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

Math 16B

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)