Student Topology Seminar
Wednesday March 23, 2016
LCB323 — 3:15  4:05
Hanna Astephan
Self Quasiisometries of Hyperbolic Space
Abstract:
We will show that a quasiisometry from ndimensional hyperbolic space to itself
induces a homeomorphism on the sphere at infinity. Along the way, we will prove the MorseMostow lemma.
Wednesday March 9, 2016
LCB323 — 3:15  4:05
Matt Smith
Soap Bubbles and Harmonic Maps
Abstract:
When soap bubbles form, their shape is determined by a harmonic function.
A classical theorem tells us that functions on Euclidean spaces are
harmonic precisely when they minimize an "energy" functional. We can
construct a similar energy functional for maps between hyperbolic
surfaces, and define harmonic maps to be minima of this functional.
Harmonic maps have strong geometric properties. In particular, we will
discuss how harmonic maps lead to quadratic differentials and a proof of
Teichmuller's theorem.
Wednesday February 24, 2016
LCB323 — 3:15  4:05
David Wang
Finite Presentation of the Mapping Class Group
Abstract:
We will give a brief introduction to the mapping class group Mod(S) and
prove it's finitely presented. The idea of the proof is to construct a
K(Mod(S),1) complex with finite 2skeleton. In the process, we will prove
contractibility of the arc complex and use some standard constructions from the cohomology of groups.
Wednesday February 17, 2016
LCB323 — 3:15  4:05
James Farre
QuasiConformal Maps
Abstract:
In this talk, we will give two definitions of quasiconformal maps: a geometric one and an analytic one. The goal of the talk will be to prove the equivalence of these two definitions.
Wednesday February 10, 2016
LCB323 — 3:15  4:05
Leonard Carapezza
Green's Functions on Riemann Surfaces
Abstract:
We will define Green's Functions subsurfaces with boundary of Riemann surfaces and prove their existence.
Tuesday February 2, 2016
LCB323 — 2:00  3:00
Radhika Gupta
Extremal Lengths
Abstract:
We will discuss finding the extremal length for a set of arcs in the complex plane. We will explicitly compute the extremal length for a rectangle and an annulus. Lastly, we will discuss extremal metrics. This talk is based on material from Conformal Invariants by Ahlfors.
Wednesday January 20 & 27, 2016
LCB323 — 3:15  4:05
Derrick Wigglesworth
Thurston's Earthquake Maps
Abstract:
We will discuss earthquake maps on the hyperbolic plane and outline Thurston's proof of the earthquake theorem. We will also discuss the role that Thurston's theorem plays in hyperbolic geometry and Teichmuller theory.
Past Semesters
Spring 2015
Fall 2014
