This project aims to build a group that brings together experts in gauge-theoretic, geometric, and group-theoretic techniques. It consists of 4 main branches:

Cobordism maps in knot Floer homology




Heegaard Floer homology and geometric structures


The Fox conjecture


Principal Investigator:

András Juhász

Low-dimensional and differential topology Heegaard Floer homology.

Postdoctoral researchers:

Paolo Aceto

Low-dimensional topology, with a particular interest in problems related to knot concordance and homology cobordisms of 3-manifolds (Sept. 2018 - Aug. 2020).

Daniele Celoria

Knot theory, 4-manifolds and knot Floer homology (Sept. 2016 - Aug. 2019).

Irena Matkovic

Contact topology and Heegaard Floer homology (Sept. 2018 - Aug. 2020).

Matthias Nagel

Concordance of links, and surfaces of minimal genus in 3- and 4-manifolds, signature and twisted Reidemeister torsion (Aug. 2018 - July 2020).

Cristina Palmer-Anghel

Quantum invariants, low-dimensional topology, algebraic geometry (Sept. 2018 - Aug. 2020).


Peter Banks


Sungkyung Kang

My research field is contact topology of 3-manifolds and Heegaard Floer homology. I am interested in problems related to Legendrian and transverse knots and their concordances in contact 3-manifolds.

Former members:

Bruce Bartlett

TQFTs, mathematical physics (Jul. - Aug. 2016).

Marco Golla

3-manifolds, smooth 4-manifolds, knot concordance, Heegaard Floer theory; complex singularities of curves and surfaces; contact and symplectic topology, Stein/symplectic fillability (Sept. 2017 - Dec. 2017).

André Henriques

Algebraic topology, higher categories, TQFTs, and Conformal field theory (Jul. 2016 - Jun. 2017).

Publications supported by the grant: