Research

When the river of morphisms between complex smooth varieties flows in you, you will see Kodaira and Atiyah's smile (Kodaira fibration). The white-haired shadow of the mapping class group is roaming like a dream, which brings you the aroma of the monodromy representation. "The woods decay, the woods decay, and fall", the curvature withers slowly in thine arms (which leads you to the garden of non-positive curvature), Alexandrov and Gromov weep their burthen to the ground. "And after many a summer dies the swan." Non-positively curved space is only cruel in immortality. In the end, even if you are still too mean to show love and sympathy to the hyperbolic groups, you will still hear "Va, je ne te hais point~" from the acylindrically hyperbolic groups. 

I am interested in the topology which is related to complex geometry. I worked on Kodaira fibrations, surface bundles, acylindrically hyperbolic groups, Kahler groups, and mapping class groups. 

1.  Bounds on degrees of covers with injective monodromy in iterated Kodaira Fibrations, arxiv.  Rocky Mountain J. Math Volume 52 (2022), No.1, 365-380.

2. Conditions on the monodromy for a surface group extension to be CAT(0), arxiv. Proc. Amer. Math. Soc. 151 (2023), pp. 4643-4651

3. Relatively geometric actions of Kahler groups on CAT(0) cube complexes (with Corey Bregman and Daniel Groves), arxiv. Algebraic & Geometric Topology, to appear.

4. A note on complex hyperbolic lattices and strict hyperbolization, arxiv.