Welcome to Hongyu He's Homepage
my vita
MY Teaching
- Math
1550---Calculus 1
- Math 4032---Advanced Calculus
II, Spring 2007
- Math 7370---Lie Groups and
Representation Theory
MY Research Interests
- Representation Theory ---
attempts to describe symmetries using algebraic analytic or geometric
tools. My interests are in theta correspondence, associated variety, and
unitary dual. My favorite group is the symplectic group.
- Geometry and Harmonic
Analysis on Lie Groups.
- Computational Biology --- My
interests are in functional genomics, DNA sequencing and Cell Modelling.
- Quantum Mechanics.
My Publications
On Geometry and Analysis of Classical Groups and Their Homogeneous Spaces
- "An Analytic
Compactification of Symplectic Group", Journal
of Differential Geometry, Vol. 51 , No. 2 (1999), 375-399.
- " Compactification of
Classical Groups", Communications in Analysis and Geometry,Vol. 10,
No.4, (2002), 709-740.
- "Functions on Symmetric Spaces and Oscillator
Representations" Journal of Functional Analysis, 244, 2007,
(536-564).
- "Orbits on Lagrangian
Grassmanian" preprint.
On Theta Correspondences
- "Theta
Correspondence in Semistable Range: Construction and Irreducibility",
Communications
in Contemporary Mathematics, Vol 2, No 2 (2000) 255-283 .
- "Nonvanishing of A Certain Sesquilinear Form
in the Theta Correspondence", AMS Journal of Representation
Theory, (2001) , 437-454.
- "Unitary Representations and Theta
Correspondence for Type I Classical Groups" , in Journal of
Functional Analysis, Vol 199, Issue 1, (2003), 92-121.
- "Compositions of Theta
Correspondences , in Advances in Mathematics, 2005.
- "Quantum Induction"
(Transparencies: My talk at the International Congress of Mathematicians
2002)
- "Unipotent Representations
and Quantum Induction"
Representation Theory
On Gene Expression
Graph Theory
Fun Stuff
