Stony Brook University
7:30 pm
Harriman Hall, P137
Friday, October 13, 2023
Arctic Circle Theorem and Limit Shapes
Prof. Alexander Abanov
How many ways can one densely tile a chessboard with dominos of the size 2 x 1? Starting with this problem, well-known in physics and mathematics, we will discuss a limit shape phenomenon -- the appearance of a most probable macroscopic state in random systems. This state is usually characterized by a well-defined geometric boundary separating "frozen" and "liquid" spatial regions. We will discuss the Arctic Circle Theorem -- a beautiful result in the domino tiling problem and will see how one can think about the limit shape problem as the optimal motion of a quantum fluid.
Alexander Abanov is a professor in the Department of Physics and Astronomy at Stony Brook University. He is known for his contributions to theoretical condensed matter physics using topological and hydrodynamic methods. He applied these methods to superconductivity studies, quantum magnetism, and the quantum Hall effect. Abanov received his Ph.D. in 1997 from the University of Chicago. After a postdoc at MIT, he joined Stony Brook University in 2000. He is a fellow of the American Physical Society and was deputy director of the Simons Center for Geometry and Physics at Stony Brook from 2012- 2022. Alexander enjoys teaching physics and mathematics at different levels. He has a lot of experience teaching students in various summer camps and math circles, including teaching for over 30 years at Krasnoyarsk Summer School for gifted high school students.
