Joint Pure Math and C&O Colloquium

The number 24 plays a central role in mathematics thanks to a series of
"coincidences" that is just beginning to be understood. One of the first
hints of this fact was Euler's bizarre "proof" that

                  1 + 2 + 3 + 4 +  ...  =  -1/12

which he obtained before Abel declared that "divergent series are the
invention of the devil". Euler's formula can now be understood rigorously
in terms of the Riemann zeta function, and in physics it explains why
bosonic strings work best in 26= 24+2 dimensions. The fact that

                  1^2 + 2^2 + 3^2 + ... + 24^2

is a perfect square then sets up a curious link between string theory, the
Leech lattice (the densest known way of packing spheres in 24 dimensions)
and a group called the Monster.  A better-known but closely related fact
is the period-12 phenomenon in the theory of modular forms.  We shall do
our best to demystify some of these deep mysteries

DC 1302

Refreshments will served in DC 1301 at 3:00pm