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Slideshow

Tags: Seminars

  Title: Arithmetic Dynamics, the geometric Frey-Mazur conjecture, and monodromy representations Abstract: Which representations of the fundamental group of a complex quasiprojective variety X arise from geometry, i.e. appear inside of the monodromy representation on the cohomology of a family of varieties over X? I'll discuss new results on this topic arising from arithmetic dynamics, p-adic transcendence theory, and the geometric…
Abstract: A polynomial can be viewed as a branched cover of the sphere over itself that is compatible with a complex structure. If handed a topological branched cover of the sphere, we can ask whether it can arise from a polynomial—and if so, which one? In 2006, Bartholdi and Nekrashevych used group theoretic methods to explicitly solve this problem in special cases, including Hubbard’s twisted rabbit problem. We introduce a new topological…
Title of talk: Acyclotomy of torsion on elliptic curves Abstract: Much past and contemporary work studies rational points on modular curves defined over number fields, i.e., finite degree extensions of Q. But what about algebraic extensions of infinite degree? Two old results provide inspiration: if A/F is an abelian variety over a number field, Ribet showed that A has finite torsion over the maximal cyclotomic extension of F and Zarhin…
  Title: Self-repulsive curvature energies for curves and surfaces: regularity theory and relation to harmonic maps Abstract:  I will talk about a class of curvature energies for curves, the O'Hara energies, that are nonlocal in nature. In particular, I will present an approach for regularity theory of minimizers and critical points for these curves which is based on a relation to (fractional) harmonic maps. Then I will present some…

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