Other Activities


Student Topology Seminar

Wednesday March 23, 2016

LCB323 — 3:15 - 4:05

Hanna Astephan

Self Quasi-isometries of Hyperbolic Space

Abstract: We will show that a quasi-isometry from n-dimensional hyperbolic space to itself induces a homeomorphism on the sphere at infinity. Along the way, we will prove the Morse-Mostow 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 2-skeleton. 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

Quasi-Conformal Maps

Abstract: In this talk, we will give two definitions of quasi-conformal 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