Teoría geométrica de Langlands
Profesor: David Kazhdan (Hebrew University of Jerusalem and Harvard University)
Puntaje: 1 puntos (Lic. y Prof.)
Correlatividades: Álgebra III
Carga horaria: 12 horas en total en 3/4 sesiones
Carreras: Licenciatura en Matemática (Or. Pura y Aplicada), Profesorado en Matemática, Doctorado en Matemática
Contenidos:
The basics of the theory of representations of reductive groups over local non-archimedian fields.
a) The structure of local non-archimedian fields $F$, the Mellin and Fourier transform.
b) The Cartan and Iwasawa decomposition of reductive groups.
c) Induced and cuspidal representations.
d) The structure of the Hecke algebra and unramified representations.
e) The Satake transform.
The class field theory and the Langlands conjecture.
a) The structure of the Galois group $Gal (\bar F/F)$ for local fields $F$.
b) Extensions of global fields and their ramifications.
c) The Chebatorev's theorem.
d) Adeles.
e) The formulation of the global class field theory.
f) A formulation of the Langlands conjecture for $GL(n)$ over global fields.
The local Langlands conjecture.
a) $L$ and $\ep$ functions on multiplicative characters of local fields.
b) $L$ and $\ep$ functions on representations of $GL(n,F)$ for local fields $F$.
c) The characterization of representations of $GL(n,F)$ in terms of their $L$ and $\ep$ functions.
d) $L$ and $\ep$ functions on representations of the Galois group $Gal (\bar F/F)$ for local fields $F$.
e) The formulation of the local Langlands conjecture.
En principio, las sesiones serán los días: miércoles 25 de febrero, viernes 27 de febrero, lunes 2 de marzo.
Para más información, comunicarse con el Prof. Fernando Cukierman.
