Related papers: Derived Categories and Birational Geometry
This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).
This is an expository paper on rationally connected varieties. The aim is to provide an introduction to the subject, as well as to discuss a recent result by T. Graber, J. Harris and J. Starr. The paper is based on the talk I gave at the…
We update the table of large undirected graphs with given degree and diameter with results obtained since the publication of the survey by M. Miller and J. \v{S}ir\'{a}\v{n} in the {\em Electronic Journal of Combinatorics} (Dynamic Survey…
This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
We show how to use information about the equations defining secant varieties to smooth projective varieties in order to construct a natural collection of birational transformations. These were first constructed as flips in the case of…
Lecture notes from a minicourse given at the ICTP in May 2002.
Recent uses of differential geometry in materials science are reviewed here, in particular the September issue of the Phil. Trans. Royal Soc., entitled ``Curvature and chemical Structure.''
We survey several results known on sampling in computational geometry.
The aggregated journal-journal citation matrix derived from the Journal Citation Reports 2001 can be decomposed into a unique subject classification by using the graph-analytical algorithm of bi-connected components. This technique was…
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.
Derived categories were invented by Grothendieck and Verdier around 1960, not very long after the "old" homological algebra (of derived functors between abelian categories) was established. This "new" homological algebra, of derived…
Small, finite entities are easier and simpler to manipulate than gigantic, infinite ones. Consequently huge chunks of mathematics are devoted to methods reducing the study of big, cumbersome objects to an analysis of their finite building…
This is a survey written for a special edition of the journal of differential geometry.
This paper is devoted to derivations in bimodules over group rings using previously proposed methods which are related to character spaces over groupoids. The theorem describing the arising spaces of derivations is proved. We consider some…
We give a corrected version of Corollary 3.33 in: H. Flenner, S. Kaliman, and M. Zaidenberg, Birational transformations of weighted graphs. Affine algebraic geometry. Osaka Univ. Press, 2007, 107-147.
We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics.…
This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…
These are notes from my lecture at 4ECM in Stockholm (June 2004).
This is a submission to the Encyclopedia of Mathematical Physics (Elsevier, 2006) and conforms to its referencing guidelines.