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Lax pair and Hamiltonian formulations of the N=4 supersymmetric Toda chain (KdV) hierarchy in N=4 superspace are proposed. The general formulae for the infinite tower of its bosonic flows in terms of the Lax operator in N=4 superspace are…
Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect…
Jacobi's elliptic functions have been constructed from a deformed Lie algebra. The generators of the algebra have been obtained from a bi-orthogonal system. The deformation parameter resembles the modulus of the relevant elliptic functions.
There is a two-component log-gas system with Boltzmann factor which provides an interpolation between the eigenvalue PDF for $\beta = 1$ and $\beta = 4$ invariant random matrix ensembles. The solvability of this log-gas system relies on the…
Given a $C^{1+\beta}$ flow $\varphi$ with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related $\varphi$-invariant probabilities by an irreducible countable topological Markov flow. As an application, we…
From any given Frobenius manifold one may construct a so-called dual structure which, while not satisfying the full axioms of a Frobenius manifold, shares many of its essential features, such as the existence of a prepotential satisfying…
Let $S$ be a compact Riemann surface and let $H$ be a finite group. It is known that if $H$ acts on $S$ then there is a $H$-equivariant isogeny decomposition of the Jacobian variety $JS$ of $S,$ called the group algebra decomposition of…
We study the interplay between the diagonal flow on, and the topology of, a stratum component of a space of rooted quadratic differentials. We prove that the flow group -- the subgroup of the fundamental group generated by almost-flow loops…
We study the connection between the $p$--Talagrand inequality and the $q$--logarithmic Sololev inequality for conjugate exponents $p\geq 2$, $q\leq 2$ in proper geodesic metric spaces. By means of a general Hamilton--Jacobi semigroup we…
The Lipshitz-Sarkar stable homotopy link invariant defines Steenrod squares on the Khovanov cohomology of a link. Lipshitz-Sarkar constructed an algorithm for computing the first two Steenrod squares. We develop a new algorithm which…
We prove that k-th singular cohomology group of the complement of the theta divisor in a hyperelliptic Jacobian is isomorphic to the k-th fundamental representation of the symplectic group Sp(2g,C). This is one of the conjectures in our…
We show that a surface group of high genus contained in a classical simple Lie group can be deformed to become Zariski dense, unless the Lie group is $SU(p,q)$ (resp. $SO^* (2n)$, $n$ odd) and the surface group is maximal in some…
We study the asymptotic behavior of the pluriclosed flow in the case of left-invariant Hermitian structures on Lie groups. We prove that solutions on 2-step nilpotent Lie groups and on almost-abelian Lie groups converge, after a suitable…
The convergence of the derivative expansion of the exact renormalisation group is investigated via the computation of the beta function of massless scalar lambda phi^4 theory. The derivative expansion of the Polchinski flow equation…
Various integrable geodesic flows on Lie groups are shown to arise by taking moments of a geodesic Vlasov equation on the group of canonical transformations. This was already known for both the one- and two-component Camassa-Holm systems.…
Motivated by our arithmetic applications, we required some tools that might be of independent interest. Let $\mathcal E$ be an absolutely irreducible group scheme of rank $p^4$ over $\mathbb Z_p$. We provide a complete description of the…
Topological filters via sheaves generalize the classical linear translation-invariant filter theory by attaching the filter computation locally to a simplicial topological space. This paper develops topological filters for causal signal…
The paper discusses four approaches to the biextension of Chow groups and their equivalences. These are the following: an explicit construction given by S.Bloch, a construction in terms of the Poincare biextension of dual intermediate…
In this paper we introduce the bosonic generators of the $sp(4,R)$ algebra and study some of their properties, based on the $SU(1,1)$ and $SU(2)$ group theory. With the developed theory of the $Sp(4,R)$ group, we solve the interaction part…
We construct real Jacobi forms with matrix index using path integrals. The path integral expressions represent elliptic genera of two-dimensional N=(2,2) supersymmetric theories. They arise in a family labeled by two integers N and k which…