Research

Publications and Preprints


11. Quantitative representation stability over linear groups, with J Miller.
ArXiv preprint ArXiv:1709.03638, Submitted. (Updated 29 Sep 2018).

10. Central stability for the homology of congruence subgroups and the second homology of Torelli groups, with J Miller and P Patzt.
ArXiv preprint ArXiv:1704.04449, Submitted. (Updated 10 Oct 2017).

9. Stability for hyperplane complements of type B/C and statistics on squarefree polynomials over finite fields, with R Jiménez Rolland.
ArXiv preprint ArXiv:1703.06349v2, Submitted. (Updated 22 Mar 2017).

8. Higher order representation stability and ordered configuration spaces of manifolds, with J Miller.
ArXiv preprint ArXiv:1611.01920. Submitted. (Updated 4 Jun 2017).

7. Generating functions and statistics on spaces of maximal tori in classical Lie groups, with J Fulman and R Jiménez Rolland.
New York Journal of Mathematics 23 (2017), 165–191.

6. Convergence criteria for FIW–algebras and polynomial statistics on maximal tori in type B/C, with R Jiménez Rolland.
Advances in Mathematics 310 (2017), 121–158.

5. FIW–modules and constraints on classical Weyl group characters.
Mathematische Zeitschrift 281 (2015), no. 1-2, 1–42.

4. FIW–modules and stability criteria for representations of classical Weyl groups.
Journal of Algebra 420 (2014), 269–332.

3. Representation stability for the cohomology of the pure string motion groups.
Algebraic & Geometric Topology 12 (2012), no. 2, 909–931.

2. Decomposing inversion sets of permutations and applications to faces of the Littlewood-Richardson cone, with R Dewji, I Dimitrov, A McCabe, M Roth, and D Wehlau.
Journal of Algebraic Combinatorics, 45 (2017), no. 4, 11739–1216.

1. The non-commutative cycle lemma, with C Armstrong, J A Mingo, and R Speicher.
Journal of Combinatorial Theory Series A 117 (2010), no. 8, 1158–1166.

Notes

These are some brief notes and graphics to illustrate the correspondence between string motions and automorphisms of the free group.

Topic Exam

I took my topic exam at the University of Chicago in February 2011. My topic proposal is available here: The Cohomology of Configuration Space and Representation Stability.

Undergraduate Projects

I received my B.Sc.H. from Queen's University in Kingston, Canada.

In the summer of 2009, I took part in a project on Littlewood Richardson Coefficients and Coxeter Groups with Mike Roth and Ivan Dimitrov, with the support of an NSERC USRA. My colleagues completed our project the following year: Decomposing Inversion Sets of Permutations and Applications to Faces of the Littlewood-Richardson Cone (with R Dewji, I Dimitrov, A McCabe, M Roth, and D Wehlau).

In the summer of 2008, I took part in a project on Free Probability and Random Matrices with Roland Speicher and James A. Mingo, supported by an NSERC USRA.
Some of our work is available here: The non-commutative cycle lemma. (with C Armstrong, J A Mingo, and R Speicher.)



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