91 citations · 220 across the 12 of their papers we have counts for
13 papers
Maurer--Cartan elements in symplectic cohomology from compactifications
Matthew Strom Borman, Mohamed El Alami, Nick Sheridan
We prove that under certain conditions, a normal crossings compactification of a Liouville domain determines a Maurer--Cartan element for the structure on its symplectic…
An structure on symplectic cohomology
Matthew Strom Borman, Mohamed El Alami, Nick Sheridan
We construct the structure on symplectic cohomology of a Liouville domain, together with an enhancement of the closed--open map to an homomorphism from symple…
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…
Existence and classification of overtwisted contact structures in all dimensions
Matthew Strom Borman, Yakov Eliashberg, Emmy Murphy
We establish a parametric extension -principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the -dimensional resul…
Quasi-morphisms on contactomorphism groups and contact rigidity
Matthew Strom Borman, Frol Zapolsky
We build homogeneous quasi-morphisms on the universal cover of the contactomorphism group for certain prequantizations of monotone symplectic toric manifolds. This is done using Gi…
Bounding Lagrangian widths via geodesic paths
Matthew Strom Borman, Mark McLean
The width of a Lagrangian is the largest capacity of a ball that can be symplectically embedded into the ambient manifold such that the ball intersects the Lagrangian exactly along…
Spherical Lagrangians via ball packings and symplectic cutting
Matthew Strom Borman, Tian-Jun Li, Weiwei Wu
In this paper we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, S^2 or RP^2, in symplectic manifolds that are rational or ruled. V…
Displacing Lagrangian toric fibers by extended probes
Miguel Abreu, Matthew Strom Borman, Dusa McDuff
In this paper we introduce a new way of displacing Lagrangian fibers in toric symplectic manifolds, a generalization of McDuff's original method of probes. Extended probes are form…
Quasi-states, quasi-morphisms, and the moment map
Matthew Strom Borman
We prove that symplectic quasi-states and quasi-morphisms on a symplectic manifold descend under symplectic reduction on a superheavy level set of a Hamiltonian torus action. Using…
Symplectic reduction of quasi-morphisms and quasi-states
Matthew Strom Borman
We prove that quasi-morphisms and quasi-states on a closed integral symplectic manifold descend under symplectic reduction to symplectic hyperplane sections. Along the way we show…
Persistent Homology for Random Fields and Complexes
Robert J. Adler, Omer Bobrowski, Matthew S. Borman +2
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to un…
Euler Integration of Gaussian Random Fields and Persistent Homology
Omer Bobrowski, Matthew Strom Borman
In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristi…
Compactness and Measures of Noncompactness in Metric Trees
A. G. Aksoy, M. S. Borman, A. L. Westfahl
A metric tree (, ), also known as -trees or -theory, is a metric space such that between any two points there is an unique arc and that arc is isometric to an…