Manoj Gopalkrishnan
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Ph. D. candidate gopalkri {at}
usc.edu |
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UPDATE: I HAVE GRADUATED, AND AM NOW A FACULTY MEMBER AT TIFR. MY HOME PAGE HAS MOVED TO http://www.tcs.tifr.res.in/~manoj .
Thank you for visiting my web page. I am a
Ph.D. candidate in computer science at the University of
Southern California,
My current research concerns self-assembly, an area that spans the borders between several traditional disciplines. I prove mathematical theorems, and perform experiments with DNA molecules. Please feel free to email me for more information.
Mathematical work
Systems of chemical reactions have been studied for over a century. Beginning with Maxwell, Boltzmann, Gibbs and others in the 19th century, and continuing with Martin Feinberg, Fritz Horn, Roy Jackson and others in the 20th century, attempts have been made to understand the kinetics of such systems.
Taking chemical kinetics as a point of departure, our group has sought to create a rigorous, mathematical theory, which we call event-systems. This work has led to a formal study of the foundations of chemical kinetics. A document describing our research is available here. We are in the process of submitting this to a journal.
In the long run, our theory is intended to be of intrinsic interest in mathematics and physics, and applicable to phenomena far beyond those occurring in chemistry. For example, event-systems are intimately related to sets of binomials over the complex numbers. There are also hints of connections with number theory.
Experimental work:
I have worked in the field of DNA
self-assembly. One broad goal is to exploit the information-carrying property
of DNA, and the specificity of DNA hybridization, for the purpose of building
nanostructures by self-assembly. This insight may be credited to Ned Seeman. Len Adleman demonstrated
experimentally that DNA
can be used to perform computations. These threads of research were
connected by Erik Winfree,
who showed that self-assembly and computation are intimately related. Simple
objects can be made to self-assemble by simple rules, to form intricate
patterns like fractals.
In early work on DNA self-assembly, Chelyapov,
Brun, Reishus, Shaw, Adleman and I have reported DNA complexes in the shape of
triangles and in the pattern of hexagonal, planar tilings This was published in
the journal of the American Chemical Society, and is available here.
Since then, Adleman's former student Paul Rothemund invented the
technique of DNA
origami --- a striking visual testimonial to the power of DNA self-assembly.
Attempting to take Paul’s ideas into three dimensions, Nikhil
Gopalkrishnan, Adleman and I have reported DNA complexes in the shape of
cylinders and Möbius strips. This was presented at DNA 14 and published in
the proceedings. A manuscript is available here. A
poster is available here.