I am a fifth year PhD student at UT. My advisor is Andrew Blumberg. I can be contacted at [username, see URL]@math.utexas.edu.


In Fall 2017, I organized Arithmetic Geometry, Homotopy, And String Theory (AGHAST).


I am interested in algebraic \(K\)-theory, particularly trace methods; equivariant stable homotopy theory; chromatic homotopy theory; and higher category theory. I am frequently interested in how these interact with arithmetic geometry, especially the subjects of \(p\)-divisible groups and crystalline cohomology.

Please enjoy the following animation of Waldhausen's \(S_\bullet\) construction (move your cursor over the entries in the diagram on the left). (If you started on a different tab, you may need to refresh the page for this to work.)

Publications and Preprints

  1. Sulyma, Y. J. F. \(\infty\)-categorical monadicity and descent. New York Journal of Mathematics 23 (2017), 749–777. arxiv version.


Witt vectors and topological cyclic homology slides from a talk at YTM 2018

Notes on stacks for WCATSS '16


Matrix visualizer

Gauss-Jordan Elimination (Row Reduction)

Volumes of revolution

3-simplex visualization