Birational Geometry and Arithmetic
(May 14 - 18, 2018)

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Description

Recent developments in the minimal model program in positive characteristic and birational geometry have found purchase within arithmetic geometry, e.g., around questions of exceptional sets involved in Manin's conjecture on points of bounded height. In turn, arithmetic perspectives afforded by Manin's conjecture are starting to shed light on the geometry of spaces of rational curves.

Our goal in this workshop is to bring together two camps of geometers (birational and arithmetic) who have had few opportunities to interact on a large scale. We plan to focus on the interplay between theoretical developments and explicit constructions, e.g., in the study of Cox rings of Fano varieties, rationality problems, Manin's conjecture.

Organizing Committee


= speaker    = poster presenter

Monday May 14, 2018
Time Description Speaker Location Abstracts Slides
9:00 - 9:25RegistrationICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space
9:25 - 9:30WelcomeICERM Director11th Floor Lecture Hall
9:30 - 10:15Heights on stacksJordan Ellenberg, University of Wisconsin11th Floor Lecture Hall
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10:30 - 11:00Coffee/Tea Break 11th Floor Collaborative Space
11:00 - 11:45Rationality constructions for cubic hypersurfacesBrendan Hassett, ICERM & Brown University11th Floor Lecture Hall
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12:00 - 2:00Break for Lunch / Free Time
2:00 - 2:45Rational points on conic bundle surfacesChristopher Frei, University of Manchester11th Floor Lecture Hall
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3:00 - 3:30Coffee/Tea Break 11th Floor Collaborative Space
3:30 - 4:15Universal torsors over degenerating del Pezzo surfacesUlrich Derenthal, Leibniz Universität Hannover11th Floor Lecture Hall
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4:30 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday May 15, 2018
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Rational Points, Height Bounds, and Weak Approximation via Higher Positive CurvatureJason Starr, Stony Brook University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space
10:30 - 11:15Manin's conjecture and the Fujita invariant of finite coversAkash Sengupta, Princeton University11th Floor Lecture Hall
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11:30 - 12:15Manin's Conjecture and rational curvesBrian Lehmann, Boston College11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15Nef anti-canonical divisors and rationally connected fibrationsYoshinori Gongyo, Graduate School of Mathematical Sciences, the University of Tokyo11th Floor Lecture Hall
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3:30 - 5:00Poster Session / Coffee Break11th Floor Collaborative Space

Wednesday May 16, 2018
Time Description Speaker Location Abstracts Slides
9:30 - 10:15Zeta functions of varieties- Tools and ApplicationsKiran Kedlaya, University of California, San Diego11th Floor Lecture Hall
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10:30 - 11:00Coffee/Tea Break 11th Floor Collaborative Space
11:00 - 11:45Computing zeta functions of nondegenerate hypersurfaces in toric varietiesEdgar Costa, Dartmouth College11th Floor Lecture Hall
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12:00 - 12:10Workshop Group Photo11th Floor Lecture Hall
12:10 - 2:00Break for Lunch / Free Time
2:00 - 2:45TBARoya Beheshti, Washington University11th Floor Lecture Hall
3:00 - 3:30Coffee/Tea Break 11th Floor Collaborative Space
3:30 - 4:15Algorithms for Cox ringsSimon Keicher, previously Universidad de Concepcion, Chile11th Floor Lecture Hall
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Thursday May 17, 2018
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Level structures on abelian varieties and Vojta's conjectureDan Abramovich, Brown University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space
10:30 - 11:15A database of genus 3 curves over QAndrew Sutherland, MIT11th Floor Lecture Hall
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11:30 - 12:15TBAAngela Gibney, University of Georgia11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15The derived category of moduli spaces of stable rational curvesAna-Maria Castravet, Northeastern University11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space
4:00 - 4:45Failure of stable rationality of various algebraic varieties via reduction modulo $p$Takuzo Okada, Saga University11th Floor Lecture Hall
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Friday May 18, 2018
Time Description Speaker Location Abstracts Slides
9:00 - 9:45The punctual Hilbert schemeJames McKernan, UCSD11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space
10:30 - 11:15TBADaniel Krashen, University of Georgia11th Floor Lecture Hall
11:30 - 12:15Birational geometry and Milnor K-theoryAlena Pirutka, Courant Institute, NYU11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time
3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space