- Start Date:
July 2, 2024
- Event Start Time:
11:45 AM
- Event End Time:
12:45 PM
- Organizers:
Lazaros Gallos
- Seminar Series:
REU Seminar
- Presenter(s):
Swee Hong Chan - Rutgers University
- Event Location:
DIMACS Seminar room
- Abstract:
A sequence of nonnegative real numbers $a_1, a_2, \\ldots, a_n$, is log-concave if $a_i^2 \\geq a_{i-1}a_{i+1}$ for all $i$ ranging from 2 to $n-1$. Log-concavity naturally arises in various aspects of mathematics, each characterized by different underlying mechanisms. Examples range from inequalities that are readily provable, such as the binomial coefficients $a_i = \\binom{n}{i}$, to intricate inequalities that have taken decades to resolve, such as the number of forests $a_i$ in a graph $G$ with $i$ edges. It is then natural to ask if it can be shown that the latter type of inequalities is intrinsically more challenging than the former. In this talk, we provide a rigorous framework to answer this type of questions, by employing a combination of combinatorics, complexity theory, and geometry. This is a joint work with Igor Pak and is intended for a general audience.
