i will discuss a far reaching conjectural link between special
values of global and p-adic l-functions which unifies and refines some
classical conjectures of stark, gross, and rubin. i will report on
progress in establishing this link emerging from my joint work with
greither in equivariant iwasawa theory and relate that to recent
results in this area due to dasgupta and his collaborators.

the (wednesday) rtg colloquium lecture will be introductory in nature. it
will be followed by a more technical (thursday) number theory seminar
lecture where the main techniques and results will be explained in more
detail.

multivariate polynomial optimization where variables and data are complex numbers is a non-deterministic polynomial-time hard problem that arises in various applications such as electric power systems, signal processing, imaging science, automatic control, and quantum mechanics. complex numbers are typically used to model oscillatory phenomena which are omnipresent in physical systems. we propose a complex moment/sum-of-squares hierarchy of semidefinite programs to find global solutions with reduced computational burden compared with the lasserre hierarchy for real polynomial optimization. we apply the approach to large-scale sections of the european high-voltage electricity transmission grid. thanks to an algorithm for exploiting sparsity, instances with several thousand variables and constraints can be solved to global optimality.

i will discuss a far reaching conjectural link between special values of global and p-adic l-functions which unifies and refines some classical conjectures of stark, gross, and rubin. i will report on progress in establishing this link emerging from my joint work with greither in equivariant iwasawa theory and relate that to recent results in this area due to dasgupta and his collaborators.

note: this is the second (more technical) lecture of a two lecture series. the first (introductory) lecture will be given in the rtg
colloquium on april 5.

introduced by hamilton about thirty-five years ago, ricci flow has developed into an integral and vital part of the geometric analysis. some of its spectacular successes include the resolution of the poincare conjecture for three manifolds and the complete classification of quarter pinched riemannian manifolds. ricci solitons, as self-similar solutions to ricci flow, play an important role in understanding the singularity formation and long time dynamics of the flow. the talk will focus on the so-called shrinking solitons. we will review their classification in dimension two and three case, and mention some recent progress made jointly with ovidiu munteanu concerning their geometry in dimension four.