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:

All packages written for the computer algebra system Magma.

- Joshua Maglione,
*Filters*, version 0.1, GitHub, 2017. https://github.com/joshmaglione/Filters - Joshua Maglione, Peter A. Brooksbank, and James B. Wilson,
*Tame Genus*, version 1.0, GitHub, 2017. https://github.com/algeboy/TameGenus - Joshua Maglione and James B. Wilson,
*Experimental Multilinear Algebra Group (eMAGma)*, version 1.2.3, GitHub, 2017. Contributions from Peter A. Brooksbank, https://github.com/algeboy/eMAGma

All packages written for the computer algebra system Magma.

Ongoing work:

*Compatible filters for isomorphism testing*.*Automorphisms from derivation algebras*, with Peter Brooksbank and James Wilson.*A correspondence for tensors, polynomials, and operators*, with Uriya First and James Wilson.*Enumerating isoclinism classes of semi-extraspecial groups*, with Mark Lewis.*On Automorphism groups of semi-extraspecial groups*, with Mark Lewis.

Presentations:

*"Tensoring" over Lie algebras: new findings & old problems II*. Algebra Seminar. Kent State University. 27 February 2018.*"Tensoring" over Lie algebras: new findings & old problems I*. Algebra Seminar. Kent State University. 20 February 2018.*A multilinear toolkit for isomorphism*. MAA Contributed Paper Session: Algebra I, JMM. San Diego, California. 10 January 2018.*Isomorphism to isotopism: building from examples*. Algebra Seminar. Kent State University. 10 October 2017.*New approaches to group isomorphism*. Algebra Seminar. Kent State University. 3 October 2017.*New tools for computing automorphism groups*.**Invited**. Algebra Seminar. Bucknell University. 14 September 2017.*A correspondence between tensors, polynomials, and operators*.**Invited**. Mathematics Colloquium. Bucknell University. 12 September 2017.*Tensors through the lens of groups*.**Invited**. Oberseminar Gruppen und Geometrie. Univeristät Bielefeld. 26 July 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.*Some Applications of filters to p-groups*.**Invited**. MFO Workshop: Computational Group Theory. Oberwolfach, Germany. 4 August 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.*p-groups and automorphisms*.**Invited**. Algebra Seminar. Bucknell, Lewisburg, PA. 26 February 2015.

*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*.**Invited**. 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.