Topics in Applied Mathematics: Foundations of Nanoscience
Instructor: M. Gopalkrishnan 

The study of nature at the nanoscale is an ongoing research endeavor
that has benefited from inputs from various disciplines including
molecular biology, statistical physics and computer science. We will
focus on the problem of designing nanosystems to exhibit a desired
complex behavior. Topics will be chosen from DNA computing and
self-assembly, tile assembly models, DNA circuits, chemical kinetics,
catalysis, Maxwell's demon, flashing ratchet models, physics of
computation, in vitro evolution. It will be assumed that participants
are familiar with, or willing to learn, the basics of chemistry,
physics, computer science, linear algebra, probability theory and
differential equations. This course may be appropriate for graduate
students from math, computer science, engineering, and the physical
sciences.

List of topics (as time permits):
+ Physics of computation: Negentropy principle, Landauer's principle,
Reversible computation.
+ Thermodynamics of computation: Maxwell's demon, Ratchet and pawl, Flashing
ratchet models.
+ DNA computing
+ Computation by self-assembly: Self-reproducing automata, Tiling problem
and its undecidability.
+ DNA self-assembly: Tile assembly models including ATAM, KTAM, DNA tilings,
DNA origami. Software: nanoengineer.
+ DNA/ RNA catalysis: Strand displacement, Hybridization chain reaction, See
saw gates, Exponential  growth. Software: webDNA, Nupack
+ DNA circuits: Programming biomolecular self-assembly pathways, Programming
see saw gates.
+ Chemical kinetics: Gillespie algorithm, DNA as a universal substrate for
chemical kinetics, Chemical reaction network theory.