Faculty & Staff Directory
- Associate Professor
A central theme of my research is applications of higher category theory to topology and differential and algebraic geometry. In particular, I am interested in derived geometry. I also maintain an active interest in field theory.
One of the larger endeavors I am working on is the development of a suitable framework for (infinite dimensional) derived differential geometry, tailored towards applications to field theory. This project is supported by a joint NSF topology grant, with Owen Gwilliam. This builds upon (still ongoing) work of mine with D. Roytenberg centered around modeling derived manifolds using differential graded manifolds.
I have also been actively researching the interaction between étale and motivic homotopy theory.
Finally, I have been working in the field of log geometry with Sarah Scherotzke, Nicolo Sibilla, and Mattia Talpo. We are currently investigating log étale K-theory.
I have many other projects as well.
- Math 639 Moduli Spaces and Invariant Theory (spring 2018)
- Math 114 Calculus II GMU, section 6 (spring 2018)
- Math 114 Calculus II GMU, sections 4 and 5 (fall 2017)
- Math 629 Algebraic Topology I GMU (spring 2017)
- Math 649 Category Theory GMU (fall 2016)
- Math 631 Graduate Topology GMU (spring 2016)
- Math 321 Abstract Algebra GMU (fall 2015)
- Math 101 (Calc II), Sec. 205 (UBC 2015)
- Master's Course on Topos Theory (University of Bonn 2013)
1. Étale Stacks as Prolongations. Advances in Mathematics (Accepted) arXiv link
2. Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity Topoi. Memoirs of the American Mathematical Society (Accepted) arXiv link
3. Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes with Scherotzke S., Sibilla N., and Talpo M. Geometry & Topology arXiv link
4. On The Homotopy Type of Higher Orbifolds and Haefliger Classifying Spaces. Advances in Mathematics, Volume 294, 14 May 2016, Pages 756–818 arXiv link
5. Correction to the article : An étalé space construction for stacks. Algebraic & Geometric Topology 16(1):541-546, February 2016
6. 5. On Theories of Superalgebras of Differentiable Functions. Theory and Applications of Categories, Vol. 28, 2013, No. 30, pp 1022-1098. with Roytenberg D.
7. An Étalé Space Construction for Stacks. Algebraic & Geometric Topology 13(2):831-903, 2013
8. Compactly Generated Stacks: A Cartesian closed theory of topological stacks. Advances in Mathematics, Volume 229, Issue 6, April 1 2012, Pages 3339-3397 arXiv link