This seminar gives graduate students the opportunity to hear and present talks on discrete mathematics, either on topics beyond a standard combinatorics class or on original research. GCS is meant to be a friendly, slightly informal speaking environment where questions are encouraged at all points throughout the talk. We only assume a basic general knowledge of combinatorics (at most, basic combinatorics one might learn in a single semester introductory course), so students in any area are welcome to attend.
Speakers for the GCS are welcome (from the math department, other departments, and elsewhere). Please email Quentin Dubroff at
Generously sponsored by DIMACS.
Click here for information about the seminar and the archive.
| Date: | October 14th 2020 |
|---|---|
| Speaker: | Quentin Dubroff |
| Time: | 12:15PM |
| Place: | Zoom: please email quentin [dot] dubroff [at] rutgers [dot] edu to be added to the mailing list |
| Title: | Too acute to be true? |
| Abstract: | Let f(d) be the maximum number of points in R^d such that every three form an acute triangle. For decades, it was thought that f(d) should grow linearly until a striking application of the probabilistic method by Erdős and Füredi showed that f(d) grows like C^d for some C>1. A few tiny improvements were made on this until very recently when a series of papers showed that f(d) is at least 2^{d-1}, nearly matching the upper bound of 2^d. I will recount this story, highlighting a few of the most clever arguments, as well as discuss its connection to a problem in coding theory which remains wide open. |