Monthly Archives: April 2018

“A 2-Dimensional Model for Ice and Alternating Sign Matrices” by Ezra Halleck


Date: April 26, 2018
Speaker: Dr. Ezra Halleck (NYCCT)
Title: A 2-Dimensional Model for Ice and Alternating Sign Matrices
Abstract: In the later part of the 20th century, physicists developed the Ising and Potts models for ice and interacting spins on a crystalline lattice. Mathematicians noticed connections to several constructs, including the alternating sign matrices illustrated above. There was much interest on the growth of these objects as the size increased. A conjecture on an exact count for a given size quickly arose. Finding a proof was a hot problem for years, with many discrete mathematicians adding pieces towards its proof. Doron Zielberger put in the final piece in 1995.
This picture-rich and proof-light treatment will begin with the bijection between the model and the matrix illustrated above but then focus on enumerative aspects of the matrix class. There will be several hands-on activities.

“Statistical Mechanics and Combinatorics” by Ezra Halleck

Date: April 19, 2018
Speaker: Dr. Ezra Halleck (NYCCT)
Title: Statistical Mechanics and Combinatorics
Abstract: In this picture-rich and proof-light treatment, I will begin with the connections between the 2 subjects but focus on enumerative and bijective aspects. One example is tiling using dimers. Another is a model of ice, again in a plane. There will be several hands-on activities as well as recursive programming examples in MATLAB, Python and R.