Hello! I am a fifth-year PhD student in mathematics at the University of Texas in Austin. My adviser is Andrew Blumberg.
Here is my CV.
Sometimes I blog here.
I am currently thinking about derived and spectral algebraic geometry in positive characteristic, as well as connections to algebraic K-theory and topological cyclic homology. I'm also interested in the role of higher category theory in various parts of homotopy theory, in particular calculus of functors and equivariant stable homotopy theory.
I previously studied generalized string topology operations as arising from a generalization of the Pontrjagin-Thom construction in a ``highly structured'' category of spectra. In particular, using the Eilenberg-Watts theorem for stable infinity-categories I proved that generalized string topology coincides with a version of derived Koszul duality. A preprint is on the arXiv.
Here's some stuff I've talked about recently:
- "Generalized String Topology is Derived Koszul Duality" - Graduate Student Topology and Geometry Conference 2013, University of Notre Dame, Spring 2013. Slides are here.
- "Algebraic K-Theory for Number Theory I" - Junior Number Theory Seminar, University of Texas, Spring 2013
- "Loop Spaces and Connections" - Student Geometry Seminar, University of Texas, Fall 2012
- "The Homotopy Type of the Cobordism Category" - Graduate Geometry & Topology Current Literature Seminar, University of Texas, Fall 2012
- "The Approximation Theorem, the Sphere Theorem, and the Plus Construction" - West Coast Algebraic Topology Summer School 2012: Advances in K-theory, Stanford University, Summer 2012
- "Fiber Bundles and Symmetry Groups" - The Undergraduate Mathematics Research Group, University of Texas, Spring 2012
I am not teaching this semester, Spring 2013.
In previous semesters I have taught:
- M408N with Prof. Amir Mohammadi, Fall 2011
- M382D with Prof. Dan Freed, Spring 2011
- M408D AP Honors with Prof. Ted Odell, Fall 2010
- M408D with Prof. Kathy Davis, Spring 2010
- M408C with Prof. Kathy Davis, Fall 2009
Email: aroyer [at] math [dot] utexas [dot] edu