Organizing Committee
Abstract

A moduli space parameterizes geometric objects with alike structures and encodes in itself the geometry of all possible families of such objects. This workshop will focus on three aspects of moduli spaces: Cycles, Geometric Invariant Theory, and Dynamics. One of our main goals is to synthesize the recent progress on moduli of abelian differentials on algebraic curves motivated by dynamics and in the GIT constructions of related moduli spaces, with the view towards better understanding of geometric cycles on these moduli spaces.

In many cases, computer programming and experiments are important tools to discover new phenomena, both in dynamics and in the study of cycles on moduli spaces. Hence many talks will emphasize computational and experimental aspects of these fields and the workshop will feature a computational problem session whose goal is to disseminate computational techniques and problems to a wider body of researchers.

An integral part of the workshop is a series of three mini-courses on the following subjects:

  • cycles and birational geometry of moduli spaces of curves,
  • geometric invariant theory, with applications to constructions of moduli spaces, and
  • affine invariant manifolds and invariants in Teichmüller dynamics.

The mini-courses will be aimed primarily at non-experts and will benefit graduate students and early career researchers in related areas, who are particularly encouraged to apply to participate in the workshop.

This workshop is partially supported by NSF CAREER award DMS-1350396.

Confirmed Speakers & Participants

Workshop Schedule

Monday, August 1, 2016
TimeEventLocationMaterials
8:30 - 8:55Registration11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:50Mini-course- Invariant theory and moduli of pointed curves - Brendan Hassett, ICERM and Brown University 
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Invariant theory of Milnor algebras - Jarod Alper, Australian National University11th Floor Lecture Hall
11:30 - 1:30Break for Lunch / Free Time  
1:30 - 2:20Mini-course- Affine invariant manifolds and invariants in Teichmüller dynamics - Martin Möller, Goethe-Universität Frankfurt11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space 
3:00 - 3:50Surfaces in the space of surfaces - Curtis McMullen, Harvard University11th Floor Lecture Hall 
4:10 - 5:00Mini-course- Birational geometry of moduli spaces of rational curves - Ana-Maria Castravet, Northeastern University11th Floor Lecture Hall
Tuesday, August 2, 2016
TimeEventLocationMaterials
9:00 - 9:50Mini-course- Birational geometry of moduli spaces of rational curves - Ana-Maria Castravet, Northeastern University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Derived category of the moduli space of stable rational curves - Jenia Tevelev, University of Massachusetts at Amherst11th Floor Lecture Hall
11:30 - 1:30Break for Lunch / Free Time  
1:30 - 2:20Mini-course- Affine invariant manifolds and invariants in Teichmüller dynamics - Martin Möller, Goethe-Universität Frankfurt11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space 
3:00 - 3:50Siegel-Veech constants and quasimodular forms - Elise Goujard, Paris-Sud University11th Floor Lecture Hall
4:10 - 5:00Mini-course- Invariant theory and moduli of pointed curves - Brendan Hassett, ICERM and Brown University 
5:15 - 6:30Welcome Reception and Poster Session11th Floor Collaborative Space
Wednesday, August 3, 2016
TimeEventLocationMaterials
9:30 - 10:20Compactification of strata of abelian differentials - Samuel Grushevsky, Stony Brook University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:50Compactifications of strata, part deux - Matthew Bainbridge, Indiana University11th Floor Lecture Hall
12:00 - 12:10Group Photo in Lecture Hall11th Floor Lecture Hall 
12:10 - 2:00Break for Lunch / Free Time  
2:00 - 2:50Spin and hyperelliptic structures on log twisted abelian differentials - Qile Chen, Boston College11th Floor Lecture Hall
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:20Tautological classes on moduli space of K3 surfaces - Zhiyuan Li, University of Bonn and Fudan University11th Floor Lecture Hall
Thursday, August 4, 2016
TimeEventLocationMaterials
9:30 - 10:20Large GL(2,R) invariant subvarities of the Hodge bundle and billiards in polygons. - Alex Wright, Stanford University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:50Cyclic covers of genus two curves and varieties linear in period coordinates - Ronen Mukamel, Rice University11th Floor Lecture Hall
12:00 - 2:00Break for Lunch / Free Time  
2:00 - 2:50Translation surfaces, K3 surfaces, and some analogies - Simion Filip, University of Chicago11th Floor Lecture Hall
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:20Cycles on Hurwitz spaces - Anand Deopurkar, Columbia University11th Floor Lecture Hall
Friday, August 5, 2016
TimeEventLocationMaterials
9:00 - 9:50Diagramming how invariant components of hyperelliptic flat surfaces are connected to each other - Kathryn Lindsey, University of Chicago11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Deligne-Riemann-Roch isometry in the non-compact orbifold setting - Gerard Freixas I Montplet, Institut de Mathématiques de Jussieu11th Floor Lecture Hall
11:40 - 12:30MacDonald formula for singular curves - Filippo Viviani, Roma Tre University11th Floor Lecture Hall

Lecture Videos