Mathematics and Physics Seminar Series
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
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,