My research interests are in 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.
I am also interested in topics related to nonassociative algebras, *-algebras, bilinear and quadratic forms, geometric invariant theory, and computational complexity theory.
Publications:
- Enumerating isoclinism classes of semi-extraspecial groups, with Mark Lewis.
- Compatible filters for isomorphism testing. (pdf)
- Most small p-groups have an automorphism of order 2, Arch. Math. (Basel) 108 (2017), no. 3, 225--232. (doi pdf)
- A fast isomorphism test for groups of genus 2, with Peter Brooksbank and James Wilson, J. Algebra 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.
- Peter A. Brooksbank, Joshua Maglione, and James B. Wilson, MatrixLie, version 0.1, GitHub, 2018. https://github.com/glaois60/MatrixLie
- Joshua Maglione, Filters, version 0.1, GitHub, 2017. https://github.com/joshmaglione/Filters
- Joshua Maglione, SemiMag, version 0.1, GitHub 2018. https://github.com/joshmaglione/SemiMag
- 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 1.2.5, GitHub, 2018. Contributions from Peter A. Brooksbank, https://github.com/algeboy/eMAGma
All packages written for the computer algebra system Magma.
Ongoing work:
- A correspondence for tensors, polynomials, and operators, with Uriya First and James Wilson.
- Automorphisms from derivation algebras, with Peter Brooksbank and James Wilson.
- On Automorphism groups of semi-extraspecial groups, with Mark Lewis.
- Quotients of Heisenberg groups over local algebras, with Peter Brooksbank and James Wilson.
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.