Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives
(October 19-23, 2015)

Description

Only recently has it become feasible to do large scale verification of the predictions of the Langlands program in higher rank cases and to present the results in a way that is accessible widely to mathematicians. Moving from the understanding of Galois representations attached to elliptic curves to those attached to surfaces and other higher-dimensional varieties poses interesting problems in both arithmetic, algebra, geometry, and analysis.

In this workshop, we will consider computational and other explicit aspects of modular forms in higher rank. Topics covered will include: K3 surfaces and their connections to modular forms on orthogonal groups, algebraic modular forms associated to classical groups and their computation, and motives arising from general Calabi-Yau varieties accessible to explicit methods, including hypergeometric motives.

This workshop will bring together researchers who approach the Langlands program from a number of different perspectives, and our goal is to work in developing both the theoretical and computational aspects in tandem.

Organizing Committee

= speaker   = poster presenter

Monday October 19, 2015
Time Description Speaker Location Abstracts Slides
8:30 - 9:15Registration121 S.Main Street, Providence, RI (11th Floor Collaborative Space)
9:15 - 9:25WelcomeICERM Director11th Floor Lecture Hall
9:30 - 10:15Modularity of K3 surfaces and Calabi-Yau threefoldsMatthias Schütt, Gottfried Wilhelm Leibniz Universität Hannover11th Floor Lecture Hall
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10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:45From K3 surfaces to noncongruence modular formsWenching Li, Pennsylvania State University11th Floor Lecture Hall
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12:00 - 2:00Break for Lunch
2:00 - 2:45Calabi-Yau modular formsHossein Movasati, IMPA11th Floor Lecture Hall
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3:00 - 3:30Coffee/Tea Break
3:30 - 4:15Brauer groups of K3 surfaces and moduli of special cubic fourfoldsAnthony Varilly-Alvarado, Rice University11th Floor Lecture Hall
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4:30 - 5:15Complete hypergeometric L-functionsDavid Roberts, University of Minnesota, Morris11th Floor Lecture Hall
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5:30 - 7:00Welcome Reception11th Floor Collaborative Space

Tuesday October 20, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Refining the Langlands correspondence for symplectic motivesBenedict Gross, Harvard University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Counting points on K3 surfaces- some complexity guesstimatesDavid Harvey, University of New South Wales11th Floor Lecture Hall
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11:30 - 12:15more elementary evaluations of some K3 point-counts and periodsNoam Elkies, Harvard University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch
2:30 - 3:15Effective computations of Hasse--Weil zeta functionsEdgar Costa, ICERM and Dartmouth College11th Floor Lecture Hall
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3:30 - 4:15Point counting on K3 surfaces and applicationsAndreas-Stephan Elsenhans, Universität Paderborn11th Floor Lecture Hall
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4:30 - 6:00Poster Session/Coffee Break 11th Floor Collaborative Space

Wednesday October 21, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 10:00One parameter families of Calabi--Yau threefolds with trivial monodromySlawomir Cynk, Jagiellonian University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15K3 surfaces with real multiplicationJoerg Jahnel, University of Siegen11th Floor Lecture Hall
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11:30 - 12:15Complex multiplication and K3 surfaces over finite fieldsLenny Taelman, University of Amsterdam11th Floor Lecture Hall
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12:30 - 12:30Group Photo in Lecture Hall11th Floor Lecture Hall
12:30 - 2:30Break for Lunch
2:30 - 5:00Discussion/ Research/ Free Time
3:30 - 4:00Coffee/Tea Break

Thursday October 22, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Mirror symmetry and K3 surface zeta functions.Ursula Whitcher, University of Wisconsin- Eau Claire11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Arithmetic Mirror Symmetry of K3 surfaces and Hypergeometric FunctionsAdriana Salerno, Bates College11th Floor Lecture Hall
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11:30 - 12:15Calabi–Yau threefolds of Borcea–Voisin type and Arithmetic Mirror SymmetryNoriko Yui, Queen's University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch
2:30 - 3:15Higher rank theta lifts and applications to modularityLassina Dembele, University of Warwick11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break
4:00 - 4:45Moduli spaces of genus 2 curves with split Jacobians through K3 surfacesAbhinav Kumar, Stony Brook University11th Floor Lecture Hall
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Friday October 23, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Testing automorphicity of lifts of Hilbert modular formsClifton Cunningham, University of Calgary11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:30Mordell-Weil group of isotrivial families of curvesRemke Kloosterman, Humboldt University of Berlin
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11:30 - 12:15Sato-Tate groups of higher weight motivesKiran Kedlaya, UCSD11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break