I'm an assistant professor at Southern University of Science and Technology (SUSTech) in Shenzhen, China. From 2013 to 2016, I was a visiting assistant professor at Northwestern University. I received my Ph.D. from the University of Minnesota in 2013. My advisor was Tyler Lawson.
My research interests are in algebraic topology and related fields, particularly in its connections to algebraic geometry and number theory via objects such as formal groups, elliptic curves, and modular forms. A central theme in my research is elliptic cohomology and power operations, which combines the classical methodology of cohomological computations in algebraic topology with modern inputs from arithmetic moduli of elliptic curves in number theory, with applications to unstable homotopy. More generally, I study moduli spaces in various aspects, including geometric, arithmetic, computational, combinatorial, categorical. I am also interested in applying topology to physics, such as configuration of line degeneracies in electron energy band structures, and to data science, such as signal processing through persistent homology.
Conferences: International Workshop on Algebraic Topology
Norm coherence for descent of level structures on formal deformations, J. Pure Appl. Algebra 224 (2020), 106382, 35 pp.
Morava E-homology of Bousfield-Kuhn functors on odd-dimensional spheres, Proc. Amer. Math. Soc. 146 (2018), 449--458.
Semistable models for modular curves and power operations for Morava E-theories of height 2, Adv. Math. 354 (2019), 106758, 29 pp.
The Hecke algebra action and the Rezk logarithm on Morava E-theory of height 2, Trans. Amer. Math. Soc. 373 (2020), 3733--3764.
The power operation structure on Morava E-theory of height 2 at the prime 3, Algebr. Geom. Topol. 14 (2014), 953--977.
Algebraic topology and arithmetic, Young Mathematician Forum, Beijing International Center for Mathematical Research, Beijing, 2019
Power operations in elliptic cohomology and related arithmetic topics, Special Session on Algebraic and Geometric Topology, AMS-CMS Joint International Meeting, Shanghai, 2018
Toward calculating unstable higher-periodic homotopy types, Electronic Computational Homotopy Theory Seminar, Zoom, 2018
Symmetry encoded by norm maps, International Workshop on Loop Spaces, Supersymmetry and Index Theory, Chern Institute of Mathematics, Tianjin, 2017
Power operation calculations in elliptic cohomology, AMS Special Session on Homotopy Theory, Joint Meetings, Baltimore, 2014
MAT8021, Algebraic Topology, Spring 2021
MAT8024, Differentiable Manifolds (in Blackboard), Spring 2020
MA327, Differential Geometry, Spring 2019