Abstracts
Alina Cojocaru
University of Illinois at Chicago and IMAR
Investigations of the Frobenius traces of an abelian variety
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Given an abelian variety A over Q, we investigate the properties of the Frobenius traces of the reductions of A modulo varying primes. These investigations echo classical ones originating in work of Hardy - Ramanujan and of Serre. The talk is based on joint work with R. Davis, A. Silverberg and K. Stange, as well as on contributions by J-P. Serre
Nikolaos Diamantis
U. Nottingham
Eichler cohomology and regularised integrals
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In a joint work with R. Bruggeman and Yj. Choie, modular forms of general real weight are cohomologically interpreted in the same setting as the Eichler cohomology and Bruggeman-Lewis-Zagier's cohomology of Mass cusp forms. We outline this interpretation on the explicit example of a certain class of weakly holomorphic modular forms. The example was analysed in a joint work with K. Bringmann and S. Ehlen. We will discuss it along with a new definition of an "inner product" of weakly holomorphic modular forms.
Gergely Harcos
A. Renyi Inst. of Mathematics
The sup-norm problem for GL(2) over number fields
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I will discuss non-trivial bounds for the sup-norm of spherical Hecke-Maass newforms of square-free level for the group GL(2) over a number field. The talk is based on joint work with Valentin Blomer, Péter Maga, Djordje Milićević.
Victor C. Garcia
( UAM-Azcapotzalco, Mexico)
Additive bases with coefficients of modular forms
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Let f(z) be a normalized Hecke eigenform of weight 2k ≥ 4 for the full modular group with integer Fourier co-
efficients c(n). There exists a constant C(f) such that every integer can be written as a sum of C(f) coefficients.
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Cristian Popescu
U. C. San Diego
Beyond the main conjecture in Iwasawa Theory
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I will report on my recent proof (joint with Corey Stone) of a conjecture of Kurihara and its generalizations relating the higher Fitting ideals of various Iwasawa modules to special values of p-adic L-functions.