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 and preprints

G. Kydonakis, C. Reid, A. Thomas.Fock bundles and Hitchin components, preprint arXiv:2310,04377, 2023.
A. Abdesselam, A. Thomas.Structure constants for simple Lie algebras from principal sl2- triple, preprint arXiv:2309.08213, 2023.
A.Thomas.Infinitesimal modular group: q-deformed sl2 and Witt algebra, preprint arXiv:2308.06158, 2023.
V. Fock, V. Tatitscheff, A. Thomas,Topological quantum field theories from Hecke algebras, to appear in Representation Theory, arXiv:2105.09622.
A.Thomas,A gentle introduction to the non-abelian Hodge correspondence, to appear in L’Enseignement Mathématique, arXiv:2208.05940
A.Thomas. Generalized punctual Hilbert schemes and g-complex structures,
Int. J. of Maths Vol. 32, No. 1, article 2250004, 2022, arXiv:1910.08504
V. Fock, A. Thomas. Higher complex structures, Int. Math. Research Notices Vol. 2021(20), p. 15873 – 15893, 2021, arXiv:1812.11199
A.Thomas,Differential operators on surfaces and rational WKB, preprint arXiv:2111.07946 , 2021
A.Thomas, Higher Complex Structures and Flat Connections, preprint arXiv:2005.14445, 2020
A.Thomas,Geometric characterizations of the cross ratio in a pencil of conics, preprint arXiv:2011.03811, 2020
(in preparation) C. Kineider, G. Kydonakis, E. Rogozinnikov, V. Tatitscheff, A. Thomas.Spectral Networks: Bridging higher rank Teichmüller theory and BPS states, book currently under review.

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