Talk

Studying the behavior of complex representations of a $p$-adic group restricted to its closed subgroup with the same derived group, we can derive useful information to establish the local Langlands correspondence for the subgroup. In this context, after reviewing the correspondences for $p$-adic inner forms of $SL(n), Sp(4),$ and others, we shall discuss the multiplicity of tempered representations of $p$-adic groups in the restriction, and relate it to its counterpart of corresponding irreducible representations of finite groups in the Langlands dual side, under some assumptions.

This talk will present a new effective Chebotarev theorem that holds for all but a possible zero-density subfamily of certain families of number fields of fixed degree. For certain families, this work is unconditional, and in other cases it is conditional on the strong Artin conjecture and certain conjectures on counting number fields. As an application, we obtain nontrivial average upper bounds on l-torsion in the class groups of the families of fields. This talk is on joint work with Lillian Pierce and Melanie Matchett Wood.

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.