Recent and Upcoming Online Graduate Courses

Please contact the instructors if you want to participate in any of the upcoming courses in Fall or Winter of 2016-17.

Algebraic topology :  Dan Christensen - Winter, 2016; upcoming: Winter, 2017

Homotopy, fundamental group, Van Kampen's theorem, covering spaces, simplicial and singular homology, homotopy invariance, long exact sequence of a pair, excision, Mayer-Vietoris sequence, degree, Euler characteristic, cell complexes, projective spaces. Applications include the fundamental theorem of algebra, the Brouwer fixed point theorem, division algebras, and invariance of domain. 

Homotopy theory: Rick Jardine - Winter, 2016

Homotopical and homological algebra, simplicial sets, fundamental groupoid, homotopy groups, homotopy colimits and limits, bicomplexes, spectral sequences, Eilenberg-Mac Lane spaces, Postnikov towers, Hurewicz Theorem, spectrum objects, stable homotopy categories. 

Local homotopy theory: Rick Jardine - upcoming: Fall, 2016
Sheaves and presheaves, stalks, simplicial presheaves and simplicial sheaves, local weak equivalences, injective fibrations, sheaf cohomology, presheaves of chain complexes and derived categories, descent, descent spectral sequences, torsors and stacks, localization, motivic homotopy theory (introduction), presheaves of spectra, T-spectra, motivic stable category.