Welcome to Hongyu He's Homepage


my vita

MY Teaching

  1. Math 1550---Calculus 1
  2. Math 4032---Advanced Calculus II, Spring 2007
  3. Math 7370---Lie Groups and Representation Theory
  4. ……a lot of classes between
  5. Math 4031---Advanced Calculus, Spring 2015
  6. Math 2057—Multivariate Calculus, Fall 2015
  7. Math 2090---Linear Algebra and Differential Equations, Fall 2015

MY Current Research Interests

My Publications

New Book: Howe’s Rank and Dual Pair Correspondence in Semistable Range (2016)

·       On Geometry and Analysis of Classical Groups and Their Homogeneous Spaces

1.       "An Analytic Compactification of Symplectic Group", Journal of Differential Geometry, Vol. 51 , No. 2 (1999), 375-399.

2.       "Compactification of Classical Groups” Communications in Analysis and Geometry, Vol. 10, No.4, (2002), 709-740.

3.       "Functions on Symmetric Spaces and Oscillator Representations" Journal of Functional Analysis, 244, 2007, (536-564).

4.       Bounds on Smooth Matrix Coefficients of L^2 spaces” Selecta Mathematica Vol 15, 2009

5.       "Symmetric Subgroup Action on Isotropic Grassmanian", joint with Huajun Huang,   Journal of Algebra.

·         General Representation Theory and Functional Analysis

1.       On Matrix Valued Square Integrable Positive Definite Function, Monatshefte fur Mathematik Volume 177, Issue 3 (2015) (437-449).

2.       Generalized Matrix Coefficients of Unitary Representations, Journal of Ramanujan Mathematical Society Vol 29 Issue 3 (2014) 253-272.

·       On Theta Correspondences

1.       "Theta Correspondence in Semistable Range: Construction and Irreducibility", Communications in Contemporary Mathematics,   Vol 2, No 2 (2000) 255-283 .

2.       "Nonvanishing of A Certain Sesquilinear Form in the Theta Correspondence” AMS Journal of Representation Theory, (2001) , 437-454.

3.       "Unitary Representations and Theta Correspondence for Type I Classical Groups" ,  Journal of Functional Analysis, Vol 199, Issue 1, (2003), 92-121.

4.       "Compositions of Theta Correspondences, in Advances in Mathematics, 2005, Vol 190.

5.       "Quantum Induction" (Transparencies: My talk at the International Congress of Mathematicians 2002)

6.       Picard Group of Siegel Modular Threefolds and Theta Lifting (joint with J. W. Hoffman (LSU), this is really an application of theta lifting to algebraic geometry), Journal of Lie Theory.

·       On Representation Theory

1.       "Associated Varieties and Howe's N Spectrum" to Pacific Journal of Mathematics, Vol 237 No. 1 (2008)

2.       "Unipotent Representations and Quantum Induction"

3.       "Restrictions of Certain Degenerate Principal Series of the Universal Covering of the Symplectic Groups",  Journal of Lie Theory 20 No 1 31-48 (2010).

4.       "Invariant Tensor product"

5.       “Unitary Representations and A Maximal Parabolic Subgroup”, Journal of Lie Theory, Vol 21 (2011) 847-860.

6.       Certain Induced Complementary Series of the Universal Covering of the Symplectic Groups

7.       Wave Front Set of Reductive Lie Group Representations, (joint with G. Olafsson and B. Harris) to appear in Duke Journal of Mathematics (2015).

·        On Branching Laws

 

1.       The Continuous Spectrum in Discrete Series Branching Laws, (joint with G. Olafsson and B. Harris)   International Mathematics Research Notice, Vol 24 Issue 7, (2013) 1-29.

2.      On the Gan-Gross-Prasad Conjecture for unitary groups, to appear in Inventiones Mathematicae (2017).

·       On Gene Expression and Biological Modeling

1.       "Modeling Gene Expression with Differential Equations" , (joint with T. Chen (USC), G. Church (Harvard)), Pacific Symposium on Biocomputing'99,
World Scientific, 29-40.  See citations of this paper (405  times so far).

2.       Equilibrium Submanifold for a Biological System, to appear in Discrete and Continuous Dynamical Systems Series B  (joint with N. Kato (LSU)).

3.       A systems model of vesicle trafficking in Arabidopsis pollen tubes  (joint with N. Kato, A. Steger (LSU)), appeared in Plant Physiology Nov 2009..

·       On Graph Theory

1.       "Reconstruction and Higher Dimensional Geometry" , Journal of Combinatorial Theory, Series B 97 2007, 421-429.

2.       "Eigenvectors and Reconstruction," Electronic Journal of Combinatorics, Vol 14 (1), 2007.

·        Other Notes

 

1.      Coadjoint Orbits of Siegel Parabolic Group

2.      Lecture Notes on Quantization (unfinished)

 

Interesting Pictures, Presentations and Links

 

 

Fun Stuff