Organizing Committee
Abstract

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.

Confirmed Speakers & Participants

Workshop Schedule

Monday, May 14, 2018
TimeEventLocationMaterials
9:00 - 9:25Registration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
9:25 - 9:30Welcome - ICERM Director11th Floor Lecture Hall 
9:30 - 10:15Heights on stacks - Jordan Ellenberg, University of Wisconsin11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break 11th Floor Collaborative Space 
11:00 - 11:45Rationality constructions for cubic hypersurfaces - Brendan Hassett, ICERM & Brown University11th Floor Lecture Hall
12:00 - 2:00Break for Lunch / Free Time  
2:00 - 2:45Rational points on conic bundle surfaces - Christopher Frei, University of Manchester11th Floor Lecture Hall
3:00 - 3:30Coffee/Tea Break 11th Floor Collaborative Space 
3:30 - 4:15Universal torsors over degenerating del Pezzo surfaces - Ulrich Derenthal, Leibniz Universität Hannover11th Floor Lecture Hall
4:30 - 6:00Welcome Reception11th Floor Collaborative Space 
Tuesday, May 15, 2018
TimeEventLocationMaterials
9:00 - 9:45Rational Points, Height Bounds, and Weak Approximation via Higher Positive Curvature - Jason Starr, Stony Brook University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15Manin's conjecture and the Fujita invariant of finite covers - Akash Sengupta, Princeton University11th Floor Lecture Hall
11:30 - 12:15The exceptional set in Manin's Conjecture - Brian Lehmann, Boston College11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Nef anti-canonical divisors and rationally connected fibrations - Yoshinori Gongyo, Graduate School of Mathematical Sciences, the University of Tokyo11th Floor Lecture Hall
3:30 - 5:00Poster Session / Coffee Break11th Floor Collaborative Space 
Wednesday, May 16, 2018
TimeEventLocationMaterials
9:30 - 10:15Zeta functions of varieties- Tools and Applications - Kiran Kedlaya, University of California, San Diego11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break 11th Floor Collaborative Space 
11:00 - 11:45Computing zeta functions of nondegenerate hypersurfaces in toric varieties - Edgar Costa, Dartmouth College11th Floor Lecture Hall
12:00 - 12:10Workshop Group Photo11th Floor Lecture Hall 
12:10 - 2:00Break for Lunch / Free Time  
2:00 - 2:45Moduli spaces of rational curves on Fano hypersurfaces - Roya Beheshti, Washington University11th Floor Lecture Hall
3:00 - 3:30Coffee/Tea Break 11th Floor Collaborative Space 
3:30 - 4:15Algorithms for Cox rings - Simon Keicher, previously Universidad de Concepcion, Chile11th Floor Lecture Hall
Thursday, May 17, 2018
TimeEventLocationMaterials
9:00 - 9:45Level structures on abelian varieties and Vojta's conjecture - Dan Abramovich, Brown University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15A database of genus 3 curves over Q - Andrew Sutherland, MIT11th Floor Lecture Hall
11:30 - 12:15Finite collineation groups and birationally rigidity - Ivan Cheltsov, University of Edinburgh11th Floor Lecture Hall 
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Failure of stable rationality of various algebraic varieties via reduction modulo $p$ - Takuzo Okada, Saga University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space 
Friday, May 18, 2018
TimeEventLocationMaterials
9:00 - 9:45The punctual Hilbert scheme - James McKernan, UCSD11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break 11th Floor Collaborative Space 
10:30 - 11:15The complexity of algebraic structures - Daniel Krashen, University of Georgia11th Floor Lecture Hall
11:30 - 12:15Birational geometry and Milnor K-theory - Alena Pirutka, Courant Institute, NYU11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
3:30 - 4:00Coffee/Tea Break 11th Floor Collaborative Space 

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Lecture Videos

The complexity of algebraic structures

Daniel Krashen
University of Georgia
May 18, 2018

Algorithms for Cox rings

Simon Keicher
previously Universidad de Concepcion, Chile
May 16, 2018

Zeta functions of varieties- Tools and Applications

Kiran Kedlaya
University of California, San Diego
May 16, 2018

Nef anti-canonical divisors and rationally connected fibrations

Yoshinori Gongyo
Graduate School of Mathematical Sciences, the University of Tokyo
May 15, 2018

Rational points on conic bundle surfaces

Christopher Frei
University of Manchester
May 14, 2018

Heights on stacks

Jordan Ellenberg
University of Wisconsin
May 14, 2018