[Colloq] Today colloquium 10:30 AM

[Francoise Niang]

Time, location:      10:30 AM, Wed 10/16, 366WVH

Title: Inverse problems in potential energy minimization, and algorithms 
for self-assembly

Speaker:               Abhinav Kumar
                  Assoc. Prof, Math, MIT


Abstract: The question of energy minimization is widely studied in physics 
and mathematics - to find a configuration of points which minimize a given
form of potential energy. I will describe some progress on the inverse
problem of contructing a potential function which has a given target
configuration as its (provable) global minimum.

For simplicity, consider a finite collection of points on a sphere in
n dimensions, though some of the techniques apply in broader
generality. I will first describe a necessary and sufficient condition
for the inverse question to have a solution, and then an algorithm
which attempts to construct a solution as a linear combination of a
finite set of specificied potential functions.

Finally, I will illustrate the technique in the case of several
symmetrical examples, such as the cube, the dodecahedron and the
120-cell. In these cases one can in fact display solutions which are
decreasing and convex as a function of distance, and use linear
programmming bounds and spherical design properties to give simple
proofs of the global minimality.

This is joint work with Henry Cohn from Microsoft Research.

Host: Ravi Sundaram


Bio: Abhinav Kumar is an associate professor of Mathematics at MIT. He
attended MIT as an undergraduate, despite obtaining the first rank in
the entrance examination for the Indian Institute of Technology (out
of a few hundred thousand applicants). He received S.B. degrees in
EECS, mathematics and physics from MIT in 2002. A two-time Putnam
Fellow, Kumar received the Jon A. Bucsela Prize for the strongest
undergraduate in mathematics at MIT. He also received the Harvard
Putnam and GSAS fellowships for graduate school at Harvard, where he
completed a Ph.D. mathematics in 2006 under the supervision of Noam
Elkies and Barry Mazur. Kumar then took a postdoctoral research
appointment at Microsoft, 2006-07, before joining the MIT mathematics
faculty as assistant professor in 2007. He was promoted to associate
professor in 2012. Professor Kumar works in the field of arithmetic
algebraic geometry, lattices and sphere packings, and combinatorics
and discrete geometry. He is also interested in related questions in
physics and computer science. In 2007, he was selected by the MIT
School of Science for support from the Solomon Buchsbaum AT&T research
fund. In 2010 he received a Faculty Early Career Development (CAREER)
award from the NSF.


Francoise Niang
Executive Assistant
College of Computer and Information Science
Northeastern University
202 West Village H
617-373-5204
fniang at ccs.neu.edu