I'm Ryan Vinroot, an Associate Professor in the Mathematics Department at the College of William and Mary. I received my PhD from Stanford University in 2004 under the advisement of Professor Dan Bump.

- Office:
**Jones 100D** - Office phone:
**221-2017** - Email:
**vinroot at math dot wm dot edu**

- Math 410-Module Theory, Fall 2020.

- Math 302-Ordinary Differential Equations, Fall 2020.

- Math 430-Abstract Algebra II, Spring 2020.

- Math 110 (COLL 200)-Literally Mathematics, Spring 2020.

- Math 410-Galois Theory, Fall 2019.

- Math 316-Euclidean and Non-Euclidean Geometry, Fall 2019.

- Math 430-Abstract Algebra II, Spring 2019.

- Math 111-Calculus I, Spring 2019.

- Math 405-Complex Analysis, Fall 2018.

- Math 111-Calculus I, Fall 2018.

- Math 432-Combinatorics, Spring 2018.

- Math 110 (COLL 200) - Literally Mathematics, Spring 2018.

- Math 426-Topology, Fall 2017.

- Math 111-Calculus I, Fall 2017.

- Math 430-Abstract Algebra II, Spring 2017.

- Math 112-Calculus II, Spring 2017.

- Math 405-Complex Analysis, Fall 2016.

- Math 111-Calculus I, Fall 2016.

- Math 309-Intermediate Linear Algebra, Spring 2016.

- Math 302-Ordinary Differential Equations, Spring 2016.

- Math 426-Topology, Fall 2015.

- Math 103-Precalculus, Fall 2015.

- Math 432-Combinatorics, Spring 2014.

- Math 412-Number Theory, Fall 2013.

- Math 426-Topology, Fall 2013.

- Math 112-Calculus II, Section 2, Spring 2013.

- Math 430-Abstract Algebra II, Spring 2013.

- Math 111-Calculus I, Section 2, Fall 2012.

- Math 412-Number Theory, Fall 2012.

- Math 307-Abstract Algebra, Spring 2012.

- Math 432-Combinatorics, Spring 2012.

- Math 307-Abstract Algebra, Fall 2011.

- Math 211-Linear Algebra, Section 1, Spring 2011.

- Math 430-Abstract Algebra II, Spring 2011.

- Math 211-Linear Algebra, Section 1, Spring 2010.

- Math 307-Abstract Algebra, Spring 2010.

- Math 111-Calculus I, Section 5, Fall 2009.

- Math 307-Abstract Algebra, Fall 2009.

- Math 112-Calculus II, Spring 2009.

- Math 430-Abstract Algebra II, Spring 2009.

- Math 214-Foundations of Mathematics, Fall 2008.

- Math 519, Spring 2008.

- Math 129, Fall 2007.

- Math 415B, Spring 2007.

- Math 415A, Fall 2006.

- Math 215, Spring 2006.

- Math 125, Fall 2005.

- If you are a William and Mary undergraduate interested in working on mathematical research
with a faculty member, please see
this information.
For an idea of the type of undergraduate projects I have supervised, here is
a summary of each, and the preprints or papers for each may be found below:

- I supervised Max Kutler, an undergraduate at Harvey Mudd College, at the
REU here at the College of William and Mary during the Summer of 2009. The
results of the project are in the paper "On

- In the Summer 2010, I supervised undergraduate Feiqi Jiang from the
University of Michigan, supported by an NSF-FRG grant. The project results
are in the paper "A semi-recursion for the number of
involutions in special orthogonal groups over finite fields" below, which has
appeared in

- During Summer 2011, I supervised a project with William and Mary
undergraduates Zach Gates (supported by an NSF-FRG grant) and Brian Goldman
(supported by the College of William and Mary), with the results in the paper
"On the number of partition weights with Kostka multiplicity one", which has
appeared in the

- I supervised Zach Gates on a senior honors thesis during the 2011-12
academic year. We extended Zach's thesis results with co-author Anupam Singh
in a paper, "Strongly real classes in finite unitary groups of odd
characteristic", which has appeared in the

- During Summer 2012, I supervised two undergraduate research projects, each
with William and Mary students. The results of the project with Johnathon
Upperman (supported by a NOYCE Fellowship), are in the paper "A weight
statistic and partial order on products of

- During the 2013-14 academic year, I supervised two honors thesis projects
at William and Mary. Stephen Cameron completed the thesis "Local zeta
functions over

- Greg Taylor worked on an honors thesis with me during the 2016-17 year,
and many of the results are in the paper "On involutions and indicators of
finite orthogonal groups" below, which has been accepted in the

- During the 2017-18 academic year, Elena Amparo and Tanner Carawan each
completed honors theses under my supervision. Elena Amparo completed the
thesis "Counting real conjugacy classes in some finite classical groups".
Elena and I wrote a paper on the main result from her thesis in the paper "On
the number of real classes in the finite projective linear and unitary
groups", available below, which has been accepted in the

- On the number of irreducible real-valued characters of a finite group, with
Nguyen Ngoc Hung, A. Schaeffer Fry, and Hung
P. Tong-Viet: pdf, in
*J. Algebra***555**(2020), 275--288.

- A note on dual modules and the transpose, with T. Madsen and A. Roche: pdf, in
*Arch. Math. (Basel)***114**(2020), no. 3, 247-257.

- A computational approach to the Frobenius-Schur indicators of finite
exceptional groups, with S. Trefethen: pdf, in
*Internat. J. Algebra Comput.***30**(2020), no. 1, 141-166.

- Totally orthogonal finite simple groups: pdf,
in
*Math. Z.***294**(2020), no. 3-4, 1759--1785.

- Galois group action and Jordan decomposition of characters of finite
reductive groups with connected center, with
B. Srinivasan: pdf, in
*J. Algebra***558**(2020), 708--727.

