Related papers: Quiver Grassmannians and their Euler characteristi…
This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…
The Euler characteristic of the link of a real algebraic variety is an interesting topological invariant in order to discuss local topological properties. We prove in the paper that an invariant stronger than the Euler Characteristic is…
Let G be a finite, complex reflection group and f its discriminant polynomial. The fibers of f admit commuting actions of G and a cyclic group. The virtual $G\times C_m$ character given by the Euler characteristic of the fiber is a…
It is well known that the Euler characteristic of the cohomology of a complex algebraic variety coincides with the Euler characteristic of its cohomology with compact support. An old result of G. Laumon asserts that a relative version of…
We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…
Let I be a finite set and CI be the algebra of functions on I. For a finite dimensional C algebra A with \CI contained in A we show that certain moduli spaces of finite dimsional modules are isomorphic to certain Grassmannian (quot-type)…
Here we review background in differential topology related to the calculation of an euler characteristic, and background on localization in equivariant cohomology. We then outline Gromov-Witten invariants in algebraic geometry and give…
We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.
This short note is an extended abstract for my talk at the Nottingham Online Algebraic Geometry Seminar on October 1, 2020. It is based on the joint works with Alexander Kuznetsov arXiv:1802.08097 and arXiv:2001.04148.
This is an extended abstract of my talk at the Oberwolfach Workshop ''Cluster Algebras and Related Topics'' (December 8 - 14, 2013). It is based on a joint work with A. Zelevinsky (arXiv:1306.3495).
This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…
These are the notes from lectures I gave at the Oberwolfach Seminar "Tensor Triangular Geometry and Interactions" which was held in October 2025. The aim of these notes is twofold: We develop notions of support for triangulated categories,…
We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop quite a general framework of noncommutative complex geometry that subsumes the one in [2]. We present transverse complex and K\"ahler…
We discuss how metric limits and rescalings of K\"ahler-Einstein metrics connect with Algebraic Geometry, mostly in relation to the study of moduli spaces of varieties, and singularities. Along the way, we describe some elementary examples,…
In this talk we recall some concepts of Noncommutative Gauge Theories. In particular, we discuss the q-deformed two-dimensional Euclidean Plane which is covariant with respect to the q-deformed Euclidean group. A Seiberg-Witten map is…
In this paper, we define the non-commuting graph associated to a Lie algebra L and obtain some basic graph properties such as connectivity, diameter, girth, Hamiltonian and Eulerian. Moreover, planarity, outer planarity and isomorphism…
This is the written version of my five lectures at the Banach Center mini-school on "Schubert Varieties", in Warsaw, May 18-22, 2003.
The Grothendieck-Ogg-Shafarevich formula expresses the Euler characteristic of an etale sheaf on a curve in terms of local data. The purpose of this paper is to prove a version of the G-O-S formula which applies to equicharacteristic…
In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of…
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.