Research

I am an algebraic geometer working on topics related to the interplay between singularity theory and different areas such as birational geometry, Hodge theory and D-module theory. The study of singularities has been the central topic in a large number of different areas of geometry.  In recent years I have been studying various invariants of singular varieties and their applications.

Publications:

  1. Multiplier ideals of analytically irreducible plane curves, preprint, arXiv:1907.06281 (2019).
  2. Hodge filtration and Hodge ideals for Q-divisors with weighted homogeneous isolated singularities , preprint, arXiv:1810.06656 (2018).
  3. Topological classification of simplest Gorenstein non-complete intersection singularities of dimension 2 (with Stephen Shing-Toung Yau, Huai-Qing Zuo), Asian J. Math. Vol.19, No. 4, pp. 651-792, September 2015.
  4. On classification of toric surface codes of low dimension (with Xue Luo, Stephen Shing-Toung Yau, Huai-Qing Zuo), Finite Fields and Applications 33 (2015), 90-102.
  5. On classication of toric surface codes of dimension seven (with Naveed Hussain, Xue Luo, Stephen Shing-Toung Yau and Huai-Qing Zuo), to appear, Comm. Anal. Geom.