Related papers: Lectures on Springer theories and orbital integral…

Let $G$ be a finite group acting linearly on $\mathbb{R}^n$. A celebrated Theorem of Procesi and Schwarz gives an explicit description of the orbit space $\mathbb{R}^n /\!/G$ as a basic closed semi-algebraic set. We give a new proof of this…

We describe a new relation between the topology of hypersurface complements, Milnor fibers and degree of gradient mappings. In particular we show that any projective hypersurface has affine parts which are bouquets of spheres. The main…

These lecture notes endeavour to collect in one place the mathematical background required to understand the properties of kernels in general and the Random Fourier Features approximation of Rahimi and Recht (NIPS 2007) in particular. We…

These notes were prepared for the introductory lectures on Higher Spin Holography presented at the Twelfth Modave Summer School in Mathematical Physics 2016, aimed at Ph.D. students and researchers new to this topic. Contents: 1. Higher…

This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular…

These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming…

The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…

We give a survey of the theory of affine spheres, emphasizing the convex cases and relationsships to Monge-Ampere equations and geometric structures on manifolds.

These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…

These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of root systems, generalized associahedra, and the combinatorics of clusters. Lectures 1-2 cover classical material:…

Extended affine root systems appear as the root systems of extended affine Lie algebras. A subclass of extended affine root systems, whose elements are called ``minimal" turns out to be of special interest mostly because of the geometric…

Poisson algebras have become an essential topic in mathematics with a rich structure and wide applicability. Despite numerous resources available on Poisson structures, the algebraic side of the story remains relatively less explored. This…

This mini-course of 20 lectures aims at highlights of spectral theory for self-adjoint partial differential operators, with a heavy emphasis on problems with discrete spectrum. Part I: Discrete Spectrum (ODE preview, Laplacian - computable…

These notes represent a much expanded and updated version of the \textquotedblleft mini course\textquotedblright that the author gave at the ETH (Z\"{u}rich) and the University of Z\"{u}rich in February of 1995. The purpose of these notes…

CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing…

Let W be a Weyl group. In my 1984 book a group was attached to any special representation of W using the theory of Springer representations. In this paper we give a new definition of this group which is purely algebraic (no use of geometry…

We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms…

Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.

This is a survey of results on surfaces in noncommutative three-dimensional Lie groups obtained by using the Weierstrass (spinor) representation of surfaces. It is based on the talk given at the conference "Geometry related to the theory of…

In this paper, as a generalization of Kirillov's orbit theory, we explore the relationship between the dressing orbits and irreducible *-representations of the Hopf C*-algebras (A,\Delta) and (\tilde{A}, \tilde{\Delta}) we constructed…