Mathematics and Physics Seminar Series

AnnouncingAnnouncing

A Seminar Presentation

on Thursday

February 15, 2018

at 11.00 am - 12.00 noon in

North Hall 102

at The University of New Haven

Exact and Approximate Counting

— Thomas Prellberg

Professor

School of Mathematical Sciences

Queen Mary University of London

Abstract: Counting may seem intuitive, but early humans probably had a number

awareness which helped them to keep track of their surroundings, rather than the exact

counting we think of today. In the continued quest for exactness, the question of “how

many” arises as a central issue in many areas of mathematics, physics, and beyond.

Due to the difﬁcult nature of some counting problems, it is sometimes helpful to modify

the question to “roughly how many,” as an approximate answer is easier to obtain and

in many cases sufﬁcient. In this presentation, I will show the relevance of “how many

structures are there of a given kind” in my own areas of specialty such as combinatorics

and statistical physics, and how the endeavor to count structures continues to advance

research. The focus will be on the counting of paths on a discrete lattice. One example

for such lattice paths is given by self-avoiding walks, which are paths on a regular lattice

that do not self-intersect. The Encyclopdia Britannica lists self-avoiding walks as one

of two examples of classical unsolved combinatorial problems. This problem has been

at the forefront of research in statistical mechanics for more than half a century; self-

avoiding walks have been of interest to chemists, physicists and mathematicians, Nobel

Laureates and Fields Medallists alike.

Fur ther Information

For further information, please contact Dr. Yasanthi Kottegoda at the Department of Mathematics and Physics,

Ofﬁce: Maxcy 315, 203-932-1206, YKottegoda@newhaven.edu.