Cycles on Moduli Spaces, Geometric Invariant Theory, and Dynamics
(August 1 – 5, 2016)

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Description

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.


Organizing Committee

= speaker    = poster presenter

Monday August 1, 2016
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:50Mini-course- Invariant theory and moduli of pointed curvesBrendan Hassett, ICERM and Brown University
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Invariant theory of Milnor algebrasJarod Alper, Australian National University11th Floor Lecture Hall
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11:30 - 1:30Break for Lunch / Free Time
1:30 - 2:20Mini-course- Affine invariant manifolds and invariants in Teichmüller dynamicsMartin Möller, Goethe-Universität Frankfurt11th Floor Lecture Hall
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2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 3:50Surfaces in the space of surfacesCurtis McMullen, Harvard University11th Floor Lecture Hall
4:10 - 5:00Mini-course- Birational geometry of moduli spaces of rational curvesAna-Maria Castravet, Northeastern University11th Floor Lecture Hall
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Tuesday August 2, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:50Mini-course- Birational geometry of moduli spaces of rational curvesAna-Maria Castravet, Northeastern University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Derived category of the moduli space of stable rational curvesJenia Tevelev, University of Massachusetts at Amherst11th Floor Lecture Hall
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11:30 - 1:30Break for Lunch / Free Time
1:30 - 2:20Mini-course- Affine invariant manifolds and invariants in Teichmüller dynamicsMartin Möller, Goethe-Universität Frankfurt11th Floor Lecture Hall
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2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 3:50Siegel-Veech constants and quasimodular formsElise Goujard, Paris-Sud University11th Floor Lecture Hall
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4:10 - 5:00Mini-course- Invariant theory and moduli of pointed curvesBrendan Hassett, ICERM and Brown University
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5:15 - 6:30Welcome Reception and Poster Session11th Floor Collaborative Space
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Wednesday August 3, 2016
Time Description Speaker Location Abstracts Slides
9:30 - 10:20Compactification of strata of abelian differentialsSamuel Grushevsky, Stony Brook University11th Floor Lecture Hall
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10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:50Compactifications of strata, part deuxMatthew Bainbridge, Indiana University11th Floor Lecture Hall
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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 differentialsQile Chen, Boston College11th Floor Lecture Hall
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3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 4:20Tautological classes on moduli space of K3 surfacesZhiyuan Li, University of Bonn and Fudan University11th Floor Lecture Hall
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Thursday August 4, 2016
Time Description Speaker Location Abstracts Slides
9:30 - 10:20Large GL(2,R) invariant subvarities of the Hodge bundle and billiards in polygons.Alex Wright, Stanford University11th Floor Lecture Hall
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10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:50Cyclic covers of genus two curves and varieties linear in period coordinatesRonen Mukamel, Rice University11th Floor Lecture Hall
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12:00 - 2:00Break for Lunch / Free Time
2:00 - 2:50Translation surfaces, K3 surfaces, and some analogiesSimion Filip, University of Chicago11th Floor Lecture Hall
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3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 4:20Cycles on Hurwitz spacesAnand Deopurkar, Columbia University11th Floor Lecture Hall
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Friday August 5, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:50Diagramming how invariant components of hyperelliptic flat surfaces are connected to each otherKathryn Lindsey, University of Chicago11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:20Deligne-Riemann-Roch isometry in the non-compact orbifold settingGerard Freixas I Montplet, Institut de Mathématiques de Jussieu11th Floor Lecture Hall
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11:40 - 12:30MacDonald formula for singular curvesFilippo Viviani, Roma Tre University11th Floor Lecture Hall
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