Related papers: Twisted geometric Langlands correspondence for a t…
Orthogonal projections of the uniform measure on the Sierpinski triangle form a family of self similar measures with overlaps. The main result of this work is to make a connection between the dimension theory of these measures and the…
We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as…
This paper introduces and studies generalized degenerate Clifford and Lipschitz groups in geometric (Clifford) algebras. These Lie groups preserve the direct sums of the subspaces determined by the grade involution and reversion under the…
Harris and Taylor proved that the supercuspidal part of the cohomology of the Lubin-Tate tower realizes both the local Langlands and Jacquet-Langlands correspondences, as conjectured by Carayol. Recently, Boyer computed the remaining part…
This communication is an introduction to the Langlands Program and to ($G$-) shtukas (over algebraic curves) over function fields. Modular curves and Drinfeld (elliptic) modules and shtukas are used in coding theory. From this point of view…
We propose a generalisation of the Jacquet-Langlands correspondence to the whole Grothendieck group of finite lenght admissible representations. As an application we prove some particular cases of the global Jacquet-Langlands…
Let G be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group ^LG in terms of spherical perverse sheaves (or D-modules) on the affine Grassmannian Gr_G=G((t))/G[[t]] of the…
In this paper we give the description of generic representations of metaplectic groups over p-adic fields in terms of their Langlands parameters and calculate their theta lifts on all levels for any tower of odd orthogonal groups. We also…
We develop a generic geometric formalism that incorporates both $T\bar{T}$-like and root-$T\bar{T}$-like deformations in arbitrary dimensions. This framework applies to a wide family of stress-energy tensor perturbations and encompasses…
We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto-Witten theory with linear matter.…
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally…
This paper presents geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL(2,R) group. We describe here geometries of…
We define and study twisted Alexander-type invariants of complex hypersurface complements. We investigate torsion properties for the twisted Alexander modules and extend classical local-to-global divisibility results to the twisted setting.…
The purpose of this paper is threefold: First of all the topological aspects of the Landau Hamiltonian are reviewed in the light (and with the jargon) of theory of topological insulators. In particular it is shown that the Landau…
Our main goal is to show that the Gelfand--Tsetlin toric degeneration of the type A flag variety can be obtained within a degenerate representation-theoretic framework similar to the theory of PBW degenerations. In fact, we provide such…
We study Gromov-Witten theory of hypertoric Deligne-Mumford stacks from two points of view. From the viewpoint of representation theory, we calculate the operator of small quantum product by a divisor, following \cite{BMO}, \cite{MO},…
We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects…
We study torsion in the homology of arithmetic groups and give evidence that it plays a role in the Langlands program. We prove, among other results, a numerical form of a Jacquet--Langlands correspondence in the torsion setting.
The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures…
We explain how the geometric Langlands program inspires some recent new prospectives of classical arithmetic Langlands program and leads to the solutions of some problems in arithmetic geometry.