Related papers: Recent developments and open problems in linear se…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
This volume contains the papers presented at LINEARITY 2016, the Fourth International Workshop on Linearity, held on June 26, 2016 in Porto, Portugal. The workshop was a one-day satellite event of FSCD 2016, the first International…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
This is the expanded version of my talk at the workshop "Groups of Automorphisms in Birational and Affine Geometry", October 29--November 3, 2012, Levico Terme, Italy. The first section is focused on Jordan groups in abstract setting, the…
This short note gives an overview of how a few conjectures and theorems of the author and collaborators fit together. It was prepared for Oberwolfach's workshop Differentialgeometrie im Gro{\ss}en, 28 June - 4 July 2015, and contains no new…
Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.
Extended abstract for the workshop "Geophysical Fluid Dynamics " held in Oberwolfach, 17 February - 23 February 2013, to be published by the Mathematisches Forschungsinstitut Oberwolfach in the "Oberwolfach Reports" series.
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
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 work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…
This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (19-24 January 2020). It introduces a geometric orbifold model for the bounded derived category of a skew-gentle…
This paper surveys some applications of moduli theory to issues concerning the distribution of rational points on algebraic varieties. It will appear on the proceedings of the Fano Conference.
These are extended lecture notes for a mini course at the Spring School on Non-Archimedean Geometry and Eigenvarieties held at Heidelberg University in March 2023. The goal of the course is to explain a modern take on the eigenvariety…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
This volume contains a selection of the papers presented at the 2nd International Workshop on Linearity (LINEARITY'2012), which took place 1 April 2012 in Tallinn, Estonia. The workshop was a one-day satellite event of ETAPS 2012, the 15th…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
We develop a moduli theory of algebraic varieties and pairs of non-negative Kodaira dimension. We define stable minimal models and construct their projective coarse moduli spaces under certain natural conditions. This can be applied to a…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…