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I'm a postdoctoral fellow in mathematics at the University of Heidelberg. Before, I was postdoc at the Max-Planck Institute in Bonn and PhD student in Strasbourg under the direction of Vladimir Fock.

I'm in the field of mathematical physics. In particular, I work on a geometric approach to higher Teichmüller theory using punctual Hilbert schemes.



athomas at mathi.uni-heidelberg dot de

Fields of interest

Differential Geometry, Mathematical Physics, Lie theory, Quantum Algebra

Key words

Character variety, Teichmüller theory, Hitchin component, Higgs bundles, flat connexions, geometric structures,

integrable systems, Hecke algebras

Papers and preprints
Curriculum Vitae
  1. G. Kydonakis, C. Reid, A. Thomas. Fock bundles and Hitchin components, preprint arXiv:2310,04377, 2023.

  2. A. Abdesselam, A. Thomas. Structure constants for simple Lie algebras from principal sl2- triple, preprint arXiv:2309.08213, 2023.

  3. A. Thomas. Infinitesimal modular group: q-deformed sl2 and Witt algebra, preprint arXiv:2308.06158, 2023.

  4. V. Fock, V. Tatitscheff, A. Thomas, Topological quantum field theories from Hecke algebras, à paraître dans Representation Theory, arXiv:2105.09622.

  5. A. Thomas, A gentle introduction to the non-abelian Hodge correspondence, à paraître dans L'Enseignement Mathématique, arXiv:2208.05940

  6. A. Thomas. Generalized punctual Hilbert schemes and g-complex structures,
    Int. J. of Maths Vol. 32, No. 1, article 2250004, 2022, arXiv:1910.08504

  7. V. Fock, A. Thomas. Higher complex structures, Int. Math. Research Notices Vol. 2021(20), p. 15873 – 15893, 2021, arXiv:1812.11199

  8. A. Thomas, Differential operators on surfaces and rational WKB, preprint arXiv:2111.07946 , 2021

  9. A. Thomas, Higher Complex Structures and Flat Connections, preprint arXiv:2005.14445, 2020

  10. A. Thomas, Geometric characterizations of the cross ratio in a pencil of conics, preprint arXiv:2011.03811, 2020

  11. (en préparation) C. Kineider, G. Kydonakis, E. Rogozinnikov, V. Tatitscheff, A. Thomas. Spectral Networks: Bridging higher rank Teichmüller theory and BPS states, livre en cours d'évaluation.


2017 - 2020     PhD, IRMA Strasbourg, advisor Vladimir Fock
2013 - 2016     Bachelor and Master at ENS Lyon

2011 - 2013      MPSI, MP*, classe préparatoire, Louis le Grand, Paris

Awards and grants

2023                Travel grant from SPP Geometry at Infinity for 4-week stay in the US
2019                 Travel grant to Stony Brook for workshop on holomorphic differentials

2017 - 2020     PhD grant from ENS Lyon

2013 - 2017      Full scholarship at ENS Lyon

2010                 First prize at ITYM (International Tournement for Young Mathematicians), Paris

2009                 Silver Medal at MEMO (Middle European Math Olympiad) at Strecno (Slovaquia)

Teaching Experience

2022                 Master Lecture on Nonabelian Hodge correspondence at University of Bonn

2017 - 2020     Teaching Assitant at University of Strasbourg
2016 - 2017      Teaching Assistant at Lycée Kléber Strasbourg (Colleur)

2013 - 2016      Animator at Math Club for highschool students in Lyon

Detailed CV :

Invited talks
























Reims, invitation par Valentin Ovsienko
Austin (University of Texas), invitation par Dan Freed

Atlanta (Georgia Tech), invitation par Michael Wolf

College Park (University of Maryland), invitation par Bill Goldman

Paris (Jussieu), invitation par Julien Marché

Saarbrücken, Chrismas workshop on geometry and number theory

Dijon, séminaire de Mathématique Physique

Paris (Sorbonne), séminaire de Combinatoire énumérative

Orsay (Paris-Saclay), séminaire de Géométrie, Topologie et Dynamique

Lyon, séminaire de physique mathématique

Bonn (online), Oberseminar, invitation Christian Kaiser

Heidelberg, geometry seminar, invitation Beatrice Pozzetti

Strasbourg (online), conference "Geometric and analytic aspects of

moduli spaces of Higgs bundles

Paris-Saclay (online), geometry seminar, invitation Luc Pirio

Singapore (online), conference "Topics at the Interface of Low

Dimensional Group Actions and Geometric Structures"

Bonn-Berlin (online), geometry seminar, invitation Gaëtan Borot

Marseille, conference "Teichmüller theory"

Nancy, Parole aux jeunes chercheurs

Heidelberg, geometry seminar, invitation Lucas Dahinden

Madrid, conference "New trends in Higgs Theory"

Moscow, workshop "Recent Developments in Higgs theory"

Nizza, geometry seminar, invitation François Labourie

Luxembourg, workshop GAAG

Strasbourg, geometry seminar, invitation Dragos Fratila

Research Experience

PhD project : "Higher complex structures and higher Teichmüller theory"  with Vladimir Fock

Objective : prove that moduli space of higher complex structures is isomorphic to Hitchin's component

Ideas : symplectic and hyperkähler aspects of punctual Hilbert scheme, parabolic reduction of connections, Hitchin-Simpson theorem,...

1-year research internship at IRMA Strasbourg, with Vladimir Fock

Master thesis : "Higher complex structures" with Vladimir Fock

Construction of a new geometric structure on surfaces generalizing the complex structure, uses punctual Hilbert scheme of the plane


2-month Internship : "The norm filtration of the homology of symmetric  groups" with Prof. Carl-Friedrich Bödigheimer

Analysis of a recent approach du to Visy for computing the homology of certain groups, called factorable


Bachelor Thesis : "Opérateurs de Yang-Baxter et invariants d'entrelacs" with Gwénaël Massuyeau

Study of link invariants coming from Yang-Baxter operators, theory developped by V. Turaev

Jugend Forscht : "Eigenartige Parkette und Heesch's Tiling Problem" together with Christoph Standke, directed by Dr. Frank Göring

Analysis of Voderberg's tile, a tiling with surprising properties, optimization of its form, convex examples for Heesch's Tiling Problem

2017 - 2020

2016 - 2017





Useful links

Youtube channel of mathematical explications



Logical-chemical Riddles



Basic Research Community for Physics


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