Related papers: Generating functions in symplectic and contact geo…

In this paper, we introduce an algebro-geometric formulation for Siegel's theorem using an improvement of Lang's version of Roth's theorem over finitely generated fields of characteristic zero. In fact, we prove that, for an affine open…

We develop the gluing theory of contact instantons in the context of open strings and in the context of closed strings \emph{with vanishing charge}, for example in the symplectization context. This is one of the key ingredients for the…

We introduce in this paper a field theory on symplectic manifolds that are fibered over a real surface with interior marked points and cylindrical ends. We assign to each such object a morphism between certain tensor products of quantum and…

In this paper, we study the behavior of the local Floer homology of an isolated fixed point and the growth of the action gap under iterations. To be more specific, we prove that an isolated fixed point of a Hamiltonian diffeomorphism…

We show that if a Lie group acts properly on a co-oriented contact manifold preserving the contact structure, then the contact quotient is topologically a stratified space (in the sense that a neighborhood of a point in the quotient is a…

We define a differential graded algebra associated to Legendrian knots in Seifert fibered spaces with transverse contact structures. This construction is distinguished from other combinatorial realizations of contact homology invariants by…

We prove that, for closed exact embedded Lagrangian submanifolds of cotangent bundles, the homomorphism of homotopy groups induced by the stable Lagrangian Gauss map vanishes. In particular, we prove that this map is null-homotopic for all…

We extend the Cohen-Jones-Segal construction of stable homotopy types associated to flow categories of Morse-Smale functions $f$ to the setting where $f$ is equivariant under a finite group action and is Morse but no longer Morse-Smale.…

Let $M$ be a compact orientable surface equipped with a volume form $\omega$, $P$ be either $\mathbb{R}$ or $S^1$, $f:M\to P$ be a $C^{\infty}$ Morse map, and $H$ be the Hamiltonian vector field of $f$ with respect to $\omega$. Let also…

We propose a novel approach to contact Hamiltonian mechanics which, in contrast to the one dominating in the literature, serves also for non-trivial contact structures. In this approach Hamiltonians are no longer functions on the contact…

We show that positive $S^1$-equivariant symplectic homology is a contact invariant for a subclass of contact manifolds which are boundaries of Liouville domains. In nice cases, when the set of Conley-Zehnder indices of all good periodic…

We find a set of generators for the automorphism group of a graph product of finitely generated abelian groups entirely from a certain labeled graph. In addition, we find generators for the important subgroup of star-automorphisms defined…

We study boundary singularities which can appear for infinitesimal generators of one-parameter semigroups of holomorphic self-maps in the unit disc. We introduce "regular" fractional singularities and characterize them in terms of the…

We describe a connection between the combinatorics of generators for certain groups and the combinatorics of Helly's 1913 theorem on convex sets. We use this connection to prove fixed point theorems for actions of these groups on…

For each contact diffeomorphism $\phi: (Q,\xi) \to (Q,\xi)$ of $(Q,\xi)$, we equip its mapping torus $M_\phi$ with a \emph{locally conformal symplectic} form of Banyaga's type, which we call the \emph{$\text{\rm lcs}$ mapping torus} of…

Two linear recurrences exhibit mirror symmetry connecting the constants $e$ and $\pi$. When parametrized, their asymptotic connection constants extend to meromorphic functions satisfying additive functional equations with rational…

We give finiteness results and some classifications up to diffeomorphism of minimal strong symplectic fillings of Seifert fibered spaces over S^2 satisfying certain conditions, with a fixed natural contact structure. In some cases we can…

Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…

Let $S$ be a closed Riemann surface of genus $g \geq 2$ and $\varphi$ be a conformal automorphism of $S$ of prime order $p$ such that $S/\langle \varphi \rangle$ has genus zero. Let ${\mathbb K} \leq {\mathbb C}$ be a field of definition of…

We exhibit the first examples of contact structures on $S^{2n-1}$ with $n\geq 4$ and on $S^3\times S^2$, all equipped with their standard smooth structures, for which every Reeb flow has positive topological entropy. As a new technical tool…