Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : à distance / remote
Adresse :IHP

Depuis le 23 mars 2020, le séminaire se tient à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.


Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or

subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.


Orateur(s) Miranda CHENG - IMJ, Paris,
Titre Umbral Moonshine and Niemeier Lattices
Horaire14:00 à 15:00
RésumeIn this talk I will discuss how a new type of moonshine – the umbral moonshine – arises from the 24 even unimodular lattices in 24 dimensions. In more details, for each of the 24 Niemeier lattices we pose an umbral moonshine conjecture identifying a specific set of mock modular forms and the graded characters of a certain natural module of a finite group arising from the automorphism of the Niemeier lattice. The construction of the set of mock modular forms relies on an ADE classification of mock modular forms of a certain type, analogous to the ADE classification of modular invariant combinations of characters of $A_1^{(1)}$ affine Kac-Moody algebra by Cappelli–Itzykson–Zuber, as well as the relation between mock modular forms and meromorphic Jacobi forms studied by S. Zwegers and Dabholkar–Murthy–Zagier. If time permits I will discuss certain mysterious group theoretic properties of this moonshine, the possible relations to certain generalised Kac-Moody algebras, or/and Gromov–Witten theory of certain Calabi–Yau three-folds. This talk is mainly based on joint work with J Duncan and J Harvey.
Salleà distance / remote