Publications
I am interested in geometric approaches to Hitchin components, via non-holomorphic methods. I also touch on TQFT in dimension 2, q-deformations of Lie algebras and integrable systems.
Publications
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C. Kineider, G. Kydonakis, E. Rogozinnikov, V. Tatitscheff, A. Thomas. Spectral Networks: Bridging higher rank Teichmüller theory and BPS states, Lect. Notes Math. 2386, Springer, 2026, arXiv/2412.03588.
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A. Thomas. Circular Isoptics in Flatland, Math. Intelligencer Vol. 47, p. 370--375, 2025, arXiv/2504.02907
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A. Thomas. A Gentle Introduction to the non-abelian Hodge Correspondence, Enseign. Math. (2) 71 Vol. 3-4, p. 261--334, 2025, arXiv/2208.05940.
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A. Abdesselam and A. Thomas. Structure constants for simple Lie algebras from a principal sl2-triple, J. Lie Theory 34 No.4, p. 829--862, 2024, arXiv/2309.08213.
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A. Thomas. Infinitesimal modular group: q-deformed sl2 and Witt algebra, SIGMA 20, 053, 2024, arXiv/2308.06158.
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V. Fock, V. Tatitscheff and A. Thomas. Topological Quantum Field Theories from the Hecke Algebra, Representation Theory 27, p. 248--291, 2023, arXiv/2105.09622.
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A. Thomas. Generalized punctual Hilbert schemes and g-complex structures,
Int. J. of Maths Vol. 32, No. 1, article 2250004, 2022, arXiv/1910.08504.
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V. Fock, A. Thomas. Higher Complex Structures, Int. Math. Research Notices Vol. 2021(20), p. 15873 – 15893, 2021, arXiv/1812.11199.
Preprints
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P. Jouteur, O. Paris-Romaskevich, A. Thomas. Plane Geometry of q-rationals and Springborn Operations, preprint arXiv/2603.04295, 2026.
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G. Kydonakis, C. Reid, A. Thomas. Fock bundles and Hitchin components, preprint arXiv/2310,04377, 2023.
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A. Thomas, Differential operators on surfaces and rational WKB, preprint arXiv/2111.07946 , 2021.
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A. Thomas, Higher Complex Structures and Flat Connections, preprint arXiv/2005.14445, 2020.
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A. Thomas, Geometric characterizations of the cross ratio in a pencil of conics, preprint arXiv/2011.03811, 2020.
Projects and internships
PhD : "Higher complex structures and higher Teichmüller theory" under the direction of Vladimir Fock
Goal: geometric approach to Hitchin components via geometric structures on the underlying surface, so-called higher complex structures
Methods: symplectic and hyperkähler aspects of the punctual Hilbert scheme, parabolic reduction of connections, Hitchin-Simpson theorem
M2 internship :"Higher complex structures" with Vladimir Fock
Construction of a new geometric structure on surfaces generalizing the complex structure, uses the punctual Hilbert scheme of the plane
M1 internship :"The norm filtration of the homology of symmetric groups" with Prof. Carl-Friedrich Bödigheimer
Analysis of a recent approach by Visy to calculate the homology of certain groups, called factorable.
L3 internship : "Yang-Baxter operators and interleaving invariants" with Gwénaël Massuyeau
Study of link invariants using Yang-Baxter operators, theory developed by Turaev.
Yugend Forscht : "Eigenartige Parkette and Heesch's Tiling Problem" joint work with Christoph Standke, under Dr. Frank Göring
Analysis of the Voderberg polygon, a tiling piece with surprising properties, optimization of its shape, convex examples for the Heesch tiling problem.
2017 - 2020
2016
2015
2014
2010