Special session on Combinatorial Algebraic Geometry

Frank Sottile and Alexander Yong, organizers

This special session will showcase three central themes of current research
in combinatorial algebraic geometry.  These themes are interconnected and 
together represent the role of this topic in mathematics:

1. Schubert calculus and combinatorial representation theory
2. Toric geometry and polyhedral combinatorics
3. Tropical geometry

    Schubert calculus and toric geometry have long been a focal point
of interaction between algebraic geometry and combinatorics.  Indeed,
recent advances in applying geometric degeneration to Schubert varieties
suggest the need for combinatorial interpretation, whereas work on
combinatorial rules in Schubert calculus call for geometric underpinnings.
Often, these techniques lead to toric varieties, and the combinatorics
concerns counting lattice points in polytopes.  A new development in
degenerations and toric are Okounkov bodies.  While an original motivation
came from flag and Schubert varieties, recent work of Khovanskii-Kuimars,
Lazarsfeld-Mustata, and others suggest that Okounkov bodies will allow
toric techniques to be applied quite generally.  Lastly, tropical geometry
is developing into a distinct subject linking classical algebraic geometry
to geometric combinatorics.

     The speakers of this session will include both established and early career
researchers.  This session will showcase this subject and further strengthen the
interactions between people working in this area.   There has long been
a history of very successful meetings on different aspects of this subject
including AMS sectional sessions at sectional meetings in 2000, 2002, and 
2004, as well as meetings at the Fields Institute (2006), Banff (2007), 
MSRI (2009) and the AIM (March 2010).