UK WILDCATS Seminar
**
****
UK
WILDCATS
Seminar **

Work,
Interactions
&
Leading
Developments

in

Combinatorics,
Algebra,
Topology
&
Statistics

845 PATTERSON OFFICE TOWER

SPRING 2010

##
"Lifting tropical curves in subvarieties"

Eric Katz

University of Texas at Austin/MSRI

###
UK
WILDCATS
Seminar

Monday, February 22, 2010

4:00 pm, 845 POT

####
Abstract:

Tropical Geometry is a new area of mathematics which transforms
questions about algebraic varieties to more combinatorial questions about
polyhedral complexes by a process called tropicalization. The polyhedral
complex reflects many of the properties of the original algebraic variety.
We give an introduction to tropical geometry and then ask questions about
which polyhedral complexes arise from algebraic varieties. We focus on the
case of one-dimensional complexes (tropical curves) in tropical
hypersurfaces, and we give necessary conditions for them to be
tropicalizations. We also explain which lifting questions are likely to be
combinatorial in nature.