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# Texas A&M Number Theory Seminar

##
Department of Mathematics

Blocker 220

Wednesdays, 1:45–2:45 PM

### Lenny Fukshansky

Claremont McKenna College

#### Friday, September 8, 2017

#### Blocker 220, 1:00PM

**Title:** *On some algebraic constructions of extremal lattices
*

**Abstract:**
A lattice in a Euclidean space is called extremal if it is a local maximum of the packing density function in its dimension. An old theorem of Voronoi gives a beautiful characterization of extremal lattices in terms of their geometric properties. We will review Voronoi's criterion, and then apply it to exhibit families of extremal lattices coming from some algebraic and arithmetic constructions.