## About Me | |
## Papers and Expository Writings | |
## Talks, Seminars and Conferences | |
## Teaching |

**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.#### Interests

I am interested in homotopy theory, higher category theory and also geometric topology. In particular, I like thinking about:
#### History

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.

Here is my CV.

- 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.

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.