[CvGmt News] avviso Seminari di Matematica dr. Lars Kuehne (24.11 e 1.12. 2014)

[Valeria Giuliani]

SEMINARI MATEMATICA



*Il dr. Lars Kuehne*

*(SNS)*



Terrà due seminari dal titolo:



*“**Modular forms**”*



secondo il seguente calendario:



Lunedì 24 novembre 2014

ore 14:00,  Aula Mancini



Lunedì 1 dicembre 2014

Ore 14:00, Aula Mancini



*Abstract: **In these two talks, a quick introduction to modular forms and
some of their arithmetic utilizations shall be given. On the one hand,
basic facts about modular forms (e.g. Atkin-Lehner theory) are given to
promote a better understanding of an upcoming talk of Rafael van Känel
about modularity and the S-unit equation. On the other hand, I highlight
some more advanced aspects of this ever-growing area of mathematical
research, which hopefully present good motivation to the novice.*
* The relation between modular forms and Dirichlet series as well as the
construction of Galois representations associated with modular forms is
covered (without complete proofs, of course). As far as time permits, I
indicate how these representations are used, in particular if they are
combined with modularity results. Such applications include congruences of
arithmetic functions, diophantine equations (Hellegouarch-Frey,
Bennett-Dahmen) and the Sato-Tate conjecture for elliptic curves. However,
the modularity results (Wiles-Taylor et al.) will be used solely as a
blackbox, avoiding a rather intricate part of modern arithmetic."*

Classe di Scienze Matematiche e Naturali
Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
tel. 050 509260
Piazza dei Cavalieri, 7
56126 Pisa
E-mail: valeria.giuliani at sns.it
E-mail: classi at sns.it
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