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Consider an absolutely simple abelian variety A defined over a number field K. For most places v of K, we study how the reduction Av of A modulo v splits up to isogeny. Assumingthe Mumford–Tate conjec...
Two types of finite-variable reductions of the dispersionless Toda hierarchy are considered in the geometric perspectives. The reductions are formulated in terms of "Landau-Ginzburg potentials" that p...
We transfer the scheme for constructing differential reductions recently developed for the Manakov-Santini hierarchy to the case of the two-component generalization of dispersionless 2DTL hierarchy. W...
Abstract: This paper deals with the study of the behaviour of the value semigroup of a curve singularity define over a global field reduced modulo a maximal ideal. We also define a global zeta functio...
We study minimal reductions of edge ideals of graphs containing a unique even cycle, and determine restrictions on the coefficients of the generators of these minimal reductions.
A higher order difference equation may be generally defined in an arbitrary nonempty set S as: fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
A higher order difference equation may be generally defined in an arbitrary nonempty set S as: fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein - Maxwell equations were made...
We discuss the problem of homotopy invariance for homology of linear groups. Some reductions we are able to make show that homotopy invariance for linear groups follows from contractibility of a cert...
We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the ...
More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein- Maxwell equations were made...
We shall present here a general apt technique to induce connections along bundle reductions which is different from the standard restriction. The technique is a generalization of the mechanism presen...
We study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by Sircar and Papanicolaou. We are first to study t...
New Completely Integrable (2+1)-System is studied. It is based on the so-called L-A-B-triples $L_t=[H,L]-fL$ where L is a 2D Schrodinger Operator. This approach was invented by S.Manakov and B.Dubrovi...
We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces and their reductions. We briefly outline the direct and the inverse scat...

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