Description

Title: Equiangular lines in Euclidean Space

Abstract: Consider the following extremal (geometric) problem: Suppose we

have a set of lines in R^d such that the angle between any two of these is

the same. How many lines can there be?

As it turns out, one can an upper bound that is quadratic in the dimension

d without too much difficulty. There are also (several) examples of sets

of lines of size $\Omega(d^2)$ in $R^d$ that form an equi-angular set.

However, in all these examples, the angle between a pair of lines goes to

0 as d goes to infinity. If we insist that the angle is fixed then the

bound becomes linear. We shall see a proof of this due to B. Bukh.

Abstract: Consider the following extremal (geometric) problem: Suppose we

have a set of lines in R^d such that the angle between any two of these is

the same. How many lines can there be?

As it turns out, one can an upper bound that is quadratic in the dimension

d without too much difficulty. There are also (several) examples of sets

of lines of size $\Omega(d^2)$ in $R^d$ that form an equi-angular set.

However, in all these examples, the angle between a pair of lines goes to

0 as d goes to infinity. If we insist that the angle is fixed then the

bound becomes linear. We shall see a proof of this due to B. Bukh.

Description

Ramanujan Hall

Date

Wed, November 9, 2016

Start Time

11:00am-12:00pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Mon, November 7, 2016 9:50am IST