Thursday, February 27, 2014 - 12:00

427 Thackeray Hall

Ivan Soprunov

Cleveland State

### Abstract or Additional Information

Coding theory is concerned with detecting and correcting
errors in data transmission. In 1982 Tsfasman, Vladut, and Zink
discovered that codes constructed from certain families of algebraic curves
have better asymptotic parameters than any previous constructions. This
motivated a great activity in applying methods of algebraic geometry to
coding.
I will talk about a relatively new family of algebraic geometry codes
called toric codes. A toric code is defined by evaluating sections of a
line bundle L on a toric variety X at a finite set of points Z on X. We
will see how basic parameters of a toric code depend on combinatorics of
the lattice polytope associated with L and on geometry of the set of
points Z.