Ryan Vinroot

I'm Ryan Vinroot, a 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.

Contact Information

• Office: Jones 100D
• Office phone: 221-5499
• Email: vinroot at math dot wm dot edu

Course Webpages

Courses at William & Mary:

• Math 311H-Honors Elementary Analysis, Fall 2023.

• Math 211-Linear Algebra, Fall 2023.

• Math 430-Abstract Algebra II, Spring 2023.

• Math 309-Intermediate Linear Algebra, Spring 2023.

• Math 403-Complex Analysis, Fall 2021.

• Math 316-Euclidean and Non-Euclidean Geometry, Fall 2021.

• Math 403-Intermediate Analysis, Spring 2021.

• Math 302-Ordinary Differential Equations, Spring 2021.

• 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.

Past Courses at the University of Arizona:

• Math 519, Spring 2008.

• Math 129, Fall 2007.

• Math 415B, Spring 2007.

• Math 415A, Fall 2006.

• Math 215, Spring 2006.

• Math 125, Fall 2005.
  

Undergraduate Research

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 q-analogs of recursions for the number of involutions and elements of prime order in symmetric groups", which has appeared in the Journal of Integer Sequences.

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 Finite Fields and their Applications.

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 Electronic Journal of Combinatorics.

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 Journal of Group Theory.

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 m-cycles", which has appeared in Discrete Mathematics, and the results with Stephen Cameron, who continued work into the 2012-13 academic year, are in the paper "A product formula for multivariate Rogers-Szegő polynomials", which has appeared in the Ramanujan Journal.

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 p-adic fields" (available from the William and Mary library: link). James Janopaul-Naylor completed the thesis "Combinatorially derived properties of Young tableaux". James and I extended the results in the paper "Kostka multiplicity one for multipartitions", available below, which has appeared in the Australasian Journal of Combinatorics.

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 Journal of the Australian Mathematical Society.

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 Glasgow Mathematical Journal. Tanner Carawan completed the thesis "Strongly real conjugacy classes in unitary groups over fields of even characteristic" (available from the William & Mary library: link, must be on campus to view).

During the 2020-21 academic year, Spencer Schrandt completed the honors thesis "Reality and strong reality in finite symplectic groups", available from the William & Mary library: link (must be on campus to view).

Publications and Preprints

• Galois automorphisms and a unique Jordan decomposition in the case of connected centralizer, with A. A. Schaeffer Fry and J. Taylor: pdf, submitted for publication.

• Budget variance analysis of n-variable products with zero or n responsibility centers, with C. M. Sorochuk and L. M. Leemis: pdf, in J. Theoretical Accounting Research 19 (2023), no. 1, 1--14.

• Some reality properties of finite simple orthogonal groups, with Jiwon Kim and S. Trefethen: pdf, in Adv. Group Theory Appl. 16 (2023), 39--66.

• 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.

Links

• 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.