Related papers: Quivers of type A, flag varieties and representati…

This note defines a flag vector for $i$-graphs. The construction applies to any finite combinatorial object that can be shelled. Two possible connections to quantum topology are mentioned. Further details appear in the author's "On quantum…

I give a summary of Section E of the seventh edition of the Conference ''Quark confinement and the hadron spectrum". Papers were presented on different subjects, from spectroscopy, including pentaquarks and hadron structure, to the quest…

Here is a list of chapters: 1 Introduction 2 Notation and preliminaries Part I: Finite quantum groups 3 2x2 Matrix quantum groups and the quantum plane 4 Quantum enveloping algebras at a root of unity Part II: q-Oscillators 5…

These are notes for a minicourse on Hall algebras given at the ICTP in Trieste in January 2006. After giving the definition and first properties of Hall algebras, we study in some details the classical Hall algebra, the Hall algebra of…

In this revised version, we add some expository material and references and make some minor corrections.

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…

In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…

In a previous paper we defined the concept of an affinized projective variety and its associated Hilbert series. We computed the Hilbert series for varieties associated to quadratic monomial ideals. In this paper we show how to apply these…

This work surveys classical and recent advances around the existence of exotic differentiable structures on spheres and its connection to stable homotopy theory.

We discuss the possibility of very regular subgroups of a Lie group, in presence of an index figure. Further, representations that reduce action to a very regular boundary.

This is a brief introduction to the quiver Hecke algebras of Khovanov, Lauda and Rouquier, emphasizing their application to the categorification of quantum groups. The text is based on lectures given by the author at the ICRA workshop in…

Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…

In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost…

Notes of an introductory course given at the conference "Torsors: Theory and Applications" in Edinburgh, January 2011.

The main goal of this paper is to give a unified description for the structure of the small quantum cohomology rings for all homogeneous spaces of SL_n(C).

We show that representations of convolution algebras such as Lustzig's graded affine Hecke algebra or the quiver Hecke algebra and quiver Schur algebra in (affine) type A can be realised in terms of certain equivariant motivic sheaves…

These are the notes for a minicourse held in Odessa (2016) and Belo Horizonte (2017). My aim was to provide a short introduction to basic notions of category theory and representation theory of finite-dimensional algebras. We learnt the…

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

These informal notes briefly discuss Fourier inversion in terms of Gauss--Weierstrass kernels and summability.

This paper discusses consistent flag bicolorings of maps and maniplexes, in their own right and as generalizations of orientations and pseudo-orientations. Furthermore, a related doubling concept is introduced, and relationships between…