### Monday October 31, 2005, 4:00 PM

### tea at
3:40 PM at the Math Department lounge (Goldsmith 300)

**Speaker**: Curt McMullen

**Title**: Minkowski's conjecture, well-rounded lattices and topological
dimension

**Abstract**: Classical sphere packing concerns lattices
*L* in **R**^{n} with the Euclidean metric.
Even a conjectural description of the densest packings is not known.
Minkowski conjectured, however, that **Z**^{n} is the
densest lattice if we replace the Euclidean metric with the norm *N(x)
= x*_{1} x_{2} .... x_{n}. We will discuss a
topological approach to this conjecture, and its relation to conjectures
of Littlewood and Margulis.