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Contact : thomas at math point unistra point fr

Presentation

I'm a PhD student in mathematics at IRMA in Strasbourg. I'm working in the field of mathematical physics. In particular, I try to construct a geometric approach to higher Teichmüller theory using punctual Hilbert schemes and integrable systems.







 

Contact

thomas at math point unistra point fr

Fields of interest

complex, symplectic and differential geometry, representation theory (Lie groups and Lie algebras), algebraic topology

Key words

Teichmüller theory, Hitchin component, punctual Hilbert scheme, Higgs bundles, flat connexions

Papers

A. Thomas: Generalized Punctual Hilbert schemes and g-complex structures, preprint arXiv:1910.08504

V.V. Fock, A. Thomas: Higher complex structures, preprint arXiv:1812.11199, submitted to IMRN journal

A. Thomas: Special affine connexions and holomorphic differentials, in preparation

Curriculum Vitae

Education

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

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

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 :

Talks

06/2019      Heidelberg, geometry seminar, invitation Lucas Dahinden
11/2018       Madrid, conference "New trends in Higgs Theory"
10/2018       Moscow, workshop "Recent Developments in Higgs theory"
07/2018      Mézeyrac, 3h-lecture at summerschool "L'Agape"

02/2018      Nizza, geometry seminar, invitation François Labourie

01/2018       Luxembourg, workshop GAAG

11/2017        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

2016

2015

2014

2011

Useful links

Institut de Recherche Mathématique Avancée

https://irma.math.unistra.fr/

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IRMA

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Logical-chemical Riddles


http://molekularis.free.fr/

Molekularis

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Basic Research Community for Physics

http://basic-research.org/

BRCP

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