38 citations · 254 across the 22 of their papers we have counts for
25 papers
Orbifold Floer spectral invariants, symmetric product links and Weyl laws
Cheuk Yu Mak, Sobhan Seyfaddini, Ivan Smith
We explain a strategy, based on spectral invariants on symmetric product orbifolds, for proving the smooth closing lemma for Hamiltonian diffeomorphisms of a symplectic manifold wh…
A universal extension of helicity to topological flows
Oliver Edtmair, Sobhan Seyfaddini
Helicity is a fundamental conserved quantity in physical systems governed by vector fields whose evolution is described by volume-preserving transformations on a three-manifold. No…
Ergodic closing lemmas and invariant Lagrangians
Erman Cineli, Sobhan Seyfaddini, Shira Tanny
Motivated by the ergodic closing lemma of Mañé, we investigate the closing lemma in higher-dimensional Hamiltonian systems, with a focus on the statistical behavior of p…
Orbifold Hamiltonian Floer theory for global quotients
Cheuk Yu Mak, Sobhan Seyfaddini, Ivan Smith
We construct bulk-deformed orbifold Hamiltonian Floer theory for a global quotient orbifold, that is the quotient of a smooth closed symplectic manifold by a finite group acting fa…
The strong closing lemma and Hamiltonian pseudo-rotations
Erman Cineli, Sobhan Seyfaddini
We prove the strong closing property, as formulated by Irie, for a class of Hamiltonian diffeomorphisms which includes all pseudo-rotations of projective spaces as well…
A Hölder-type inequality for the distance and Anosov-Katok pseudo-rotations
Dušan Joksimović, Sobhan Seyfaddini
We prove a Hölder-type inequality for Hamiltonian diffeomorphisms relating the norm, the norm of the derivative, and the Hofer/spectral norm. We obtain as a consequence…
Quantitative Heegaard Floer cohomology and the Calabi invariant
Daniel Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak +2
We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi…
PFH spectral invariants on the two-sphere and the large scale geometry of Hofer's metric
Dan Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini
We resolve three longstanding questions related to the large scale geometry of the group of Hamiltonian diffeomorphisms of the two-sphere, equipped with Hofer's metric. Namely: (1)…
The Anosov-Katok method and pseudo-rotations in symplectic dynamics
Frédéric Le Roux, Sobhan Seyfaddini
We prove that toric symplectic manifolds admit Hamiltonian pseudo-rotations with a finite, and in a sense minimal, number of ergodic measures. The set of ergodic measures of these…
Proof of the simplicity conjecture
Dan Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving homeomorphisms of the -ball is simple for , asked if the same statement holds…
An Arnold-type principle for non-smooth objects
Lev Buhovsky, Vincent Humilière, Sobhan Seyfaddini
In this article we study the Arnold conjecture in settings where objects under consideration are no longer smooth but only continuous. The example of a Hamiltonian homeomorphism, o…
Barcodes and area-preserving homeomorphisms
Frédéric Le Roux, Sobhan Seyfaddini, Claude Viterbo
In this paper we use the theory of barcodes as a new tool for studying dynamics of area-preserving homeomorphisms. We will show that the barcode of a Hamiltonian diffeomorphism of…
The action spectrum and C^0 symplectic topology
Lev Buhovsky, Vincent Humilière, Sobhan Seyfaddini
Our first main result states that the spectral norm on the group of Hamiltonian diffeomorphisms, introduced in the works of Viterbo, Schwarz and Oh, is continuous with respect to t…
A C^0 counterexample to the Arnold conjecture
Lev Buhovsky, Vincent Humilière, Sobhan Seyfaddini
The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold must have at least as many fixed points as the minimal number of critic…
Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces
Vincent Humilière, Frédéric Le Roux, Sobhan Seyfaddini
Inspired by Le Calvez' theory of transverse foliations for dynamical systems of surfaces, we introduce a dynamical invariant, denoted by N, for Hamiltonians of any surface other th…
Reduction of symplectic homeomorphisms
Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini
In a previous article, we proved that symplectic homeomorphisms preserving a coisotropic submanifold C, preserve its characteristic foliation as well. As a consequence, such symple…
Spectral killers and Poisson bracket invariants
Sobhan Seyfaddini
We find optimal upper bounds for spectral invariants of a Hamiltonian whose support is contained in a union of mutually disjoint displaceable balls. This gives a partial answer to…
Unboundedness of the Lagrangian Hofer distance in the Euclidean ball
Sobhan Seyfaddini
Let L denote the space of Lagrangians Hamiltonian isotopic to the standard Lagrangian in the unit ball in Euclidean space. We prove that the Lagrangian Hofer distance on L is unbou…
The displaced disks problem via symplectic topology
Sobhan Seyfaddini
We prove that a --small area preserving homeomorphism of a closed surface with vanishing mass flow can not displace a topological disk of large area. This resolves the displac…
Coisotropic rigidity and C^0-symplectic geometry
Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini
We prove that symplectic homeomorphisms, in the sense of the celebrated Gromov-Eliashberg Theorem, preserve coisotropic submanifolds and their characteristic foliations. This resul…
A note on C^0 rigidity of Hamiltonian isotopies
Sobhan Seyfaddini
We show that a symplectic isotopy that is a limit of Hamiltonian isotopies is itself Hamiltonian, if the corresponding sequence of generating Hamiltonians converge in $L^{(1,…
New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians
Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini
We prove a new variant of the energy-capacity inequality for closed rational symplectic manifolds (as well as certain open manifolds such as cotangent bundle of closed manifolds...…
Descent and C^0-rigidity of spectral invariants on monotone symplectic manifolds
Sobhan Seyfaddini
We obtain estimates showing that on monotone symplectic manifolds (asymptotic) spectral invariants of Hamiltonians which vanish on a non-empty open set, U, descend to Ham_c(M\setmi…
C^0-limits of Hamiltonian paths and the Oh-Schwarz spectral invariants
Sobhan Seyfaddini
In this article we study the behavior of the Oh-Schwarz spectral invariants under C^0-small perturbations of the Hamiltonian flow. We obtain an estimate, which under certain assump…