Publications and Preprints |
Notes and reviews |
I am a graduate student at l'Institut de Recherche Mathématique Avancée (IRMA), Unité Mixte de Recherche 7501 du CNRS et de l'Université de Strasbourg, and a member of the research group Algèbre, topologie, groupes quantiques, représentations.
I am doing my PhD under the supervision of Vladimir Fock.
I am very interested in the interface between mathematics and high-energy physics.
I am currently working on higher Teichmüller theory, integrable systems, cluster algebras and varieties, supersymmetric quantum field theories, string theory, and holography through dimer models.
I am keen to have a better understanding of the web of relationships tying together these different topics.
Monshine correspondences have also piqued my interest.
Here are my CV current as of Nov. 2021 and my research statement current as of Nov. 2021, my personal webpage on Inspire-hep and Arxiv.
I am fond of climbing, camping, hiking and other outdoor activities. I enjoy listening to (any kind of) music and also playing, especially when it is with other people. I can play the trumpet!
Publications and preprints
- Inverse algorithm and triple point diagrams, Tatitscheff, V.,
Arxiv preprint hep-th/2111.02195, Nov. 2021.
- Topological quantum field theories from Hecke algebras, Fock, V., Tatitscheff, V., Thomas, A.,
Arxiv preprint math.QA/2105.09622, June 2021.
- Dimers in a bottle, Garcia-Valdecasas, E., Meynet, S., Pasternak, A. and Tatitscheff, V.,
Journal of High Energy Physics 2021(4), 274 (2021).
- Dimers Orientifolds and Anomalies, Argurio, R., Bertolini, M., Franco, S., Garcia-Valdecasas, E., Meynet, S., Pasternak, A. and Tatitscheff, V.,
Journal of High Energy Physics 2021(2), 153 (2021).
- Dimers, orientifolds and stability of supersymmetry breaking vacua, Argurio, R., Bertolini, M., Franco, S., Garcia-Valdecasas, E., Meynet, S., Pasternak, A. and Tatitscheff, V.
Journal of High Energy Physics, 2021(1), 61 (2021).
- The Octagon and the Non-Supersymmetric String Landscape, Argurio, R., Bertolini, M., Franco, S., Garcia-Valdecasas, E., Meynet, S., Pasternak, A. and Tatitscheff, V.,
Physics Letters B, 815, 136153.
- A short introduction to Monstrous Moonshine, Tatitscheff, V.,
Arxiv preprint math.NT/1902.03118, Feb. 2019.
- Cusps, congruence groups and Monstrous dessins, Tatitscheff, V., He, Y.-H., McKay, J.,
Indagationnes Mathematicae, 2020, 31(6), 1015:1065
The files below are incomplete notes on various topics. They are not research papers, and probably contain typos or (even worse) wrong statments (however I hope there are not too many of these), more than if they were proof-read and complete, for sure.
They are accessible here in case they might be useful to some. I will greatly appreciate remarks and comments!
Notes and reviews
- Introduction to cluster objects is the expanded version of the notes of an eponymic talk I gave in Vautouraude, 2019 - a very stimulating unformal conference in Bretagne.
The goal of the presentation was to introduce cluster algebras and varieties, and then present some applications of the theory as well as some occurences of these cluster structures in mathematics (Teichmüller theory) and in physics (Seiberg duality).
- Dimer integrable systems is the expanded (and incomplete) version of the notes of the second talk I gave in Vautouraude, 2019.
After a general introduction to integrability from physical principles, I explain the construction of dimer integrable systems.
- Phases of SQCD is a wrap-up of the construction of the phase diagram of four-dimensional super quantum chromodynamics with one supersymmetry, with emphasis on Seiberg duality.
My main source (if not the only one) is Matteo Bertolini's Lectures on Supersymmetry,
which is of course way nicer, more complete and more pedagogical.
- Introduction to Seiberg-Witten theory are a set of notes based on W. Lerche's lectures on the matter.
I would still like to expand these with material I have collected here and there, and also with related and complementary ideas such as brane constructions.
- These are notes on the construction of the irreducible characters of the general linear groups over finite fields in terms of symmetric functions.
- Here is the master thesis I wrote under the supervision of Vladimir Fock.
The subject is the construction of cluster coordinates on the super-Teichmüller space of type X of a punctured Riemann surface.
- Here is a short note on a geometric approach to BRST quantization.
- Together with Arnaud Vanhaecke we wrote a review of the disproof of Kontsevich's conjecture on
polynomial countability of the finite fields points of graph schemes. Mnëv's universality theorem on matroids is a cornerstone of the proof, and hence is reviewed thoroughly.
- My bachelor thesis can be found here (it is written in French!).
The first part (under the supervision of Thierry Lévy, Jussieu) is about the differential geometry behind classical field theories.
The second part (under the supervision of Roberto Salerno, CMS) is a phenomenological study of the self-coupling of the Higgs field with the perspective of the CMS detector at CERN, in some beyond-the-Standard-Model theories.
A "khôlle" is an oral exercise session that students in "Classes Préparatoires" attempt weekly, to prepare for the competitive exam they have to pass in order to enter a "Grande Ecole".
In a typical khôlle three students share a blackboard and solve problems at the same time while the examiner discusses with each of them in turn and asks questions about what is done, just as in the oral exams of the "Concours".
- Fall 2021: Algèbre S2A - 26h Cours Magistral + 26h Travaux dirigés, University of Strasbourg.
Algèbre S2A is a class intended to first year maths students about the basics of linear algebra (vector spaces, dimension, rank, linear maps matrices).
- Fall 2021: Géométrie S4A - 20h Cours Magistral, University of Strasbourg.
Géométrie S4A is intended to second-year maths students about affine geometry, euclidean geometry and conics.
- Fall 2020: Maths pour la Science 1 - 42h + Algèbre 1 - 6h, University of Strasbourg.
Maths pour la Science 1 is a class intended to first-year scientific students which are not in maths; the main topics are complex numbers, partial fraction decompositions, functions, limits, continuity, derivation.
- Spring 2020: Maths pour la Science 2 - 32h, University of Strasbourg.
Maths pour la Science 2 is a class intended to first-year scientific students which are not in maths; the topic is linear algebra.
- Spring 2018: Introduction to Mathematical Physics (third year of bachelor) and Applied Maths (second year of bachelor), City, University of London.
I have replaced Prof. Yang-Hui He for a few hours in these classes, and lectured on the Schrödinger equation on the one hand, springs and harmonic oscillators on the other.
- 2016-2017: Khôlles in Mathematics in PCSI - 1h/week, Lycée Stanislas, Paris.
- 2015-2016: Khôlles in Chemistry/Physics in PSI* - 1h/week, Mathematics in MPSI - 1h/week, Mathematics in PCSI - 1h/week, Lycée Stanislas, Paris.
- 2014-2015: Khôlles in Chemistry, PSI* - 1h/week, Lycée Stanislas, Paris.
My office is UFR 114, 7, rue René Descartes, 67084 Strasbourg Cedex, France.
Please send me letters, and come and say hi if you are around!
Feel free to email me at email@example.com.