Campbell Wheeler

Campbell Wheeler

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I started a postdoc at the Institut des Hautes Études Scientifiques in September 2023 in the group of Maxim Kontsevich. Before that I was a PhD student at the Max Planck Institute for Mathematics from September 2018 to April 2023. My supervisor was Don Zagier and I was co-supervised by Stavros Garoufalidis. Before that I completed my masters degree at the university of Melbourne where I was supervised by Paul Norbury.

Conference on quantum topology

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I am helping organise a conference at the MPIM in Bonn with Christian Blohmann, Ingrid Irmer, Roland van der Veen, and Tao Yu. This is related to some recent developments in quantum topology. This happens to coincide with Stavros's 60th birthday so should be a lot of fun! You can find the website and the link to registration here. The deadline for applications is the 16th of March.

Interests

Maths: I'm interested in interactions between geometry, low dimensional topology, number theory, and physics. In particular I like computing quantities, arising from enumerative geometry and quantum topology, and exploring their geometric, combinatorial and number theoretic properties.

Nonmaths: I enjoy playing music and play the saxophone well-ish and attempt to play other things. If you want, you can check out my old band from Melbourne The Cactus Channel. I'm always up for games and making things most recently some practical knot theory leading to a beanie.

CV

You can find my CV here.

Papers

  • The Habiro ring of a number field. (arXiv:2412.04241)

    This is joint work with Stavros Garoufalidis, Peter Scholze and Don Zagier.

  • Summability for State Integrals of hyperbolic knots. (arXiv:2410.20973)

    This is joint work with Veronica Fantini.

  • Quantum modularity for a closed hyperbolic 3-manifold. (Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)) (arXiv:2308.03265)

    This work appeared in a similar form in my thesis.

  • Perturbative invariants of cusped hyperbolic 3-manifolds. (arXiv:2305.14884)

    This is joint work with Stavros Garoufalidis and Matthias Storzer.

  • Resurgence, Habiro elements and strange identities. (arXiv:2304.07001)

    This is joint work with Samuel Crew, Veronica Fantini, Ankush Goswami and Robert Osburn.

  • Periods, the meromorphic 3d-index and the Turaev-Viro invariant. (arXiv:2209.02843)

    This is joint work with Stavros Garoufalidis.

  • Modular q-holonomic modules. (arXiv:2203.17029)

    This is joint work with Stavros Garoufalidis.

  • Resurgence of Chern-Simons theory at the trivial flat connection. (Communications in Mathematical Physics) (arXiv:2111.04763)

    This is joint work with Stavros Garoufalidis, Jie Gu and Marcos Mariño.

  • Around the combinatorial unit ball of measured foliations on bordered surfaces. (International Mathematics Research Notices) (arXiv:2110.12538)

    This is joint work with Gäetan Borot, Séverin Charbonnier, Vincent Delecroix, Alessandro Giacchetto.

  • On the Kontsevich geometry of the combinatorial Teichmuller space. (arXiv:2010.11806)

    This is joint work with Jørgen Andersen, Gäetan Borot, Séverin Charbonnier, Alessandro Giacchetto, Danilo Lewanski.

  • Topological recursion for Masur-Veech volumes. (Journal of the London Mathematical Society)(arXiv:1905.10352)

    This is joint work with Jørgen Andersen, Gäetan Borot, Séverin Charbonnier, Vincent Delecroix, Alessandro Giacchetto, Danilo Lewanski.  

    Collaborators

    People I have worked with since starting the PhD are:

  • Jørgen Ellegaard Andersen
  • Gaëtan Borot
  • Séverin Charbonnier
  • Vincent Delecroix
  • Veronica Fantini
  • Stavros Garoufalidis
  • Alessandro Giacchetto
  • Jie Gu
  • Maxim Kontsevich
  • Danilo Lewanski
  • Marcos Mariño
  • Peter Scholze
  • Matthias Storzer
  • Don Zagier

    • Seminar on resurgence and quantum modularity

    With Veronica Fantini, we organised a seminar on quantum modularity and resurgence at IHES for the first half of 2024. You can find the webpage here.

    Doctoral Thesis

    My PhD was focused on investigating the asymptotic and quantum modular properties of q-hypergeometric functions. These functions are important in quantum topology where they arise as invariants of three manifolds. q-holonomic modules and state integrals provide some of the most important tools in their study. q-hypergeometric functions also provide an interesting playground to study resurgence both at the classical and q level. A simple hyperbolic closed manifold was studied in detail which leads to unification of various conjectures through quantum modularity. You can find a copy here. I defended my thesis on Wednesday the 26th of April 2023.

    Masters Thesis

    You can find my old masters thesis here.

     

     

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    Last modified: January 27th 2025.