Related papers: Recent developments and open problems in linear se…
This volume contains a selection of papers presented at Linearity&TLLA 2020, namely the Second Joint International Workshop on Linearity & Trends in Linear Logic and Applications, held on June 29-30, 2020 online. (The workshop was supposed…
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining…
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.
This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, $\mathcal{U}$-frequent hypercyclicity, reiterative hypercyclicity, operators of C-type, Li-Yorke and…
These are lecture notes for a short course about spectral sequences that was held at M\'alaga, October 18--20 (2016), during the "Fifth Young Spanish Topologists Meeting". The approach was to illustrate the basic notions via fully computed…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
This document contains notes from the lectures of Corti, Koll\'ar, Lazarsfeld, and Musta\c{t}\u{a} at the workshop ``Minimal and canonical models in algebraic geometry" at MSRI, Berkeley, April 2007. The lectures give an overview of the…
These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…
This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. The emphasis is on the interplay between regularity,…
These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were…
These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected…
This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.
We describe the boundary of linear subvarieties in the moduli space of multi-scale differentials. Linear subvarieties are algebraic subvarieties of strata of (possibly) meromorphic differentials that in local period coordinates are given by…
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.
ICM lecture on minimal models and moduli of varieties.
For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
These are the lecture notes of a 2-hour mini-course on Lie groups over local fields presented at the "Workshop on Totally Disconnected Groups, Graphs and Geometry" at the Heinrich-Fabri-Institut Blaubeuren in May 2007. The goal of the notes…
The paper gives a collection of open problems on abstract polytopes that were either presented at the Polytopes Day in Calgary or motivated by discussions at the preceding Workshop on Convex and Abstract Polytopes at the Banff International…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…