I work on several topics, the common thread being
geometry. Most of my problems involve
nontrivial patterns in space; frequently the problem
is to determine the qualitative nature of the ground state
(or equilibrium phase).
For a summary of the four areas we do research on,
see "Research Interests" , below.
I depend partly on undergrad researchers
to keep moving in all four areas.
Currently (fall 2012) only "spins and electrons"
group is meeting; quasicrystals and biol. physics only
one-on-one meetings. Group meeting days/times are
irregular in early fall -- to attend, please contact
CLH to get on the email list.
Typically on the computational-analytic borderline, with a
focus on: what are unbiased ways to get information out of
the (experimental or numerical) data?
There are two threads currently:
(1) How to characterize the (maybe exotic)
ground state of a quantum model from the exact diagonalization
of a finite-sized system. (Recent theses: Nai-gong Zhang '02,
Siew-Ann Cheong '06.)
(2) Phenomenological modeling to describe
STM (scanning tunneling microscope) experimental data from
high-Tc cuprates, taken in the Seamus Davis group at Cornell.
(Current grad : Sumiran Pujari)
This category includes
(1) magnetic ordering in frustrated vector antiferromagnets,
and (2) the statistical physics of discrete
spin models that map to rough interface models
(related to conformal field theories).
Quasicrystals are complex metal alloys with highly ordered, yet non-periodic
structures.
We want to determine their structure and understand why
they form.
Thus our work breaks down into
(1) atomic structure fitting and structural energies;
(2) random tiling ensembles;
I work on two major topics in biological physics
They involve statistical mechanics plus spatial patterning.
(1) We study the assembly of virus shells ("capsids"),
via growth models (i.e. statistical physics) and also
a kind of multiscale modeling, in which we infer
effective lumped spring constants for whole protein units
from all-atom simulations.
(Recent Ph.D.: Steve Hicks, spring 2010).
(2)
Physical mechanisms causing macroscopic Left/Right asymmetry
(handedness) in animals and plants.
I belong to the Cornell Center for Materials Research.
I was once active in a research group within the CCMR
on "Energetic Surface Processing", which involved models
of the growth of crystals by atom deposition.
