My research interests are in

I am also interested in topics related to nonassociative algebras, *-algebras, bilinear and quadratic forms, geometric invariant theory, and computational complexity theory.

*p*-groups and computational group theory. I'm interested in developing algorithms to aid in distinguishing*p*-groups (the group isomorphism problem). However, most of my work takes me to different areas of research in algebra, geometry, and computer science.I am also interested in topics related to nonassociative algebras, *-algebras, bilinear and quadratic forms, geometric invariant theory, and computational complexity theory.

Publications:

*Most small p-groups have an automorphism of order 2*, Arch. Math. (Basel)**108**(2017), no. 3, 225--232. (doi pdf)with Peter Brooksbank and James Wilson, J. Algebra*A fast isomorphism test for groups of genus 2*,**473**(2017), 545--590. (doi pdf)*Efficient characteristic refinements for finite groups*, J. Symbolic Comput.**80**(2017) part 2, 511--520. (doi pdf)*Longer nilpotent series for classical unipotent groups*, J. Grp. Theory**18**(2015), no. 4, 569--585. (doi pdf)*Economical generating sets for the symmetric and alternating groups consisting of cycles of a fixed length,*with Scott Annin, J. Algebra Appl.**11**(2012), no. 6, 1250110--1250118. (doi)

Software:

- Multilinear Algebra, with James Wilson for the computer algebra system Magma.
- Nonassociative Algebras, with James Wilson for the computer algebra system Magma.

Presentations:

*Zeta functions and the PORC conjecture*. Graduate Student Algebra Seminar. Colorado State University. 25 April 2017.*Computing new isomorphism invariants of groups*. Southern Regional Algebra Conference. Mobile, Alabama. 18 March 2017.*New characteristic structure from filters*. Invited. AMS Special Session: Group Cohomology and Representation Theory, JMM. Atlanta, Georgia. 4 January 2017.*Working with tensors: a lesson from examples*. Algebraic Combinatorics Seminar. Colorado State University. 11 November 2016.*New tools for computing automorphism groups*. Invited. AMS Sectional Meeting, Special Session: Groups and Representation Theory. University of Denver. 8 October 2016.*Operators, polynomials, and tensors: a love triangle*. Graduate Student Seminar. Colorado State University. 29 September 2016.*Group theory without doing group theory*. Graduate Student Algebra Seminar. Colorado State University. 21 September 2016.*Some Applications of filters to p-groups*. Invited. MFO Workshop: Computational Group Theory. Oberwolfach, Germany. 4 August 2016.*Surreal Numbers*. Graduate Student Seminar. Colorado State University. 5 May 2016.*Simple Structure in Nilpotent Groups*(Poster). Princeton University. 2 November 2015.*Automorphisms of small p-groups*. Algebraic Combinatorics Seminar. Colorado State University. 9 October 2015.*An isomorphism test on the edge of wilderness*. Graduate Student Seminar. Colorado State University. 1 October 2015.*p-groups and automorphisms*. Invited. Algebra Seminar. Bucknell, Lewisburg, PA. 26 February 2015.*p-groups, algebras, and bilinear maps*. Graduate Student Seminar. Colorado State University. 4 December 2014.

*Finding chief series in large unipotent groups of Lie type*. BIRS: Algorithms for Linear Groups. Banff, Alberta. 19 November 2014.

*An introduction to LaTeX*. SIAM and Upsilon Pi Epsilon student workshop. Colorado State University. 4 November 2014.

*Longer characteristic series and its applications*. Groups, Computation & Geometry Conference. Pingree Park, Colorado. 10 June 2014.*Longer nilpotent series for unipotent groups*. Algebraic Combinatorics Seminar. Colorado State University. 22 November 2013.*Module isomorphism testing*. Graduate Student Seminar. Colorado State University. 24 October 2013.

Ongoing work:

*Pseudo-isometries from derivation algebras*, with Peter Brooksbank and James Wilson.*Polynomial-identity tensors and their invariants*, with Uriya First and James Wilson.*On automorphisms of p-groups*.