César Lecoutre
Mathematics Teacher
UFR de mathématiques, Université Clermont Auvergne (France)
Email: Cesar.Lecoutre[at]uca.fr
Teaching 2023 - 2024
1) Refresher course pre-university level
Basic numerical and algebraic computation, first and second degree equations, line in the plane, classical functions
2) Mathematical complement, first year
Function composition, vector geometry, integration
3) First year semester one
Linear system, limit, continuity, IVT, polynomial, complex numbers, polynomials
4) First year semester two
Taylor expansion, vector space, linear application, numerical sequence
5) Groups and Applications, third year
Cyclic group, Symetric group, quotient group, isomorphism theorem
6) Rings and Applications, third year
Ring, field, units, ideal, quotient ring, arithmetic in principal ideal domain, polynomial of endomorphism
7) Scientific software, Fourth year (highschool teacher formation)
Classical algorithm
Programing with Scratch and Python
Research interests
Poisson varieties, deformations of Poisson algebras, quantum algebras, Artin-Schelter regular algebras, enveloping algebras, non commutative and Poisson birational equivalences.
A link to my PhD thesis
Publications and preprints
A quadratic Poisson Gel’fand-Kirillov problem in prime characteristic, Transactions of the American Mathematical Society 368 (2016), 755-785, arXiv1302.2046, with Stéphane Launois.
Poisson Deleting Derivations Algorithm and Poisson Spectrum, Communications in Algebra 45 (2017), 1294-1313, arXiv1409.4604, with Stéphane Launois.
A new family of Poisson algebras and their deformations, Nagoya Mathematical Journal 233 (2019), 32-86, arXiv1611.04306, avec Susan Sierra.
On the semi-centre of a Poisson algebra, Algebra and Representation Theory, 23(3) (2020), 875-886, arXiv1707.09006, with Lewis Topley.
Rational equivalence for enveloping algebras of three-dimensional Lie algebras, Journal of Pure and Applied Algebra, 228(4) (2024), arXiv:2211.05706, with Jacques Alev and François Dumas.
Rank two Artin-Schelter regular algebras and non communting of derivations, arXiv:2402.09832, avec Vincent Beck.
Some research activities
June 2023 - Invited talk, Journées d’algèbre en l’honneur de F. Dumas et T. Lambre, Clermont-Ferrand (FRANCE)
July 2023 - Invited talk, Workshop in Noncommutative Algebra and Representation Theory , Canterbury (UK)
Fall 2021 - Serie of two talks, Groupe de Travail Inter-universitaire en Algèbre (GTIA), IHP Paris (FRANCE)
October 2020 - Invited talk, Séminaire GAAO, Clermont-Ferrand (FRANCE)
November 2018 - Invited talk, Conference Representation in Lie Theory and interactions, CIRM Marseille (FRANCE)
June 2017 - Invited talk, Workshop Linking noncommutative rings and algebraic geometry, Edinburgh (UK)
June 2015 - Invited talk, Conference AMS-EMS-SPM International Meeting 2015 , Porto (PORTUGAL)
July 2014 - Conference organisation: Kent Algebra Day Young Researchers, Canterbury (UK)
2012 - Report of a meeting in the honour of Agata Smoktunowicz, London Mathematical Society Newsletter n° 414