Related papers: On the geometry of spherical varieties

A short informal survey on the topics listed in the title. For the proceedings of the International Conference on Rings and Algebras X.

We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.

We discuss invariants in equivariant birational geometry.

Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…

In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective…

In this paper, we explore the structure of the Hitchin map for higher dimensional varieties with emphasis on the case of algebraic surfaces.

This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the…

We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.

In this paper give a survey about L^2-invariants focusing on 3-manifolds.

This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.

These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.

We study a class of 3-dimensional paracontact metric manifolds and we revise some of the results obtain in \cite{SS}.

We lay down the foundations for a systematic study of differentiable and algebraic supervarieties, with a special attention to supergroups.

A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.

This is a survey on recent results on the Loewner theory in one and several complex manifolds

We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…

The theory of permutation orbifolds is reviewed and applied to the study of symmetric product orbifolds and the congruence subgroup problem. The issue of discrete torsion, the combinatorics of symmetric products, the Galois action and…

Computations in the cohomology of finite groups.

We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.

Convex geometry and complex geometry have long had fascinating interactions. This survey offers a tour of a few.