Related papers: LS-Galleries, the path model and MV-cycles

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $\Gamma$-spaces. We show that equivariant principal $G$-bundles over split $\Gamma$-CW complexes $X$ can be effectively classified by means of…

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…

Let $G$ be a linear connected non-compact real simple Lie group and let $K\subset G$ be a maximal compact subgroup of $G$. Suppose that the centre of $K$ isomorphic to $\mathbb{S}^1$ so that $G/K$ is a global Hermitian symmetric space. Let…

We construct a mathematical theory of Witten's Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with non-Abelian gauge group. Both the Gromov-Witten theory of a Calabi-Yau complete…

Let $S$ be a closed oriented surface and $G$ a finite group of orientation preserving automorphisms of $S$ whose orbit space has genus at least $2$. There is a natural group homomorphism from the $G$-centralizer in $Diff^+(S)$ to the…

We generalise the analysis carried out in [arXiv:0710.5796], and find that our previous results can be extended beyond the case of SL(N,C). In particular, we show that an equivalence--at the level of the holomorphic chiral algebra--between…

In this doctoral thesis, we will determine the image of Artin groups associated to all finite irreducible Coxeter groups inside their associated finite Iwahori-Hecke algebra. This was done in type $A$ by Brunat, Magaard and Marin. The…

We study the periodic cyclic homology groups of the cross-product of a finite type algebra $A$ by a discrete group $\Gamma$. In case $A$ is commutative and $\Gamma$ is finite, our results are complete and given in terms of the singular…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

Let G be a semisimple group over an algebraically closed field. Steinberg has associated to a Coxeter element w of minimal length r a subvariety V of G isomorphic to an affine space of dimension r which meets the regular unipotent class Y…

This work explores the topological properties of virtual Artin groups, a recent extension of the ``virtual" concept - initially developed for braids - to all Artin groups, as introduced by Bellingeri, Paris, and Thiel. For any given Coxeter…

The purpose of the present article is to show the multilinearity for symbols in Goodwillie-Lichtenbaum complex in two cases. The first case shown is where the degree is equal to the weight. In this case, the motivic cohomology groups of a…

We prove that geometric intersections between Weinstein handles induce algebraic relations in the wrapped Fukaya category, which we use to study the Grothendieck group. We produce a surjective map from middle-dimensional singular cohomology…

We extend the theory of combinatorial link Floer homology to a class of oriented spatial graphs called transverse spatial graphs. To do this, we define the notion of a grid diagram representing a transverse spatial graph, which we call a…

Let $S$ be a compact Riemann surface and $G$ a group of conformal automorphisms of $S$ with $S_0 = S/G$. $S$ is a finite regular branched cover of $S_0$. If $U$ denotes the unit disc, let $\Gamma$ and $\Gamma_0$ be the Fuchsian groups with…

We study the equivariant cohomology of spherical perverse sheaves on the affine Grassmannian of a connected reductive group $G$ with support in the affine Grassmannian of any Levi subgroup $L$ of $G$. In doing so, we extend the work of…

Let G be a simply-connected simple compact Lie group over the complex numbers. The affine Grassmannian is a projective ind-variety, homotopy-equivalent to the loop space of G and closely analogous to a maximal flag variety of the classical…

We begin with a short exposition of the theory of lattice varieties. This includes a description of their orbit structure and smooth locus. We construct a flat cover of the lattice variety and show that it is a complete intersection. We…

Consider $(G, V)$ a finite-dimensional representation of a connected reductive complex Lie group $G$ and $\mathbb{P}\left( V\right) $ the projective space of $V$. Denote by $G'$ the derived subgroup of $G$ and assume that the categorical…

Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…