Related papers: A survey of J-spaces
The paper presents a counterexample to the Hodge conjecture.
An exposition of the basic geometry of twistor integrals, intended for mathematicians.
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some…
This is an expository survey of the Jacobian problem for the class of Pluriharmonic functions.
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane curves using the…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
The purpose of this note is to give a self contained description of Walls finiteness obstruction.
The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.
Methods for the statistical characterization of the large-scale structure in the Universe will be the main topic of the present text. The focus is on geometrical methods, mainly Minkowski functionals and the J-function. Their relations to…
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
Some comments are made on the usefulness or otherwise of the concept of `expanding space' in cosmology. These notes are an expanded version of material first published in 2001 but not previously available online except at…
These notes deal with some recent assertions about truncations $f \mapsto |f|$ and compositions $f \mapsto g\circ f$ in the spaces $A^s_{p,q}(\mathbb{R}^n)$, $A \in \{B,F \}$.
It is shown that, in a generalized S-space-form, $F_{7}$ always equals $F_{8}$.
The aim of these lecture notes is, after having quickly described various compactifications of the Teichm\"{u}ller space of a compact connected oriented surface minus finitely many points, to give a construction, by the equivariant Gromov…
In this paper, we give a class of reconstructible graphs.
The space of smooth curves admits a beautiful compactification by the moduli space of Deligne-Mumford stable curves. In this paper, we undertake a systematic investigation of alternate modular compactifications of the space of smooth…
This is a survey note of the author's observations on the discrete-time analogues of It\^o formulas.