The course will study several examples of beauty in mathematics. We will not attempt to define beauty. Many of our examples will be drawn from the work of László Lovász. This year's broad focus will be geometry.
Topics:
- Geometric representations.
Spectral/geometric charachterizations of discrete/topological properties
(the Theta function, the Colin de Verdiere number, spectral clustering,
Euclidean embeddings of metrics).
- Lattice theory.
Duality and fundamental algorithmic problems
(shortest vector, integer programming, random lattices).
- Random walks in geometric spaces.
The localization lemma, isoperimetric inequalities
(sampling convex sets, sampling log-concave functions, sampling lattice points).
Santosh Vempala vempala@math.mit.edu