Schedule

Date	Day	#	Lecture Topics	Links	Handouts
05/29	T	17	Presentations.
05/24	Θ	16	Presentations.
05/22	T		No class. Work on projects!		Presentation papers: – Coordinate-free – Sensor networks – Splitting – Greedy generators
05/17	Θ	15	PL functions; Morse lemma; Euler characteristic	– Inside the Klein bottle
05/15	T	14	Persistence algorithm; Morse functions	– Morse theory Gert Vegter's Animations: – Bulged Sphere – Torus Levels – Attaching a saddle	– Computing Persistent Homology
05/10	Θ	13	Filtrations; theory of persistent homology		– Barcodes
05/08	T	12	Nerve Lemma; Complexes: Čech, Vietoris-Rips, α, witness	– Alpha Shapes	– Witness complex – 6. Homology
05/03	Θ	11	Field coefficients; Duality; Data structures;		– Quad-Edge (with Code) – Edge-Facet (from Ernst Mücke's thesis)
05/01	T	10	Hauptvermutung; Poincaré Conjecture; Computing Homology	– Poincaré Conjecture @ Clay Institute – Scientific Comic Books	– 5. Homotopy – Poincaré Conjecture – Topo the World – Homework Four
04/26	Θ	9	Homology	– The Poincaré Conjecture Proved	Hardcopy handouts: – The Mathematics of Three-dimensional Manifolds – The Shapes of Space
04/24	T	8	Homotopy; Markov's undecidability		– 4. Group Theory – Homework Three – Markov's Proof
04/19	Θ	7	Finitely generated groups; presentations; functors
04/17	T	6	Groups; subgroups; factor groups		– Homework Two
04/12	Θ	5	Triangulation; orientability; Euler characteristic		– 3. Simplicial Complexes
04/10	T	4	Simplicial complexes; subcomplexes		– Homework One
04/05	Θ	3	Conway's ZIP; sphere eversions; k-simplex	– Smale's Paradox – The Optiverse – Outside In	– Conway's ZIP – Max's Eversion
04/03	T	2	Manifolds; basic 2-manifolds		– 2. Surface Topology
03/29	Θ	1	Introduction; topological spaces		– 1. Point Set Topology – 0. Introduction