- Email: montekg (at) umich (dot) edu
- Office: East Hall 5840
I am a fifth year PhD student in the Department of Mathematics
at the University of Michigan
. My advisor is Igor Kriz
Here is my CV
I am interested in homotopy theory, higher category theory and also geometric topology. In particular, I like thinking about:
- The computation of homotopy groups and various (co)homology theories.
- Higher/derived/brave new/homotopy coherent algebra, via spectra and operads.
- The higher categorical aspects of the above, via (∞,1)-categories (quasicategories), model categories and simplicially enriched categories.
- Properties of 3-manifold groups, the Thurston geometries on 3-manifolds and moduli and Teichmüller spaces of geometric structures on surfaces.
On February 17th, 2017, I passed my preliminary exam (aka qualifying exam). Here is the syllabus
In September 2015, I graduated from the University of Sydney
with an M.Sc. by research under the supervision of Stephan Tillmann
. My thesis
formulated a framework for constructing representations of the fundamental groups of triangulated 3-manifolds using combinatorial data which unified methods of Rubinstein-Tillmann and Luo, and studied and found a counterexample to a conjecture of Luo concerning a strong residual finiteness property of 3-manifold groups.
In December 2014, I graduated from the University of Sydney
with a B.Sc.(Advanced Mathematics), including an Honours year, after which I was awarded the University Medal.