- On the number of real classes in the finite projective linear and unitary
groups, with E. Amparo: pdf, in
*Glasg. Math. J.***62**(2020), no. 1, 93-107.

- Real representations of finite symplectic groups over fields of
characteristic two: pdf,
in
*Int. Math. Res. Not. IMRN*, 2020, no. 5, 1281--1299.

- Fields of character values for finite special unitary groups, with
A. Schaeffer Fry: pdf, in
*Pacific J. Math.***300**(2019), no. 2, 473-489.

- On involutions and indicators of finite orthogonal groups, with
G. K. Taylor: pdf,
in
*J. Austral. Math. Soc.***105**(2018), no. 3, 380-416.

- A factorization result for classical and similitude groups, with A. Roche:
pdf,
in
*Canad. Math. Bull.***61**(2018), no. 1, 174-190.

- Dualizing involutions for classical and similitude groups over local
non-archimedean fields, with A. Roche: pdf,
in
*J. Lie Theory***27**(2017), no. 2, 419-434.

- Kostka multiplicity one for multipartitions, with
J. Janopaul-Naylor: pdf,
in
*Australas. J. Combin.***68(2)**(2017), 153-185.

- Real classes of finite special unitary groups, with A. Schaeffer
Fry: pdf, in
*J. Group Theory***19**(2016), no. 5, 735-762.

- Jordan decomposition and real-valued characters of finite reductive groups
with connected center, with B. Srinivasan: pdf,
in
*Bull. Lond. Math. Soc.***47**(2015), no. 3, 418-426.

- A product formula for multivariate Rogers-Szegő polynomials, with
S. Cameron: pdf, in
*Ramanujan J.***35**(2014), no. 3, 479-491.

- Generating functions for real character degree sums of finite general
linear and unitary groups, with
J. Fulman: pdf,
in
*J. Algebraic Combin.***40**(2014), no. 2, 387-416.

- Strongly real classes in finite unitary groups of odd characteristic, with
Z. Gates and A. Singh: pdf, in
*J. Group Theory***17**(2014), no. 4, 589-617.

- A weight statistic and partial order on products of
*m*-cycles, with J. Upperman: pdf, in*Discrete Math.***315-316**(2014), 9-17.

- On the number of partition weights with Kostka multiplicity one, with
Z. Gates and B. Goldman: pdf,
in
*Electron. J. Combin.***19**(2012), no. 4, Paper 52, 22 pp.

- Strong reality properties of normalizers of parabolic subgroups in finite
Coxeter groups, with K. Lux and A. Schaeffer
Fry: pdf,
in
*Comm. Algebra*.**40**(2012), no. 8, 3056-3070.

- An enumeration of flags in finite vector spaces:
pdf, in
*Electron. J. Combin.***19**(2012), no. 3, Paper 5, 9 pp.

- Supercharacters, symmetric functions in noncommuting variables, and related
Hopf algebras, with AIM Workshop participants:
pdf,
in
*Adv. Math.***229**(2012), no. 4, 2310-2337.

- Semisimple symplectic characters of finite unitary
groups, with B. Srinivasan: pdf,
in
*J. Algebra***351**(2012), no. 1, 459-466.

- A semi-recursion for the number of involutions in special orthogonal
groups over finite fields, with F. Jiang: pdf,
in
*Finite Fields Appl.***17**(2011), no. 6, 532-551.

- Klyachko models of
*p*-adic special linear groups, with J. M. Lansky: pdf, in*Proc. Amer. Math. Soc.***139**(2011), no. 6, 2271-2279.

- Character degree sums and real representations of finite classical
groups of odd characteristic: pdf, in
*J. Algebra Appl.***9**(2010), no. 4, 633-658.

- Duality, central characters, and real-valued
characters of finite groups of Lie type: pdf,
in
*Osaka J. Math.***47**(2010), no. 2, 523-534.

- Shintani lifting and real-valued
characters: pdf, in
*Manuscripta Math.***132**(2010), no. 1-2, 145-158.

- On
*q*-analogs of recursions for the number of involutions and prime order elements in symmetric groups, with M. B. Kutler: pdf, in*J. Integer Seq.***13**(2010), no. 3, Article 10.3.6, 12 pp.

- Gelfand-Graev characters of the finite unitary groups, with N. Thiem: pdf,
in
*Electron. J. Combin.***16**(2009), no. 1, Research Paper 146, 37 pp.

- Values of character sums for finite unitary groups, with N. Thiem: pdf,
in
*J. Algebra***320**(2008), no. 3, 1150-1173.

- Involution models of finite Coxeter groups: pdf,
in
*J. Group Theory***11**(2008), no. 3, 333-340.

- Extending real-valued characters of finite general linear and unitary groups
on elements related to regular unipotents, with R. Gow: pdf,
in
*J. Group Theory***11**(2008), no. 3, 299-331.

- On the characteristic map of the finite unitary groups, with N. Thiem: pdf,
in
*Adv. Math.***210**(2007), no. 2, 707-732.

- A note on the orthogonal similitude group: pdf,
in
*Linear and Multilinear Algebra***54**(2006), no. 6, 391-396.

- Involutions acting on representations: pdf, in
*J. Algebra***297**(2006), no. 1, 50-61.

- Twisted Frobenius-Schur indicators of finite symplectic groups: pdf,
in
*J. Algebra***293**(2005), no. 1, 279-311.

- A factorization in GSp(V): pdf, in
*Linear and Multilinear Algebra***52**(2004), no. 6, 385-403.

- My collaborator Mandi Schaeffer Fry's homepage.
- My collaborator Bhama Srinivasan's homepage.
- My collaborator Nat Thiem's homepage.
- This website was designed by my good friend Angie Heile.