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

This is a survey of the language of polyhedral divisors describing T-varieties. This language is explained in parallel to the well established theory of toric varieties. In addition to basic constructions, subjects touched on include…

These notes are the written version of my lectures at the Banach Center mini-school "Schubert Varieties" in Warsaw, May 18-22, 2003. Their aim is to give a self-contained exposition of some geometric aspects of Schubert calculus.

The Witt ring of a complex flag variety describes the interesting -- i.e. torsion -- part of its topological KO-theory. We show that for a large class of flag varieties, these Witt rings are exterior algebras, and that the degrees of the…

We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units.…

We prove that each semi-invariant ring of the complete triple flag of length $n$ is an upper cluster algebra associated to an ice hive quiver. We find a rational polyhedral cone ${\sf G}_n$ such that the generic cluster character maps its…

These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed…

The Khovanov-Springer variety X(n) is a certain subvariety of the variety of flags of length 2n, which has been studied from various different points of view. We give a new proof of the ring structure of the cohomology of X(n) and relate it…

This is a survey of noncommutative generalizations of the spectrum of a ring, written for the Notices of the American Mathematical Society.

In this paper we describe the twisted Hall algebra of bound quiver with small homological dimension. The description is given in the terms of the quadratic form associated with the corresponding bound quiver.

The recent results on hadron multiplicities in heavy and light quark fragmentation, multiplicity local fluctuations and multiparticle correlations submitted to the Conference are reviewed.

A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.

Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.

Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians. For type A flag varieties, we obtain characterizations of flatness, irreducibility and normality of these degenerations via rank tuples. Some of…

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

The earlier work of the first and the third named authors introduced the algebra $\mathbb{A}_{q,t}$ and its polynomial representation. In this paper we construct an action of this algebra on the equivariant K-theory of certain smooth strata…

Important objects of study in $\tau$-tilting theory include the $\tau$-tilting pairs over an algebra on the form $kQ/I$, with $kQ$ being a path algebra and $I$ an admissible ideal. In this paper, we study aspects of the combinatorics of…

Let $\mathcal{M}$ be an abelian model category (in the sense of Hovey). For a large class of quivers, we describe associated abelian model structures on categories of quiver representations with values in $\mathcal{M}$. This is based on…

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

In this article a non--technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras…