Andrej Vukovic, Carleton University
“Enumerative Combinatorics and the Geometry of Number”
In the early 1900s, a versatile class of problem-solving technqiues known as the ”geometry of numbers” (or in a recent reincarnation, ”arithmetic geometry”) emerged that has proved essential to research in analytic number theory, algebraic geometry, and enumerative combinatorics. I will explain some elementary but nontrivial tricks of this sort, motivating them by their application to counting things. On the way, we will touch on a few modern areas of research, such as the theory of elliptic curves and string theory. If you like (asymptotically) finding the number of lattice points inside a circle, or counting the number of elements of some space of matrices (mod p), this is the talk for you!
MC 5403