NTS Spring 2014/Abstracts
|Majid Hadian-Jazi (UIC)|
|Title: On a motivic method in Diophantine geometry|
Abstract: By studying the variation of motivic path torsors associated to a variety, we show how certain nondensity assertions in Diophantine geometry can be translated to problems concerning K-groups. Then we use some vanishing theorems to obtain concrete results.
|Alexander Fish (University of Sydney, Australia)|
|Title: Ergodic Plunnecke inequalities with applications to sumsets of infinite sets in countable abelian groups|
Abstract: By use of recent ideas of Petridis, we extend Plunnecke inequalities for sumsets of finite sets in abelian groups to the setting of measure-preserving systems. The main difference in the new setting is that instead of a finite set of translates we have an analogous inequality for a countable set of translates. As an application, by use of Furstenberg correspondence principle, we obtain new Plunnecke type inequalities for lower and upper Banach density in countable abelian groups. Joint work with Michael Bjorklund, Chalmers.
|John Voight (Dartmouth)|
|Title: Numerical calculation of three-point branched covers of the projective line|
Abstract: We exhibit a numerical method to compute three-point branched covers of the complex projective line. We develop algorithms for working explicitly with Fuchsian triangle groups and their finite index subgroups, and we use these algorithms to compute power series expansions of modular forms on these groups. This is joint work with Michael Klug, Michael Musty, and Sam Schiavone.
|Nir Avni (Northwestern)|
|Title: Representation zeta functions|
Abstract: I will talk about connections between the following: 1) Asymptotic representation theory of an arithmetic lattice G(Z). More precisely, the question of how many n-dimensional representations does G(Z) have. 2) The distribution of a random commutator in the p-adic analytic group G(Z_p). 3) The complex geometry of the moduli spaces of G-local systems on a Riemann surface, and, more precisely, the structure of its singularities.
|Jennifer Park (MIT)|
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