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.

Image for "Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics"

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, August 1, 2016
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:50am EDTMini-course- Invariant theory and moduli of pointed curves - Brendan Hassett, ICERM and Brown University 
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTInvariant theory of Milnor algebras - Jarod Alper, Australian National University11th Floor Lecture Hall
11:30 - 1:30pm EDTBreak for Lunch / Free Time  
1:30 - 2:20pm EDTMini-course- Affine invariant manifolds and invariants in Teichmüller dynamics - Martin Möller, Goethe-Universität Frankfurt11th Floor Lecture Hall
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:00 - 3:50pm EDTSurfaces in the space of surfaces - Curtis McMullen, Harvard University11th Floor Lecture Hall 
4:10 - 5:00pm EDTMini-course- Birational geometry of moduli spaces of rational curves - Ana-Maria Castravet, Northeastern University11th Floor Lecture Hall
Tuesday, August 2, 2016
TimeEventLocationMaterials
9:00 - 9:50am EDTMini-course- Birational geometry of moduli spaces of rational curves - Ana-Maria Castravet, Northeastern University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTDerived category of the moduli space of stable rational curves - Jenia Tevelev, University of Massachusetts at Amherst11th Floor Lecture Hall
11:30 - 1:30pm EDTBreak for Lunch / Free Time  
1:30 - 2:20pm EDTMini-course- Affine invariant manifolds and invariants in Teichmüller dynamics - Martin Möller, Goethe-Universität Frankfurt11th Floor Lecture Hall
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:00 - 3:50pm EDTSiegel-Veech constants and quasimodular forms - Elise Goujard, Paris-Sud University11th Floor Lecture Hall
4:10 - 5:00pm EDTMini-course- Invariant theory and moduli of pointed curves - Brendan Hassett, ICERM and Brown University 
5:15 - 6:30pm EDTWelcome Reception and Poster Session11th Floor Collaborative Space
Wednesday, August 3, 2016
TimeEventLocationMaterials
9:30 - 10:20am EDTCompactification of strata of abelian differentials - Samuel Grushevsky, Stony Brook University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:50am EDTCompactifications of strata, part deux - Matthew Bainbridge, Indiana University11th Floor Lecture Hall
12:00 - 12:10pm EDTGroup Photo in Lecture Hall11th Floor Lecture Hall 
12:10 - 2:00pm EDTBreak for Lunch / Free Time  
2:00 - 2:50pm EDTSpin and hyperelliptic structures on log twisted abelian differentials - Qile Chen, Boston College11th Floor Lecture Hall
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:20pm EDTTautological 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 - 10:20am EDTLarge GL(2,R) invariant subvarities of the Hodge bundle and billiards in polygons. - Alex Wright, Stanford University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:50am EDTCyclic covers of genus two curves and varieties linear in period coordinates - Ronen Mukamel, Rice University11th Floor Lecture Hall
12:00 - 2:00pm EDTBreak for Lunch / Free Time  
2:00 - 2:50pm EDTTranslation surfaces, K3 surfaces, and some analogies - Simion Filip, University of Chicago11th Floor Lecture Hall
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:20pm EDTCycles on Hurwitz spaces - Anand Deopurkar, Columbia University11th Floor Lecture Hall
Friday, August 5, 2016
TimeEventLocationMaterials
9:00 - 9:50am EDTDiagramming how invariant components of hyperelliptic flat surfaces are connected to each other - Kathryn Lindsey, University of Chicago11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am EDTDeligne-Riemann-Roch isometry in the non-compact orbifold setting - Gerard Freixas I Montplet, Institut de Mathématiques de Jussieu11th Floor Lecture Hall
11:40 - 12:30pm EDTMacDonald formula for singular curves - Filippo Viviani, Roma Tre University11th Floor Lecture Hall

Lecture Videos

MacDonald formula for singular curves

Filippo Viviani
Roma Tre University
August 5, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Cycles on Hurwitz spaces

Anand Deopurkar
Columbia University
August 4, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Translation surfaces, K3 surfaces, and some analogies

Simion Filip
University of Chicago
August 4, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Tautological classes on moduli space of K3 surfaces

Zhiyuan Li
University of Bonn
August 3, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Spin and hyperelliptic structures on log twisted abelian differentials

Qile Chen
Boston College
August 3, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Compactification of strata of abelian differentials

Samuel Grushevsky
Stony Brook University
August 3, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Mini-course- Invariant theory and moduli of pointed curves II

Brendan Hassett
ICERM/Brown University
August 2, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Siegel-Veech constants and quasimodular forms

Elise Goujard
Paris-Sud University
August 2, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Mini-course- Affine invariant manifolds and invariants in Teichmüller dynamics II

Martin Möller
Goethe-Universitat Frankfurt
August 2, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Derived category of the moduli space of stable rational curves

Jenia Tevelev
University of Massachusetts Amherst
August 2, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Mini-course- Affine invariant manifolds and invariants in Teichmüller dynamics I

Martin Möller
Goethe-Universitat Frankfurt
August 1, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Mini-course- Invariant theory and moduli of pointed curves I

Brendan Hassett
ICERM/Brown University
August 1, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract

Scalable algorithms for Markov process parameter inference

Darren Wilkinson
Newcastle University
July 22, 2016
Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
Play     Abstract     Slides