I am an Assistant Professor at Sam Houston State University, Math & Stats.
My research is in the area of Geometric Topology known as higher rank Teichmuller theory.
I received my Ph.D from University of Southern California with advisor Francis Bonahon.
Prior to SHSU, I was a postdoc at University of Michigan, Ann Arbor and Yale University.
Office. Lee Drain Building, 411
Email. gxm120 [at] shsu [dot] edu
CV. [ PDF ] (Last updated: July 2026)
Links. [arXiv] [Google Scholar][MathSciNet]
Holmes-Thompson area of inscribed polygons and convex projective structures, with X. Flamm, arXiv:2601.04009 [ Abstract | PDF ]
Topology of the space of d-pleated surfaces, with S. Maloni, F. Mazzoli, and T. Zhang, arXiv:2508.04813 [ Abstract | PDF ]
Correlation number for potentials with entropy gaps and cusped Hitchin representations, with L.-Y. Kao
Ergodic Theory Dynam. Systems, 46(7) (2026), 1755–1799 [ Abstract | PDF | Journal ]
d-pleated surfaces and their shear bend coordinates, with S. Maloni, F. Mazzoli, and T. Zhang
Proc. Lond. Math. Soc. 133(1) (2026), e70174, 147 pp. [ Abstract | PDF | Video | Journal ]
Pressure metrics for cusped Hitchin components, with H. Bray, R. Canary, and L.-Y. Kao
Adv. Math. 435 (2023), Paper No. 109352, 24 pp. [ Abstract | PDF | Journal ]
A closed ball compactification of a maximal component via cores of trees, with C .Ouyang, and A. Tamburelli
Algebr. Geom. Topol. 24 (2024), 3693–3717 [ Abstract | PDF | Journal ]
Counting, Equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations, with H. Bray, R. Canary, and L.-Y. Kao
J. Reine Angew. Math. (Crelles) 791 (2022), 1–51 [ Abstract | PDF | Video | Journal ]
Correlation of the renormalized Hilbert length for convex projective surfaces, with X. Dai
Ergodic Theory Dynam. Systems, 43(9) (2023), 2938–2973 [ Abstract | PDF | Video | Journal ]
Sequences of Hitchin representations of Tree-type, arXiv:1910.13585 [ Abstract | PDF | Video ]
Positive configurations of flags in a building and limits of positive representations
Math. Z. 293 (2019), no. 3-4, 1337–1368 [ Abstract | PDF | Journal ]
Positively ratioed representations, with T. Zhang
Comment. Math. Helv. 94 (2019), no. 2, 273–345 [ Abstract | PDF | Journal ]
Sam Houston State University. Elementary Functions (F25, S25); Introduction to Math Thought (F24); Graduate Topology (S24);
College Mathematics (F25, S24, F23); Calculus II (F24, F23)
Yale University. Linear algebra (S23); Calculus of Functions of One Variable I (F22)
University of Michigan. Linear algebra (Inquiry based learning) (W19, W20, W22, F21); Explorations in Mathematics (W21);
Applied Linear Algebra (F19,F20); Calculus 1 (F18)
University of Southern California. Topology (Graduate) (F17); Geometry and transformations (F17); Calculus II for Engineers and Scientists (F16);
Calculus I (F15); Linear Algebra and Linear Differential Equations (F14); Precalculus (F13, F14)
GT Webinar, with Arielle Leitner. All information is available on the webinar's Webpage
Junior Colloquium, with Tiffany Frugé Jones and Naomi Krawzik
Junior Colloquium Capstone Conference, Upcoming
Part of his material is based upon work supported by the U.S. National Science Foundation under Grant No. 2524159.
Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.