Dr Daniel Mathews

Research Overview

Most of my mathematical research has been in the broad field of geometry and topology.

I'm interested in low-dimensional topology, including knots and their polynomials, geometric structures on 3-manifolds, sutured manifolds, hyperbolic 3-manifolds, contact 3-manifolds, and related algebra and representation theory, including character varieties.
I'm interested in quantum topology, including quantum invariants (coloured Jones) and Yang-Baxter equations, skein modules and algebras, and cluster algebras.  
I'm interested in symplectic and contact topology, particularly in 3 and 4 dimensions, including Floer homology, contact homology, contact categories, convex surfaces, dividing sets.  
I'm interested in planar graphs, their combinatorics, polynomial invariants, and their relationship to geometry, topology, and knots.
I'm interested in mathematical physics, including topological quantum field theories, Clifford algebras, and spinors. 
I'm interested in combinatorics, enumeration, and generating functions for the above.

Selected Publications

[1] Kálmán, Tamás ; Mathews, Daniel V. "Tight contact structures on Seifert surface complements". In: Journal of Topology. 2020 ; Vol. 13, No. 2. pp. 730-776. https://doi.org/10.1112/topo.12144

[2] Mathews, Daniel. "Strand algebras and contact categories". In: Geometry and Topology. 2019 ; Vol. 23, No. 2. pp. 637-683. https://doi.org/10.2140/gt.2019.23.637

[3] Mathews, Daniel V. "Strings, fermions and the topology of curves on annuli". In: Journal of Symplectic Geometry. 2017 ; Vol. 15, No. 2. pp. 421-506. https://doi.org/10.4310/JSG.2017.v15.n2.a2

[4] Mathews, Daniel ; Schoenfeld, Eric. "Dimensionally reduced sutured Floer homology as a string homology". In: Algebraic & Geometric Topology. 2015 ; Vol. 15, No. 2. pp. 691-731. https://doi.org/10.2140/agt.2015.15.691

[5] Mathews, Daniel. "Sutured Floer homology, sutured TQFT and noncommutative QFT". In: Algebraic & Geometric Topology. 2011 ; Vol. 11, No. 5. pp. 2681 - 2739. https://doi.org/10.2140/agt.2011.11.2681