Related papers: Derived structures in the Langlands Correspondence
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
In this paper we identify the cotangent to the derived stack of representations of a quiver $Q$ with the derived moduli stack of modules over the Ginzburg dg-algebra associated with $Q$. More generally, we extend this result to finite type…
We study certain complexes of differential forms, including reverse de Rham complexes, on (real or complex) Poisson manifolds, especially holomorphic log-symplectic ones. We relate these to the degeneracy divisor and rank loci of the…
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…
This survey studies equivariant harmonic maps arising from Higgs bundles. We explain the non-abelian Hodge correspondence and focus on the role of equivariant harmonic maps in the correspondence. With the preparation, we review current…
In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…
Let $K$ be a local non-Archimedean field of positive characteristic and let $L$ be the degree-$n$ unramified extension of $K$. Via the local Langlands and Jacquet-Langlands correspondences, to each sufficiently generic multiplicative…
This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.
This article deals with the tamely ramified geometric Langlands correspondence for GL_2 on $\mathbf{P}_{\mathbf{F}_q}^1$, where $q$ is a prime power, with tame ramification at four distinct points $D = \{\infty, 0,1, t\} \subset…
We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are "componentwise" tensor…
Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf…
In this paper, we will consider derived equivalences for differential graded endomorphism algebras by Keller's approaches. First we construct derived equivalences of differential graded algebras which are endomorphism algebras of the…
This is the final paper in the series of five, in which we prove the geometric Langlands conjecture (GLC). We conclude the proof of GLC by showing that there exists a unique (up to tensoring up by a vector space) Hecke eigensheaf…
We develop some foundations for the theory of formal derived algebraic geometry, which parallel the theory of formal spectral algebraic geometry by Jacob Lurie. For this, we establish a close connection between algebro-geometric objects in…
Lattice calculations for hadrons are now entering the domain of resonances and scattering, necessitating a better understanding of the observed discrete energy spectrum. This is a reviewing survey about recent lattice QCD results, with some…
We review Hodge structures, relating filtrations, Galois Theory and Jordan-Holder structures. The prototypical case of periods of Riemann surfaces is compared with the Galois-Artin framework of algebraic numbers.
In this paper we investigate the relationships between envelopes of circle families and some special curves in the plane, such as evolutes, pedals, evolutoids and pedaloids.
We introduce a new approach to constructing derived deformation groupoids, by considering them as parameter spaces for strong homotopy bialgebras. This allows them to be constructed for all classical deformation problems, such as…
We construct exotic Hecke correspondences between the special fibers of different PEL type Shimura varieties, when the local groups are restrictions of scalars of unramified groups. In particular, the local groups themselves are not…