Persistent homology and Floer–Novikov theory

Hofer’s metrics and boundary depth

(2017) Michael Usher   ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE

An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves

(2016) John Pardon   GEOMETRY & TOPOLOGY

An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves

(2016) John Pardon   GEOMETRY & TOPOLOGY

Coisotropic rigidity and $C^{0}$ -symplectic geometry

(2015) Vincent Humilière et al.   DUKE MATHEMATICAL JOURNAL

Decomposition of pointwise finite-dimensional persistence modules

(2015) William Crawley-Boevey   JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules

(2015) Leonid Polterovich et al.   Selecta Mathematica-New Series

Topological Persistence for Circle-Valued Maps

(2013) Dan Burghelea et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Displacement of polydisks and Lagrangian Floer theory

(2013) Kenji Fukaya et al.   Journal of Symplectic Geometry

Precise Arrhenius Law for p-forms: The Witten Laplacian and Morse–Barannikov Complex

(2012) Dorian Le Peutrec et al.   ANNALES HENRI POINCARE

Dualities in persistent (co)homology

(2011) Vin de Silva et al.   INVERSE PROBLEMS

Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds

(2011) Michael Usher   ISRAEL JOURNAL OF MATHEMATICS

DUALITY IN FILTERED FLOER–NOVIKOV COMPLEXES

(2010) MICHAEL USHER   Journal of Topology and Analysis

Topology and data

(2009) Gunnar Carlsson   BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

Rigidity and uniruling for Lagrangian submanifolds

(2009) Paul Biran et al.   GEOMETRY & TOPOLOGY

Spectral numbers in Floer theories

(2008) Michael Usher   COMPOSITIO MATHEMATICA