We meet in the lecture room of the library in the G-building.
We regularly hold two seminars:
Everyone is invited to attend! For more information, please contact Gabor Wiese.
|20/02/2014||Mehmet Haluk Sengün (Warwick)||Torsion Homology of Bianchi Groups and Arithmetic|
|05/03/2014, 16:00||Santiago Molina||Shimura Curves and Isogeny Classes of Abelian Surfaces with Quaternionic Multiplication|
|26/03/2014, 16:00||Santiago Molina||Shimura Curves and Isogeny Classes of Abelian Surfaces with Quaternionic Multiplication (II)|
|08/04/2014, 09:45||Jayanta Manoharmayum (Sheffield)||Universal deformation rings and the inverse deformation problem|
|30/04/2014, 14:00||Santiago Molina||p-adic measures attached to modular/automorphic forms (1)|
|07/05/2014, 14:15||Santiago Molina||p-adic measures attached to modular/automorphic forms (2)|
|21/05/2014, 14:15||Jan Tuitman (KU Leuven)||Counting points on curves using a map to P^1|
|28/05/2014, 14:15||Hwajong Yoo||Rational points on X_0(pq)|
|11/06/2014, 13:30||Hwajong Yoo||Non-optimal levels of reducible mod l modular representations|
Mehmet Haluk Sengün (Warwick): Torsion Homology of Bianchi Groups and Arithmetic
Bianchi groups are groups of the form SL(2;R) where R is the ring of
integers of an imaginary
quadratic eld. They form an important class of arithmetic Kleinian
groups and moreover they hold a key
role for the development of the Langlands program for GL(2) beyond
totally real fields.
In this talk, I will discuss several interesting questions related to the torsion in the homoloy of Bianchi groups. I will especially focus on the recent results on the asymptotic behavior of the size of torsion, and the reciprocity and functoriality (in the sense of the Langlands program) aspects of the torsion. Joint work with N.Bergeron and A.Venkatesh on the cycle complexity of arithmetic manifolds will be discussed at the end.
Jayanta Manoharmayum (Sheffield): Universal deformation rings and the inverse deformation problem
A good way of understanding a group is to look at its representations into the group of invertible n by n invertible matrices. One can organise such representations into families by first fixing a representation into GL_n of a finite field and then lifting it to `bigger' rings. By a theorem of Mazur, under certain hypothesis the liftings fit into a nice universal family. I will discuss the inverse problem of realizing rings as the coefficient rings of such a universal family and results in this direction (joint work with Tim Eardley).
Jan Tuitman (KU Leuven): Counting points on curves using a map to P^1
About 15 years ago Kedlaya introduced an algorithm to compute the zeta function of a hyperelliptic curve over a finite field of relatively small characteristic. I will speak about an extension of Kedlaya's algorithm to a very general class of curves (potentially any curve) introduced in a recent preprint of mine. This will include a demonstration of my implementation of this algorithm (the pcc_p and pcc_q MAGMA packages that can be found on my webpage).
Last modification: 5 June 2014.