Ryan Vinroot

I'm Ryan Vinroot, an Assistant 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 130
• Office phone: 221-2017
• Email: vinroot at math dot wm dot edu

Course Webpages

Present Courses at William & Mary:

• Math 307-Abstract Algebra, Spring 2012.

• Math 432-Combinatorics, Spring 2012.

Past Courses at William & Mary:

• 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.

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

In the Spring 2007 semester while I was at the University of Arizona, I advised, along with Professor Klaus Lux at the Univeristy of Arizona, a research project for Julio Brau entitled "Involutions and representations of the finite orthogonal groups".

During the 2007-08 academic year at the University of Arizona, I advised senior Matthew Hall for his Honors Thesis project, entitled "Representations of the symmetric groups and combinatorics of the Frobenius-Young correspondence".

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, and can be found below in the list of Publications and Preprints.

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 preprint below, entitled "A semi-recursion for the number of involutions in special orthogonal groups over finite fields".

If you are an undergraduate interested in working on mathematical research with a faculty member, please see this information.

Publications and Preprints

• Multivariate Rogers-Szegö polynomials and flags in finite vector spaces: pdf, submitted for publication.

• Strong reality properties of normalizers of parabolic subgroups in finite Coxeter groups, with K. Lux and A. Schaeffer Fry: pdf, to appear in Comm. Algebra.

• 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.

• 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.

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

• 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

• GAP manual.
• My collaborator Nat Thiem's homepage.