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

 

MY Research Interests

My Publications

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,   preprint (1-27).

 

1.       On Matrix Valued Square Integrable Positive Definite Function (preprint)

 

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" , in Journal of Functional Analysis, Vol 199, Issue 1, (2003), 92-121.

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

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).

 

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" to appear in Journal of Lie Theory (2010).

4.       "Invariant Tensor product"

5.       “Unitary Representations and A Maximal Parabolic Subgroup”

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

 

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.

 

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.

 

Interesting Pictures, Presentations and Links

 

 

Fun Stuff