Lizhen Ji

Current Research Interests:

I. Large scale geometry and integral Novikov conjectures:

Asymptotic dimension of arithmetic groups

Applications of compactifications of symmetric spaces to Novikov conjectures

Geometry of S-arithmetic groups and buildings, and applications to Novikov conjectures

Mapping class groups, Teichmuller spaces: universal spaces for proper actions and compactifications

II. Spectral theory of locally symmetric spaces:

The Weyl upper on the discrete spectrum

Relations between the scattering matrices and scattering geodesics, flats

The Selberg trace formula

III. Compactifications of symmetric spaces

Compactifications of Riemannian symmetric spaces and applications to potential theory

Harmonic analysis on symmetric spaces

Uniform construction of compactifications of symmetric spaces

IV. Compactifications of locally symmetric spaces

Geometric and uniform construction of compactifications of locally symmetric spaces

Spectral theory of locally symmetric spaces and relations to compactifications

Toroidal compactifications of Hermitian locally symmetric spaces

V. Buildings and their compactifications