Adviser: Andrew Obus

Areas of Interest

  • Arithmetic geometry (covers of curves, wild ramification, étale fundamental groups, formal orbifolds)

  • Algebraic geometry (stacky curves, deformation theory)

  • Number theory (modular curves, class field theory, analogies between number fields and curves)

  • Topology (homotopy theory in algebraic geometry, analogies between algebraic topology and algebraic geometry)


  • (with Hugh Howards) Crossing number bounds in knot mosaics. Journal of Knot Theory and its Ramifications (July 2018). Available at arXiv:1405.7683v2 [math.GT] (


  • (with Libby Taylor) A¹-local degree via stacks (in preparation)

  • Wild ramification in stacky curves (dissertation in progress)

  • Class field theory and the study of symmetric n-Fermat primes (Master’s thesis)

  • Saturation in knot mosaics (senior thesis)


I keep notes on many courses and seminars I have been a part of. There are sure to be some errors, both cosmetic and mathematical, so if you find any, please contact me at ak5ah (at) virginia (dot) edu. Also, LaTeX files are available upon request. 

Although my philosophy is that 'all math is connected', I have grouped many of the above notes by area for ease of cross-reference. These larger files are available below. 

Thanks to Matt Feller, George Seelinger, Richard Vradenburgh and many others for noticing errors!