Combinatorics and Theoretical Computer Science Seminars - 2016

Date Speaker and Affiliation Title of the Talk (Click on title to view abstract)
09/11/16 Niranjan Balachandran, IIT Bombay

Equiangular lines in Euclidean Space

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.

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