Research

"I shall now perish at the hands of mother homotopy turned evil sorceress."
-Saad Slaoui

Preprints:

• Moduli stack of oriented formal groups and cellular motivic spectra  
  arXiv:2111.15212 [math.AT]   (Dec 1, 2021)

• Moduli stack of oriented formal groups and the chromatic filtration  
  arXiv:2111.15202 [math.AT]   (Nov 30, 2021)

• Moduli stack of oriented formal groups and periodic complex bordism  
  arXiv:2107.08657 [math.AG]   (Jul 19, 2021)

• The Devinatz-Hopkins Theorem via Algebraic Geometry 
  arXiv:2103.07436 [math.AG]   (Mar 12, 2021)

Here are slides from a talk at the University of Kentucky in Spring 2022

Also, if you're really curious, here are some pre-baked pre-prerints:

• The Crystalline Space and Divided Power Completion
A very sketchy draft discussing a derived approach to crystals and pd-completions.

• Koszul duality for local systems
A slightly sketchy, but as of yet woefully incomplete, short note about Koszul duality (more accurately: Bar-Cobar duality) between modules and comodules.

• Musings on E_n-crystals
A short meditation on E_n-crystals (also known as E_n-D-modules). To be explored further in forthcoming joint work with David Ben-Zvi and Pavel Safronov.