I am a fifth year graduate student in the mathematics department at the University of Notre Dame. I received my B.A. in mathematics from Hope College in 2008. In my free time I like to read, play ultimate frisbee, and visit Lake Michigan as much as possible. Feel free to contact me with any questions, or check out my CV.

## Research

I study Lie algebras and algebraic groups with my advisor Sam Evens. I am drawn to this area by the rich interplay between examples whose structure is well understood and open questions about the geometric structure of certain varieties. Right now, I'm primarily focused on Hessenberg varieties. Hessenberg varieties are a family of closed subvarieties of the flag variety which include Springer varieties. This means that as sets, Hessenberg varieties are contained in the flag variety, but the conditions defining them are more restrictive than those defining the flag variety. Using combinatorial and geometric tools we can study them using the structure they inherit from the flag variety. Most recently, I've generalized methods used to study Springer varieties and applied them to Hessenberg varieties. My work can be found in my paper, "Affine pavings of Hessenberg varieties for semisimple groups," to appear in Selecta Mathematica. It is available online at SpringerLink here and on the arXiv: arXiv:1205.3976v2.

Here is a copy of my dissertation: Affine pavings of Hessenberg varieties for semisimple groups.

### Teaching

I have enjoyed be the instructor and teaching assistant for several different calculus courses. For a summary of my teaching evaluations, click here.

• Teaching Assistant, F 2009, S 2010, S 2012: Calculus III Tutorial
• Instructor, F 2011: Calculus III
• Teaching Assistant, F 2012: Calculus A Tutorial

At Notre Dame I get to work with gifted and driven students, including those students pursuing an honors major in mathematics.

• Instructor, Summer 2011/2012: Linear Algebra, SUMR
• Teaching Assistant, F 2010, S 2011: Honors Calculus Tutorial

### Post-PhD Plans

My graduate work at Notre Dame has confirmed my desires to pursue both research and teaching in an academic setting after graduating this May. For more information on my research plans, see my research statement, and for more on my approach to teaching check out my teaching statement. This Fall I'll begin a postdoc at Baylor University.

### Contact Information

E-mail: mprecup@nd.edu
University of Notre Dame, Department of Mathematics
Hurley Hall 281, Notre Dame, IN 46556