Related papers: Cartan decomposition for complex loop groups

Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We…

Using tools from the theory of Lie groupoids, we study the category of logarithmic flat connections on principal $G$-bundles, where $G$ is a complex reductive structure group. Flat connections on the affine line with a logarithmic…

We construct a family of plane curves as pull-backs of a conic for abelian coverings of P^2. If the conic is tangent to the ramification lines one obtains a family of curves of degree 2n with 3n singularities of type A_{n-1}. We calculate…

We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers. In doing so, we unify some matrix decompositions: For…

We survey some recent advances in the homotopy theory of classifying spaces, and homotopical group theory. We focus on the classification of p-compact groups in terms of root data over the p-adic integers, and discuss some of its…

We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…

After summarising the physical approach leading to twisted homotopy and after developing the cohomological approach further with respect to our previous work we propose a third alternative approach to twisted homotopy based on group…

The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in…

For all n > 0 there is a homomorphism from the smooth concordance group of knots in dimension 2n + 1 to an algebraically defined group called the rational algebraic concordance group. This algebraic concordance group splits as a direct sum…

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…

We construct an explicit, embedded degeneration of the general torus orbit closure in the maximal orthogonal Grassmannian OG(n,2n+1) into a union of Richardson varieties. In particular, we deduce a formula for the cohomology class of the…

Part of these notes was written as the author's 2013 master thesis. For proper flat schemes over a complete discrete valuation ring of mixed characteristic, we construct an isomorphism of certain subgroups of the Picard group and the first…

A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…

This paper gives an extension of the classical Zariski-van Kampen theorem describing the fundamental groups of the complements of plane singular curves by generators and relations. It provides a procedure for computation of the first…

In this paper we compute the homotopy groups of the symplectomorphism groups of the 3-, 4- and 5-point blow-ups of the projective plane (considered as monotone symplectic Del Pezzo surfaces). Along the way, we need to compute the homotopy…

The motivation of this paper is to construct a deformation theory of coderivations of coassociative coalgebras. We introduce a notion of a Coder pair, that is, a coassociative coalgebra with a coderivation. Then we define a proper…

We show how wall-crossing formulas in coupled 2d-4d systems, introduced by Gaiotto, Moore and Neitzke, can be interpreted geometrically in terms of the deformation theory of holomorphic pairs, given by a complex manifold together with a…

Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are few explicit examples of stratifications. The main goal of this paper is to construct…

We compute the topological complexity of Eilenberg-Mac Lane spaces associated to the group of automorphisms of a finitely generated free group which act by conjugation on a given basis, and to certain subgroups.

This is a survey paper dealing with holomorphic G-structures and holomorphic Cartan geometries on compact complex manifolds. Our emphasis is on the foliated case: holomorphic foliations with transverse (branched or generalized) holomorphic…