1 view

Skip to first unread message

Feb 15, 2019, 5:17:40 AM2/15/19

to akls-s...@googlegroups.com

Dear colleagues,

The next ABKLS seminar will take place in Lille, on Wednesday, February 27.

Hope to see you in Lille!

Best regards,

Valery and Aloys

56th Seminar Aachen-Bonn-Köln-Lille-Siegen

on Automorphic Forms

University of Lille, February 27, 2019

Organizers: K. Bringmann, J. Bruinier, V. Gritsenko, A. Krieg, P. Moree,

G. Nebe, N-P. Skoruppa, S. Zwegers

When: Wednesday, February 27, 2019

Where: University of Lille, Cité Scientifique, Villeneuve d’Ascq, Bat.

M2, la salle de réunion

14.00 – 15.00 Haowu Wang (LabEx CEMPI, Lille). The Weyl-invariant weak

Jacobi forms for the root system E_8.

The Chevalley type theorem for affine root systems is equivalent to the

fact that the bigraded ring of the Weyl-invariant weak Jacobi forms for

a classical root system R is a pure polynomial algebra. The

corresponding generators play an important role in the theory of

Frobenius varieties. This subject was developed by E. Looijenga, K.

Saito, J. Bernstein, O. Schwarzman, K. Wirthmüller, B. Dubrovin, M.

Bertola and others. In 1992, Wirthmüller proved that the bigraded ring

of W(R)-invariant weak Jacobi forms is a polynomial algebra over the

ring of SL(2, Z) modular forms except the root system E8. It is still an

open problem how to extend the Wirthmuller's theorem to the case R=E_8.

The Weyl invariant E_8 Jacobi forms have many applications in

mathematics and physics, but very little has been known about its

structure. In this talk, I will present a description of

W(E_8)-invariant Jacobi forms of small indices . As a corollary we give

the negative answer on this old problem: the ring of W(E_8)-invariant

weak Jacobi forms is NOT a polynomial algebra. Thus a Chevalley type

theorem is NOT true for the root system E_8. Then I give a proper

extension of the Chevalley type theorem to the case of the affine root

system E_8.

15.15 – 16.15 Amir-Kian Kashani-Poor (Laboratoire de physique théorique

de l’ENS, Paris)

Curve counting and (extended) Weyl invariant Jacobi forms.

Packaging enumerative invariants into generating functions has proven to

be a powerful strategy to compute them. Symmetries underlying the

geometry act on such functions, and in propitious cases, substantially

simplify their computation. In this talk, I will address curve counting

in elliptically fibered Calabi-Yau manifolds from this vantage point.

After a short excursion into how the problem fits into physics, I will

discuss the structure of the topological string partition function

Z_top, a physically motivated generating function for curve counting

invariants, on a class of such geometries. Weyl invariant Jacobi forms —

Lie algebras make an appearance due to the Kodaira classification of

singularities of elliptic fibers — will play an important role in the

construction of Z_top. To fully exploit the symmetries of the problem, I

will introduce a subring of such forms, invariant also under diagram

symmetries of the associated affine Dynkin diagrams.

16:15—17:15 Coffee Break

17.15 – 18.15 Shoyu Nagaoka (Kindai University)

Theta Operator for Modular Forms.

Theta operator \Theta is a kind of differential operator operating on

modular foms. It is a generalization of the classical Ramanujan's

\theta-operator. For a prime p, the mod p kernel of the theta operator

is defined as the set of modular form F such that \Theta (F) \equiv 0

\mod p. Namely, the element in the set can be interpreted as a mod p

analogue of the singular modular form. In this talk, I will give

examples of modular forms in the mod p kernel of the theta operator.

18:30 Buffet (in the building M2)

For further informations concerning this meeting please send an email to

Valery.G...@math.univ-lille1.fr. For the previous meetings see

http://www.matha.rwth-aachen.de/en/forschung/abkls/

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu