Euclidean ends (connected sums of $\R^3$ and a compact manifold) with perturbations which approximate $*dx_3$ at infinity, and describe the structure of the moduli spaces. The setup…
There have been comments on this paper which point out unclear motivation and definitions on noncommutative momentum introduced. Therefore, this paper is withdrawn by the author for more clear presentation.
These are notes from a basic course in Several Complex Variables
The goal of these lecture notes is to introduce the developing research area of gravitational-wave phenomenology. In more concrete terms, they are meant to provide an overview of gravitational-wave sources and an introduction to the…
Certain aspects of nonrelativistic diffeomorphisms in 2+1 dimensions are investigated. These include a nonrelativistic limit of some relativistic actions in 3 dimensions, the Seiberg-Witten map, a modification of the viscosity tensor in…