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We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of…
Let $(\mathfrak{g},[p])$ be a finite dimensional restricted Lie algebra over a perfect field $\mathbbm{k}$ of characteristic $p\!\ge \!3$. By combining methods from recent work of Benson-Carlson \cite{BC20} with those of \cite{CF21,Fa17} we…
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is…
A holographic perspective to study and characterize field spaces that arise in string compactifications is suggested. A concrete correspondence is developed by studying two-dimensional moduli spaces in supersymmetric string…
Let $X$ be a smooth projective and geometrically irreducible curve over the finite field $\mathbb{F}_q$ with $q$ elements and $K$ be its function field. Let $\infty$ be a fixed closed point on $X$ and $A$ be the ring of functions regular…
We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting…
We generalize the notions of the Futaki invariant and extremal vector field of a compact K\"ahler manifold to the general almost-Kahler case and show the periodicity of the extremal vector field when the symplectic form represents an…
We define a new class of completions of locally symmetric varieties of type IV which interpolates between the Baily-Borel compactification and Mumford's toric compactifications. An arithmetic arrangement in a locally symmetric variety of…
In this article we perform an extensive study of the spaces of automorphic forms for GL(2) of weight two and level N, for N an ideal in the ring of integers of the quartic CM field generated by the twelfth roots of unity. This study is…
Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data - S, T and fusion matrices - are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain…
We introduce a theory of motivic cohomology for quasi-compact quasi-separated schemes, which generalises the construction of Elmanto--Morrow in the case of schemes over a field. Our construction is non-$\mathbb{A}^1$-invariant in general,…
We prove a compactness result for gradient flow lines in a general set-up which comprises both the situation of Morse gradient flow lines as well as Floer cylinders converging to a critical submanifold respectively. For the compactness…
The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this…
We elaborate an explicit version of the relative trace formula on $\PGL(2)$ over a totally real number field for the toral periods of Hilbert cusp forms along the diagonal split torus. As an application, we prove (i) a spectral…
Using the framework relating hypergeometric motives to modular forms, we define an explicit family of weight 2 Hecke eigenforms with complex multiplication. We use the theory of ${}_2F_1(1)$ hypergeometric series and Ramanujan's theory of…
Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the Laplacian and are quite distinct from Maass forms. These…
This paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear Monge-Amp\'ere equation and a transport equation. The system is the Eulerian formulation in the dual…
We prove generic regularity and Uhlenbeck-type compactification theorems for the moduli spaces of PU(2)-monopoles. Generic regularity is NOT obtained in the usual way (by applying Sard theorem to a smooth parameterized moduli space), since…