Finding the Symmetry Group and the Three-Dimensional Shape of Symmetric Molecules that we Don't Know How to Crystallize

MEMBERS SEMINAR
Topic:Finding the Symmetry Group and the Three-Dimensional Shape of Symmetric Molecules that we Don't Know How to Crystallize
Speaker:Shamgar Gurevich
Affiliation:Member, School of Mathematics
Date:Monday, December 7
Time/Room:2:00pm - 3:00pm/S-101

I will report on a joint work with Ronny Hadani (UT Austin) and Amit Singer (Princeton). We give an algorithmic solution to the two problems that appear in the title. The input is the numerical data (roughly, random plane sections of the molecule) obtained from the microscope. The output is the symmetry group and the shape of the molecule. In the lecture I will explain our algorithm and show how the representation theory of SO(3) and its finite subgroups (Cyclic C_n, Dihedral D_n, Tetrahedral A_4, Octahedral S_4, Icosahedral A_5) is responsible for the correctness of the algorithm.