Related papers: A symplectic version of Suslin's $n!$-theorem

In this short note we give some corollaries of the polynomial inverse function theorem for large fields. We prove inverse and implicit function theorems for Nash maps over large fields, characterize large fields as fields satisfying inverse…

We present an array of new calculations in Lagrangian Floer theory which demonstrate observations relating to symplectic reduction, grading periodicity, and the closed-open map. We also illustrate Perutz's symplectic Gysin sequence and the…

We compute the $2$-completed integral motivic homology, effective algebraic K-theory, and very effective hermitian K-theory of the geometric classifying space of the cyclic group of order two over algebraically closed fields, the real…

In these notes, we prove a semi-adelic version of the Kuznetsov formula over arbitrary number fields. The extent is the set of those automorphic vectors which are not necessarily spherical in the archimedean aspect and a class of weight…

We prove that a finite von Neumann algebra ${\mathcal A}$ is semisimple if the algebra of affiliated operators ${\mathcal U}$ of ${\mathcal A}$ is semisimple. When ${\mathcal A}$ is not semisimple, we give the upper and lower bounds for the…

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions…

Given a finite set $S$ of places of a number field, we prove that the field of totally $S$-adic algebraic numbers is not Hilbertian.

We show that whenever a closed symplectic manifold admits a Hamiltonian diffeomorphism with finitely many simple periodic orbits, the manifold has a spherical homology class of degree two with positive symplectic area and positive integral…

We introduce "neutrabelian algebras", and prove that finite, hereditarily neutrabelian algebras with a cube term are dualizable.

We classify fields having finitely many finite non-commutative (not necessarily central) division algebras over them. In the process, we introduce the notion of anti-closure of a field and also make comments on fields having a linear…

We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting interest in finding an elementary proof. Our result is…

For a complete symplectic manifold $M^{2n}$, we define the $L^{2}$-hard Lefschetz property on $M^{2n}$. We also prove that the complete symplectic manifold $M^{2n}$ satisfies $L^{2}$-hard Lefschetz property if and only if every class of…

We generalize to the case of Lie superalgebras the classical symplectic double extension of symplectic Lie algebras introduced in [2]. We use this concept to give an inductive description of nilpotent homogeneous-symplectic Lie…

A Lie 2-algebra is a "categorified" version of a Lie algebra: that is, a category equipped with structures analogous those of a Lie algebra, for which the usual laws hold up to isomorphism. In the classical mechanics of point particles, the…

We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically…

In the long paper "Family Blowup formula, Admissible Graphs and the Enumeration of Singular Curves (I)" (appearing in JDG), the author solved the enumeration problem of nodal (or general singular) curve counting on algebraic surfaces by…

We explore the natural analogues of the Brylinksi condition, Strong Lefschetz condition, and $d\delta$-lemma in Symplectic Geometry originally explored by Brylinksi, Mathieu, Yan, and Guillemin in the Symplectic Lie Algebroid case. The…

Let G be a special orthogonal group or an inner form of a symplectic group over a number field F such that there exists a non-empty set S of real places of F at which G has discrete series and outside of which G is quasi-split. We prove…

For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by certain kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of a suitable…

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to non-semisimple orbits, have infinite dimension. We spell out a new criterium to show that a…