# Ruoguang (Roger) Tian

Current Office: MSB 2145

E-mail: rgtian[at]math.ucdavis.edu (replace [at] with @)

I am a lecturer in the Mathematics Department at UC Davis. My graduate adviser was Anne Schilling.

My research focus is on card shuffling (from a combinatorial perspective), Young tableaux and their statistics, and generally combinatorics on words.

My other interests include algebraic geometry and its applications to number theory.

## Teaching

2011 Summer Session II
2011 Fall

Math 21D
2012 Summer Session I

Math
16C
2013 Summer Session I

Math
16B
2015 Summer Session II

Math
145
2017 Winter

Math
16A
Math
25 B01
Math
25 B02
2018 Winter

Math
16B
Math
17A
2018 Spring

Math
16C
Math
25
## Papers

The following is a list of mathematical papers I've written.

*Characterization of B(infinity) using marginally large tableaux and rigged configurations in the A_n case via integer sequences*. Journal of Combinatorics (2018), Vol. 9, No. 2, 345-399. arXiv version (2016).
*Generalizations of an Expansion Formula for Top to Random Shuffles*. Annals of Combinatorics (2016), 20(4), 899-916. arXiv version (2014).

Here I give a bijective proof for an expansion formula derived (non-bijectively) by Adriano Garsia in his paper On the Powers of Top to Random Shuffling (link here), and then use this bijection to generalize the expansion formula in various directions.
*On the Diophantine Equation 2^a3^b + 2^c3^d = 2^e3^f + 2^g3^h *. Preprint, arXiv version (2009).

Here I solve, through elementary means, the Diophantine equation (m+1)^k(m^p-1) = m^q-1 for the case that m is even.
*Identities of the Function f(x,y) = x^2 + y^3 *. Preprint, arXiv version (2009).

Here I give some partial results on an open problem of Harvey Friedman.
## Talks Given

Expansion Formulae for Top to Random Shuffling, October 2015, AMS Central Fall Sectional Meeting (link)
Expansion Formulae for Top to Random Shuffling, March 2015, UC Davis/Berkeley Combinatorics Gathering II
Expansion Formulae for Top to Random Shuffling, October 2014, Student-Run Applied & Math Seminar, UC Davis
Generalizing an Expansion Formula in the Algebra of Shuffles, October 2013, Student-Run Applied & Math Seminar, UC Davis
Expansion Formulae in the Algebra of Shuffles, December 2012, Student-Run Applied & Math Seminar, UC Davis
Representation of Quivers, June 2012, Student-Run Algebraic Geometry Seminar, UC Davis
On the Diophantine equation (m+1)^k(m^p-1) = m^q-1, October 2010, Student-Run Applied & Math Seminar, UC Davis
## Conferences/Workshops Attended

26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC), June - July 2014, DePaul University, Chicago, Illinois (link)
ICERM workshop Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series, January - May 2013, Brown University, Providence, RI (link)
Automorphic Forms, Representations, and Combinatorics (A Conference in Honor of Daniel Bump), August 2012, Stanford University, Palo Alto, CA (link)