Hang Huang, Assistant Research Professor

Teaching

• MATH 2660, Linear Algebra, Fall 2023

Research Interests

• My research primarily focuses on the interactions between representation theory, algebraic geometry, and commutative algebra.A broad theme in my work is the geometry of algebraic varieties under the presence of symmetries. For instance, whenever we are working in coordinates but the properties we are studying are invariant under changes of bases, it is helpful to utilize the action of the general linear group of changes of bases to organize our calculations.
• One aspect of my research is to find (minimal) defining equations of varieties equipped with actions of some algebraic group G and computing syzygies of G-invariant ideals. In particular, I enjoy exploiting hidden or existing structures and symmetries to simplify computation. Another direction is the study of various secant varieties and using symmetries to compute lower bounds of various tensor ranks.

Papers

• Equations of Kalman Varieties, preprint at arXiv:1707.08699. To appear in Proceedings of the AMS.
• Computing Schur complexes, with Michael K. Brown, Robert P. Laudone, Michael Perlman, Claudiu Raicu, Steven V Sam, João Pedro Santo, preprint at arXiv:1812.00790. J. Softw. Algebra Geom. 9 (2019), no. 2, 111–119.
• Minimal Set of Generators of Ideals Defining Nilpotent Orbit Closures, preprint at arXiv: 2008.03166.To appear in Proceedings of the AMS .
• Syzygies of Determinantal Thickenings, preprint at arXiv:2008.02690. Submitted.
• Relations between the 2x2 minors of a generic matrix, with Michael Perlman, Claudia Polini, Claudiu Raicu, Alessio Sammartano, preprint at arXiv:1909.11705. Adv. Math. 386 (2021), Paper No. 107807, 29 pp.
• Vanishing Hessian, wild forms and their border VSP, with Mateusz Michałek, Emanuele Ventura, preprint at arXiv:1912.13174. Math. Ann. 378 (2020), no. 3-4, 1505–1532.
• Bad and good news for Strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity, with Austin Conner, J. M. Landsberg, preprint at arXiv:2009.11391. Found Comput Math (2022). https://doi.org/10.1007/s10208-022-09579-3.
• The InvariantRing package for Macaulay2, with Luigi Ferraro, Federico Galetto, Francesca Gandini, Matthew Mastroeni, Xianglong Ni, preprint at arXiv:2010.15331. Submitted.
• Geometry of backflow transformation ansatz for quantum many-body fermionic wavefunctions, with J.M. Landsberg and Jianfeng Lu, preprint at arXiv:2111.10314. To appear in Comm Math Sci.
• On Linear spaces of matrices of bounded rank, with J.M. Landsberg, preprint at arXiv:2306.14428v1. Submitted.
• Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2X2 permanents of a 2Xn matrix, with Fulvio Gesmundo, Hal Schenck, Jerzy Weyman, Submitted. Available upon request.