Related papers: A geometric approach to large class groups: a surv…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…
We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.
We have found a "non-purely-constructive" method of acquiring algebraic cycles involving multiple steps. This note tries to present the main idea in the last step by concentrating on an example of 4-folds. The method demonstrates a contrast…
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular,…
This note is a survey of $J$-spaces.
In this work we study, in greater detail than before, J.H. Conway's topographs for integral binary quadratic forms. These are trees in the plane with regions labeled by integers following a simple pattern. Each topograph can display the…
The goal of this survey is to give a list of resent results about topology of manifolds admitting different metrics with the same geodesics. We emphasize the role of the theory of integrable systems in obtaining these results.
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
We use class field theory to search for curves with many rational points over small finite fields. By going through abelian covers of curves of small genus we find a number of new curves. In particular, we settle the question of how many…
In this expository article, we survey the rapidly emerging area of random geometric simplicial complexes.
A general proposition is proved relating multiplicities (of restriction of a representation of a group to a subgroup) under basechange, and used to calculate some multiplicities for cuspidal representations which become principal series…
This survey paper, written in spanish, is an extended version of lecture notes for a mini-course taught at the 2022 Summer School in Geometric Group Theory, which took place in the Centro de Ciencias Matem\'aticas in Morelia, Mexico in July…
In this paper we study a certain class of polycyclic groups. We outline a method for constructing a poly-$\mathbb{Z}$ group $G_n$ by describing a process for selecting maps that are used to extend $G_i$ to $G_{i+1}$ for $1 \leq i \leq n-1$…
This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.