Related papers: Intrinsic Mirrors for Minimal Adjoint Orbit (ICM G…
These are notes from the lectures I gave at the Oberwolfach seminar `Tensor Triangular Geometry and Interactions' which was held in October 2025. The aim of these notes is to give an introduction to tensor triangular geometry, for both…
This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)
This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of…
This is an expository paper about applications of ruled surface theory in incidence geometry. It surveys the results that have been proven, gives an overview of the methods, and discusses some open problems and further directions. It will…
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.
We propose and prove a mirror theorem for the elliptic quasimap invariants for smooth Calabi-Yau complete intersections in projective spaces. The theorem combined with the wall-crossing formula appeared in paper (arXiv:1308.6377) implies…
The purpose of this note is to correct an inaccuracy in the paper: R.P. Agaev and P.Yu. Chebotarev, "On Determining the Eigenprojection and Components of a Matrix," Autom. Remote Control, 2002, vol. 63, pp. 1537-1545 [arXiv:math/0508197],…
This is an appendix to the Handbook of Tilting Theory, edited by Angeleri-Huegel, Happel and Krause, to be published soon. Part 1 of the appendix provides an outline of the core of tilting theory. Part 2 is devoted to topics where tilting…
In these lectures my aim is to review enough of conformal differential geometry in four dimensions to give an account of Penrose's conformal cyclic geometry.
Mostly inspired by recent work by Katzarkov, Kontsevich, and Sheshmani, combined with previous work by Aganagic, Ooguri, Saulina and Vafa with regard to BPS black hole microstate counting in terms of topological field theory calculations,…
On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the…
We sketch an assortment of problems that were posed -- and not yet solved -- during problem sessions at the conference ``Approximation Theory and Numerical Analysis meet Algebra, Geometry, and Topology'', which was held at the Palazzone…
This is a written version of the invited lecture at the 9th European Congress of Mathematics in July 2024 in Sevilla. We review certain new symmetries of Grothendieck rings that have emerged in representation theory.
This paper is a survey of some of the developments in coarse extrinsic geometry since its inception in the work of Gromov. Distortion, as measured by comparing the diameter of balls relative to different metrics, can be regarded as one of…
This article is an extended version of the minicourse given by the second author at the summer school of the conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification", held in June…
It is shown that for any two compact metric spaces there exists an "optimal" correspondence which the Gromov-Hausdorff distance is attained at. Each such correspondence generates isometric embeddings of these spaces into a compact metric…
These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight…
We summarize the main results of 19 talks presented at the QG3 session (loop quantum gravity: cosmology and black holes) of the 16th Marcel Grossmann Meeting held online from July $5^{\mathrm{th}}$-10$^{\mathrm{th}}$, 2021.
It is proved that the Gromov-Hausdorff metric on the space of compact metric spaces considered up to an isometry is strictly intrinsic, i.e., the corresponding metric space is geodesic. In other words, each two points of this space (each…
This is the extended abstract of the talk given at the workshop "Geometry and physics of Higgs bundles", held at the Mathematisches Forschungsinstitut Oberwolfach in May 2019.