Centre for Mathematical Sciences
Cambridge CB3 0WB, UK
1 September 2020 - July 2021:
Institute for Advanced Study
1 Einstein Dr
Princeton, NJ 08540
I am an
in the Department of Pure Mathematics and Mathematical
University of Cambridge
(temporarily on leave September 2020-July 2021, for a fellowship at the Institute for Advanced Study at Princeton).
As a low-dimensional topologist, I study
relationships among Heegaard Floer theory
and various non-gauge-theoretic
structures in 3 and 4 dimensions,
such as left-invariant fundamental group orders,
taut foliations, tight contact structures,
and complex surface singularities.
My PhD (Harvard) is in mathematics but I have bachelors' degrees both in mathematics and in physics, I deferred my admission at Harvard's math PhD program to spend a year in Stanford's theoretical physics PhD program, and before that I had some undergraduate training and work experience in biomedical engineering.
My earlier mathematical-physics training was in mirror symmetry and string theory,
and I am still a fan of both.
2018-19 Part III 3-manifolds (Lent).
2017-18 Part III 3-manifolds.
Part III Differential Geometry:
Part II Algebraic Geometry: Supervisions.
Warwick, UK (remotely):
Geometry & Topology Seminar,
4 Aug 2020.
16-22 Feb 2020.
Quanta Magazine article on this conference (spot my arm holding a yellow die!)
Low dimensional topology workshop,
6-10 January 2020.
Monash University, Australia:
Topology Seminar, 16 October 2019.
Providence, USA (as co-organizer):
ICERM Perspectives on Dehn Surgery,
15-19 July 2019.
Athens, GA, USA:
2019 Georgia Topology Conference,
22-26 May 2019.
Santa Barbara, CA, USA:
KITP Quantum Knot Invariants and Supersymmetric Gauge Theories,
13-21 Nov 2018.
Workshop on Gauge theory and topological applications,
23-27 July 2018.
Princeton University, USA:
Mini-conference on low-dimensional topology,
20-22 June 2018.
Geometric structures on 3 and 4 manifolds,
11-15 June 2018.
Oxford University, UK:
4 June 2018.
Perspectives on bordered Heegaard Floer theory school,
8-11 May 2018.
Simons CRM Invited Scholar in Residence
1 Apr - 30 May 2018.
Aspen, CO, USA:
Physics cafe: "Knots and physics" public outreach talk, 7 Mar 2018.
Aspen, CO, USA:
Quantum knot homology and supersymmetric gauge theories conference,
4-10 Mar 2018.
Geometric topology in low dimensions workshop,
18-22 Sept 2017.
XXVI International Fall Workshop on Geometry and Physics,
4-7 Sept 2017.
BIRS Thirty Years of Floer Theory for 3-Manifolds,
30 July - 4 Aug 2017.
Isle of Skye, UK:
Low-dimensional topology on Skye,
12-16 June 2017.
25 Apr 2017.
Georgia Tech & University of Georgia, USA:
Joint Topology Seminar,
3 Apr 2017.
Washington University in St. Louis, USA:
lecture series, 27-31 Mar 2017.
Rényi Insitute, Budapest:
Algebraic Geometry and Differential Topology Seminar,
24 Feb 2017.
Newton Institute, UK:
30 Jan - 3 Feb 2017.
Durham University, UK:
Pure Maths Colloquium,
21 Nov 2016.
Singularities Workshop, 25 Sept - 1 Oct 2016.
31st British Topology Meeting, 29-31 Aug 2016.
University of Oregon, USA:
26 July 2016.
Ronsfest: Perspectives in topology and geometry of 4-manifolds,
6-10 June 2016.
University of Glasgow, UK:
Geometry and Topology Seminar,
1 Feb 2016.
University of Cambridge, UK:
Differential Geometry and Topology Seminar,
27 May 2015.
"Taut foliations and fundamental group left orders in Heegaard genus 2,"
Workshop Report 2020, 8.
"Taut foliations on graph manifolds," with
Jacob Rasmussen, and
Compositio Mathematica, 156 (3), 604-612, 2020.
"L-space surgeries on satellites by algebraic links,"
Journal of Topology 13 (4), 1333-1387, 2020.
"Heegaard Floer theory, semigroups, and a new characterization of rational
Oberwolfach Reports: “Singularities,”
13 (3), 2652-2655 (2016).
"L-space intervals for Graph Manifolds and Cables."
Compositio Mathematica, 153 (5), 1008-1049, 2017.
"Floer Simple Manifolds and L-space Intervals," with
Advances in Mathematics, 322 (2017) 738-805.
"A number theoretic result for Berge's conjecture,"
Harvard University PhD Thesis, 2009,
125 pp. ISBN: 978-1109-25330-6, ProQuest LLC,