Mathematics Program and Computer Science Program Present
Pseudolattices, Geometry, and Mirror Symmetry
Wednesday, April 12, 2023
RKC 111
12:00 pm – 1:00 pm EDT/GMT-4
12:00 pm – 1:00 pm EDT/GMT-4
Alan Thompson, Loughborough University
A pseudolattice is a (multidimensional) grid of points, equipped with a function that takes two points from the grid and returns an integer. A simple example would be the grid of points (x,y) in the plane with integer coordinates x and y, along with the dot product which takes two such points (a,b) and (c,d) and returns the integer ac+bd. I begin with a gentle introduction to the theory of pseudolattices, before presenting two settings in which they show up in geometry. The first describes configurations of points and curves on surfaces, whilst the second encodes the geometry of families of tori over a disc. Interestingly, despite the fact that the two settings seem unrelated, the pseudolattices that show up in each setting are identical. This is an example of the general phenomenon of "mirror symmetry," first discovered by theoretical physicists, which says that many geometric objects which seem to be unrelated nonetheless share fascinating properties.For more information, call 845-758-6822, or e-mail [email protected].
Time: 12:00 pm – 1:00 pm EDT/GMT-4
Location: RKC 111