# Ruoguang (Roger) Tian

Current Office: MSB 1105

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
2018 Fall

Math
16B
Math
22A
2019 Winter

Math
16A
Math
21A
## 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)