Anthony Conway


AnthonyConway

Contact :

Department of Mathematical Sciences
Lower Mountjoy Stockton Road
Durham, DH1 3LE
United Kingdom

Office: CM123

Email: Anthonyyconway(at)gmail(dot)com


From January 2018 to July 2019, I am a postdoc at Durham University (funded by the Swiss National Science Foundation) where I mostly work with Mark Powell. Before that, from September 2014 to October 2017, I was a Ph.D student at the University of Geneva under the supervision of David Cimasoni. I also spent the fall of 2016 at Indiana University, Bloomington and the winter of 2017 at UQAM, Montréal. Here is a more detailed CV.

Together with Marco Golla, we are organising a conference in Le Croisic on "knot concordance and low-dimensional manifolds", 17-21 June 2019.
More information (as well as a registration form) can be found here.


Research Interests :

My research interests lie in low dimensional topology with a focus on knot theory: I am interested in various topics related to links (such as link concordance, splitting numbers, SU(2)-representations of link groups), braids and manifolds of dimension 3 and 4. I also have a side interest in surgery theory and high-dimensional manifolds.


Publications and preprints

  1. The Levine-Tristram signature: a survey
    March 2019, preprint
  2. Enumerating homotopy-ribbon slice discs
    (with Mark Powell)
    February 2019, preprint
  3. Stably slice disks of links
    (with Matthias Nagel)
    January 2019, preprint
  4. Twisted Blanchfield pairings, twisted signatures and Casson-Gordon invariants
    (with Maciej Borodzik and Wojciech Politarczyk)
    September 2018, preprint
  5. A multivariable Casson-Lin type invariant
    (with Léo Bénard)
    May 2018, preprint
  6. Conway's potential function via the Gassner representation
    (with Solenn Estier)
    September 2017, preprint
  7. Linking forms revisited
    (with Stefan Friedl and Gerrit Herrmann)
    Pure and Applied Mathematics Quarterly 12 (2016), 493-515.
  8. An explicit computation of the Blanchfield pairing for arbitrary links
    Canadian Journal of Mathematics 70 (2018), 983-1007.
  9. Multivariable signatures, genus bounds and 0.5-solvable cobordisms
    (with Matthias Nagel and Enrico Toffoli)
    Michigan Math. J. (to appear)
  10. The Blanchfield pairing of colored links
    (with Stefan Friedl and Enrico Toffoli)
    Indiana Univ. Math. J. 67 (2018), 2151-2180.
  11. L^2-Burau maps and L^2-Alexander torsions
    (with Fathi Ben Aribi)
    Osaka J. Math. 55 (2018), 529-545.
  12. A Burau-Alexander 2-functor on tangles
    (with David Cimasoni)
    Fund. Math. 240 (2018), 51-79.
  13. Splitting numbers and signatures
    (with David Cimasoni and Kleopatra Zacharova)
    Proc. Amer. Math. Soc. 144 (2016), 5443-5455.
  14. Burau maps and twisted Alexander polynomials
    Proc. Edinburgh Math. Soc. 61 (2018) 479-497
  15. Colored tangles and signatures
    (with David Cimasoni)
    Math. Proc. Cambridge Philos. Soc. 164 (2018), 493-530.

Phd Thesis

Invariants of colored links and generalizations of the Burau representation .

Unpublished notes :

Some notes on Algebraic concordance and the Casson-Gordon invariants.
Lecture notes for an introductory course on differential topology and surgery theory.

 Organisation of seminars and conferences:

Together with Mark Powell, we recently organised a workshop in Durham on "twisted and quantum knot invariants", 13-15 December 2018.
More information can be found here.

When I was in Geneva, I co-organized
-the Topology and Geometry seminar (Autumn 2017 and previous semesters);
-the Graduate Seminar: Spring 2017 and previous semesters.

Teaching:

As a postdoc in Durham, I taught a course on differential topology and surgery theory.

As a PhD student in Geneva, I was a TA for the following courses: Linear Algebra, Analysis 1, Analysis 2, Algebra and Geometry 3 (fundamental group and covering spaces) Knot theory and category theory.