# IMath Seminar: Prof. William J. Martin

You are all invited to a seminar featuring **Prof. William J. Martin** (Department of Mathematical Sciences, Worcester Polytechnic Institute, USA). This is an in-person event and it will be held on** Thursday**,

**13 June 2024, 10:30 to 11:30 AM**at the

**Math Bldg Room 300**.

** Prof. William J. Martin** (Department of Mathematical Sciences, Worcester Polytechnic Institute, USA)

**Almost orthogonal vectors**

*Title:***How many lines can one pack into \(d\)-dimensional real space \(\mathbb{R}^d\), all passing through the origin, in such a way that the angle formed by any pair of these lines is at least \(89^{\circ}\)? I found the answer to this question surprising. In this talk, this problem will be the entry point to a collection of questions about large sets of unit vectors in \(\mathbb{R}^d\) all having inner products close to zero. Among the topics I will mention in the survey are equiangular lines, quantum measurements, linear programming bounds, connections to coding theory and data science. There won’t be many proofs and no prior advanced knowledge will be assumed.**

*Abstract:*