Research Summary

I do basic research in algebraic geometry and commutative algebra. This means I study geometric objects (schemes) and the functions that live on them. My particular interest is singularities, and I have worked extensively in positive characteristic (a clock arithmetic world where addition works like 5+10=3, 10 hours after 5:00 is 3:00). Recenlty, I've also been studying mixed characteristic which interpolates between the classical and positive characteristic worlds.


  • AAS, General Studies, Bellevue Community College
  • B.A., Mathematics, Whitman College
  • Ph.D., Mathematics, University of Washington. Project: On F-injective and Du Bois singularities


Karl Schwede received his BA from Whitman College in Walla Wallla Washington in 1999. After working as a computer programmer writing educational software for Havas Interactive / Vivendi Universal in 1999-2000, he began his Ph.D. studies at the University of Washington which he finished in 2006 under the direction of Sándor Kovács.  In August 2006, he moved to the University of Michigan where he was an NSF postdoc under the direction of Karen Smith.  After visiting the University of Utah in Fall 2010, he began a tenure track position at the Pennsylvania State University in January 2011.  In Fall 2014, he returned to the University of Utah as an Associate Professor and was promoted to Professor in 2018.

Karl Schwede has published more than 60 papers mostly on topics in geometry and algebra and especially in what is called positive characteristic. Positive characteristic is the study of arithmetic under a clock-like arithmetic, (5 hours after 10 o'clock is 3 o'clock, or 5+10=3). Karl Studies geometry under this sort of arithmetic and is focused on connecting geometry from this world to our usual geometry.  Positive characteristic arithmetic and geometry helps form a basis for our modern secure communication systems.