Related papers: Unlikely intersections in Shimura varieties and be…
In this article, we study the question of existence of leafwise intersection points for contact manifolds which are not necessarily of restricted contact type. Moreover we can find a leafwise intersection point on the symplectization for…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
Fano varieties are subvarieties of the Grassmannian whose points parametrize linear subspaces contained in a given projective variety. These expository notes give an account of results on Fano varieties of complete intersections, with a…
The Poincar\'e torsor of a Shimura family of abelian varieties can be viewed both as a family of semi-abelian varieties and as a mixed Shimura variety. We show that the special subvarieties of the latter cannot all be described in terms of…
We give a detailed overview over known results for (no-)collision of a body with the boundary of its container.
I partially review our current knowledge on microquasars, making special emphasis on radio interferometric observations, and I comment on emerging trends in this field of astrophysics.
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
We describe a singular variety associated to the smallest degree Pinchuk map and calculate its intersection homology. The result describes the geometry at infinity of the Pinchuk's map.
The main purpose of this paper is to make Nakayama's theorem more accessible. We give a proof of Nakayama's theorem based on the negative definiteness of intersection matrices of exceptional curves. In this paper, we treat Nakayama's…
Our goal is to provide a survey of some topics in quasiconformal analysis of current interest. We try to emphasize ideas and leave proofs and technicalities aside. Several easily stated open problems are given. Most of the results are joint…
These notes aim to give a first introduction to intersection cohomology and perverse sheaves with applications to representation theory or quantum groups in mind.
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
The purpose of this note is to give a self contained description of Walls finiteness obstruction.
In this note we build on our previous work with Takehiko Yasuda to prove a precise version of inversion of adjunction for varieties which are local complete intersections.
This is a survey of old and recent results about the asymptotic Plateau problem. Our aim is to give a fairly complete picture of the field, and present the current situation.
Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation,…
It will be attempted to present a coherent view on the current ideas regarding the origin of the stripe instability. Special emphasis will be put on the problem of how to combine the microscopic pictures, leaning on spin-charge topological…
We propose an axiomatic approach towards studying unlikely intersections by introducing the framework of distinguished categories. This includes commutative algebraic groups and mixed Shimura varieties. It allows us to define all basic…
The purpose of this note is to share some observations and speculations concerning the asymptotic behavior of Gromov-Witten invariants. They may be indicative of some deep phenomena in symplectic topology that in full generality are outside…
We survey recent joint work with M. Rapoport and W. Zhang related to the arithmetic Gan-Gross-Prasad conjecture for Shimura varieties attached to unitary groups.