13 citations · 23 across the 12 of their papers we have counts for
12 papers · 1 filter
Homological Mirror Symmetry for Affine Log Calabi-Yau Surfaces
Umut Varolgunes
Let be a smooth complex affine log Calabi--Yau surface, and let be its complete finite-type Liouville manifold, equipped with its natural grading structure. We gi…
Contact big fiber theorems
Yuhan Sun, Igor Uljarevic, Umut Varolgunes
We prove contact big fiber theorems, analogous to the symplectic big fiber theorem by Entov and Polterovich, using symplectic cohomology with support. Unlike in the symplectic case…
Descent with algebraic structures for symplectic cohomology
Umut Varolgunes
We formulate and prove a chain level descent property of symplectic cohomology for involutive covers by compact subsets that take into account the natural algebraic structures that…
A characterization of heaviness in terms of relative symplectic cohomology
Cheuk Yu Mak, Yuhan Sun, Umut Varolgunes
For a compact subset of a closed symplectic manifold , we prove that is heavy if and only if its relative symplectic cohomology over the Novikov field is non-zero.…
Closed string mirrors of symplectic cluster manifolds
Yoel Groman, Umut Varolgunes
For the base of a Maslov Lagrangian torus fibration with singularities consider the sheaf assigning to each the relative symplectic cohomology in degree of…
Framed structures in Floer theory
Mohammed Abouzaid, Yoel Groman, Umut Varolgunes
We resolve the long-standing problem of constructing the action of the operad of framed (stable) genus- curves on Hamiltonian Floer theory; this operad is equivalent to the fram…
Locality of relative symplectic cohomology for complete embeddings
Yoel Groman, Umut Varolgunes
A complete embedding is a symplectic embedding of a geometrically bounded symplectic manifold into another geometrically bounded symplectic manifold of the same…
Quantum cohomology as a deformation of symplectic cohomology
Matthew Strom Borman, Nick Sheridan, Umut Varolgunes
We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement…
On certain quantifications of Gromov's non-squeezing theorem
Kevin Sackel, Antoine Song, Umut Varolgunes +1
Let and let be the Euclidean -ball of radius with a closed subset removed. Suppose that embeds symplectically into the unit cylinder $\mathbb{D}^2 \times…
Super-rigidity of certain skeleta using relative symplectic cohomology
Dmitry Tonkonog, Umut Varolgunes
This article uses relative symplectic cohomology, recently studied by the second author, to understand rigidity phenomena for compact subsets of symplectic manifolds. As an applica…
Mayer-Vietoris property for relative symplectic cohomology
Umut Varolgunes
In this paper, we construct a Hamiltonian Floer theory based invariant called relative symplectic cohomology, which assigns a module over the Novikov ring to compact subsets of clo…
On the equatorial Dehn twist of a Lagrangian nodal sphere
Umut Varolgunes
Let be a geometrically bounded symplectic manifold, and a Lagrangian nodal sphere such that . We show that an equatorial Dehn twist of $L…