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.

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

Lecture Videos

Birational geometry and Milnor K-theory

Alena Pirutka
NYU
May 18, 2018
Birational Geometry and Arithmetic
Play     Abstract

The complexity of algebraic structures

Daniel Krashen
Rutgers University
May 18, 2018
Birational Geometry and Arithmetic
Play     Abstract

The punctual Hilbert scheme

James McKernan
UCSD
May 18, 2018
Birational Geometry and Arithmetic
Play     Abstract

Failure of stable rationality of various algebraic varieties via reduction modulo $p$

Takuzo Okada
Saga University
May 17, 2018
Birational Geometry and Arithmetic
Play     Abstract

Finite collineation groups and birationally rigidity

Ivan Cheltsov
University of Edinburgh
May 17, 2018
Birational Geometry and Arithmetic
Play

A database of genus 3 curves over Q

Andrew Sutherland
Massachusetts Institute of Technology
May 17, 2018
Birational Geometry and Arithmetic
Play     Abstract     Slides

Level structures on abelian varieties and Vojta's conjecture

Dan Abramovich
Brown University
May 17, 2018
Birational Geometry and Arithmetic
Play     Abstract     Slides

Algorithms for Cox rings

Simon Keicher
n/a (previously Universidad de Concepcion, Chile)
May 16, 2018
Birational Geometry and Arithmetic
Play     Abstract     Slides

Moduli spaces of rational curves on Fano hypersurfaces

Roya Beheshti
Washington University
May 16, 2018
Birational Geometry and Arithmetic
Play     Abstract

Computing zeta functions of nondegenerate hypersurfaces in toric varieties

Edgar Costa
Dartmouth College
May 16, 2018
Birational Geometry and Arithmetic
Play     Abstract     Slides

Zeta functions of varieties- Tools and Applications

Kiran Kedlaya
University of California, San Diego
May 16, 2018
Birational Geometry and Arithmetic
Play     Abstract     Slides

Nef anti-canonical divisors and rationally connected fibrations

Yoshinori Gongyo
University of Tokyo
May 15, 2018
Birational Geometry and Arithmetic
Play     Abstract

The exceptional set in Manin's Conjecture

Brian Lehmann
Boston College
May 15, 2018
Birational Geometry and Arithmetic
Play     Abstract

Manin's conjecture and the Fujita invariant of finite covers

Akash Sengupta
Princeton University
May 15, 2018
Birational Geometry and Arithmetic
Play     Abstract

Rational Points, Height Bounds, and Weak Approximation via Higher Positive Curvature

Jason Starr
Stony Brook University
May 15, 2018
Birational Geometry and Arithmetic
Play     Abstract

Rational points on conic bundle surfaces

Christopher Frei
University of Manchester
May 14, 2018
Birational Geometry and Arithmetic
Play     Abstract

Rationality constructions for cubic hypersurfaces

Brendan Hassett
ICERM/Brown University
May 14, 2018
Birational Geometry and Arithmetic
Play     Abstract     Slides

Heights on stacks

Jordan Ellenberg
University of Wisconsin
May 14, 2018
Birational Geometry and Arithmetic
Play     Abstract

Sphere packing, lattice packing, and related problems

Abhinav Kumar
Stony Brook University
April 25, 2018
Birational Geometry and Arithmetic
Play     Abstract     Slides