Related papers: Explicit Shimura's conjecture for Sp3 on a compute…

We use E. Lau's classification of 2-divisible groups using Dieudonn\'e displays to construct integral canonical models for Shimura varieties of abelian type at 2-adic places where the level is hyperspecial. We apply this to prove the Tate…

Shimura curves are moduli spaces of abelian surfaces with quaternion multiplication. Models of Shimura curves are very important in number theory. Klein's icosahedral invariants $\mathfrak{A},\mathfrak{B}$ and $\mathfrak{C}$ give the…

Recently, Gunningham \cite{G} calculated all spin Hurwitz numbers in terms of combinatorics of Sergeev algebra. In this paper, we use a spin curve degeneration to obtain a recursion formula for degree three spin Hurwitz numbers.

Let $\Lambda$ be an order in a division algebra over a number field. We prove, under some conditions, that $SL_3(\Lambda)$ is boundedly generated by elementary matrices.

We present an alternative approach to the result of Guentner, Higson, and Weinberger concerning the Baum-Connes conjecture for finitely generated subgroups of SL(2,C). Using finite-dimensional methods, we show that the Baum-Connes assembly…

Let S be a nonsingular projective K3 surface. Motivated by the study of the Gromov-Witten theory of the Hilbert scheme of points of S, we conjecture a formula for the Gromov-Witten theory (in all curve classes) of the Calabi-Yau 3-fold S x…

In this article we continue to develop the theory of generating symmetries for integrable equations. A technique for computation of generating symmetries using Maple is presented. The technique is based on the standard symmetry method. By…

We formulate an integral Frobenius period map for the framed crystalline prismatization of the $p$-integral model $\mathcal{S}$ of a Shimura variety with good reduction. By analyzing reductions of this map, we derive a period map from the…

We explore a generalization of the Markov numbers that is motivated by a specific generalized cluster algebra arising from an orbifold, in the sense of Chekhov and Shapiro. We give an explicit algorithm for computing these generalized…

Recently we have presented in hep-th/9811071 an ansatz which allows us to construct skyrmion fields from the harmonic maps of $S\sp2$ to $CP\sp{N-1}$. In this paper we examine this construction in detail and use it to construct, in an…

We compute the monodromy group of irreducible holomorphic symplectic manifolds of OG10 type, confirming a conjecture of Markman.

The local Langlands conjectures imply that to every generic supercuspidal irreducible representation of $G_2$ over a $p$-adic field, one can associate a generic supercuspidal irreducible representation of either $PGSp_6$ or$PGL_3$. We prove…

In this paper we establish an exponential covering theorem implying a conjecture formulated by A. Zygmund circa 1935 whose three-dimensional case was obtained by the first named author in 1978.

We prove that if an $n$-vertex graph with minimum degree at least $3$ contains a Hamiltonian cycle, then it contains another cycle of length $n-o(n)$; this implies, in particular, that a well-known conjecture of Sheehan from 1975 holds…

We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its orbifold generalization, the $qr$-ELSV…

We use the generalised rational map ansatz introduced by Ioannidou et al. to construct analytically some topologically non-trivial solutions of the generalised SU(3) Skyrme model defined by adding a sixth order term to the usual Lagrangian.…

Analogous to the sl(n) case, we address the computation of the index of seaweed subalgebras of sp(2n) by introducing graphical representations called symplectic meanders. Formulas for the algebra's index may be computed by counting the…

In this paper, we will give another proof of Zhi-Wei Sun's three conjectures on Ap\'{e}ry-like sums involving harmonic numbers by proving some identities among special values of multiple polylogarithms.

We consider the three conjectures stated in a 2003 paper of Wu, concerning the asymptotics of particular sums of products of binomials, powers and logarithms. These sums relate to the form of the regularised integrals used in loop…

Let S be a K3 surface obtained as triple cover of a quadric branched along a genus 4 curve. Using the relation with cubic fourfolds, we show that S has finite dimensional motive, in the sense of Kimura. We also establish the Kuga-Satake…