a name="one"></a> 
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<p>
<!-- NAME (AFFILIATION) -->
Izzet Coskun (MIT)
<br>
<!-- TITLE -->
<strong>
The geometry of the space of rational curves
</strong>
<br><!-- ABSTRACT -->
In this talk I will survey some recent results about the birational
geometry of the Kontsevich moduli spaces of genus zero stable maps. In
particular, I will describe joint work with Joe Harris and Jason Starr on
the ample and effective cones of the Kontsevich moduli spaces. I will pose
the problems that led us to study these cones and discuss some
applications.

</p>
<hr>  
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<a name="two"></a> 
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<p>
<!-- NAME (AFFILIATION) -->
Marco Gualtieri (MIT)
<br>
<!-- TITLE -->
<strong>
D-branes on Poisson varieties
</strong>
<br><!-- ABSTRACT -->
I will describe how the study of generalized complex manifolds
leads to the notion of D-branes on Poisson varieties, and how these are
subsequently described by generalized Kahler geometry.  I will also outline
the relation between these insights and the study of noncommutative
algebraic varieties, specifically rational surfaces.
</p>
<hr>  
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<a name="three"></a> 
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<p>
<!-- NAME (AFFILIATION) -->
Christopher Hacon
(University of Utah) 
<br>
<!-- TITLE -->
<strong>
Existence of minimal models for varieties of log general type I
</strong>
<br><!-- ABSTRACT --> 
In this talk I will describe the main results contained in the preprint "Existence of
minimal models for varieties of log general type" (joint with Birkar, Cascini and
McKernan; arXiv.math.AG/0610203). I will then illustrate some consequences of these
results and discuss some open problems.
</p>
<hr>  
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<a name="four"></a> 
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<p>
<!-- NAME (AFFILIATION) -->
James McKernan
(UCSB)
<br>
<!-- TITLE -->
<strong>
Existence of minimal models for varieties of log general type II
</strong>
<br><!-- ABSTRACT -->


</p>
<hr>  
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<a name="five"></a> 
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<p>
<!-- NAME (AFFILIATION) -->
Dragos Oprea
(Stanford University) 
<br>
<!-- TITLE -->
<strong>
The rank-level duality for non-abelian theta functions
</strong>
<br><!-- ABSTRACT -->
The moduli spaces of bundles on a smooth projective curve can be regarded
as higher-rank (non-abelian) analogues of the Jacobian variety. Much like
the Jacobian, these moduli spaces carry naturally defined "theta" line
bundles, whose global sections are the non-abelian theta functions.

Different spaces of non-abelian theta functions are related by a geometric
isomorphism, oftentimes termed "strange duality." This interchanges two
discrete invariants of the thetas: the "rank" and the "level". The
isomorphism can be viewed as a non-abelian generalization of the classical
Wirtinger duality.

This is the result of joint work with Alina Marian.


</p>
<hr>  
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<a name="six"></a> 
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<p>
<!-- NAME (AFFILIATION) -->
Alexander Polishchuk
(University of Oregon) 
<br>
<!-- TITLE -->
<strong>
Algebraic cycles on Jacobians and symmetric powers of curves
</strong>
<br><!-- ABSTRACT --> 
In this talk I will describe algebras of operators acting on the relative Jacobian
and on the symmetric powers for a family of curves. I will also discuss tautological
subalgebras in the corresponding Chow groups.

</p>
<hr>  
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<a name="seven"></a> 
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<p>
<!-- NAME (AFFILIATION) -->
Justin Sawon
(Colorado State University) 
<br>
<!-- TITLE -->
<strong>
Lagrangian fibrations
</strong>
<br><!-- ABSTRACT -->
(Holomorphic) Lagrangian fibrations on holomorphic symplectic
manifolds are generalizations of elliptic fibrations on K3 surfaces. In
this talk I will describe some results related to existence and
classification of Lagrangian fibrations. The goal is to use Lagrangian
fibrations to classify holomorphic symplectic manifolds up to deformation.
</p>
<hr>  
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