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The Geometry and Arithmetic of Banana Nano-Manifolds

Offered By: M-Seminar, Kansas State University via YouTube

Tags

Algebraic Geometry Courses Modular Forms Courses Gromov-Witten Theory Courses Arithmetic Geometry Courses Calabi-Yau Manifold Courses Donaldson-Thomas Theory Courses

Course Description

Overview

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Explore the intricate world of Calabi-Yau threefolds in this M-Seminar lecture from Kansas State University. Delve into the construction of four new examples of rigid Calabi-Yau threefolds with Picard number 4, known as "banana type" manifolds. Discover how these structures possess some of the smallest known values for Calabi-Yau Hodge numbers. Examine the partial computation of Donaldson-Thomas partition functions and learn how the associated genus g Gromov-Witten potential relates to Siegel paramodular forms. Investigate the arithmetic modularity of these manifolds, exploring the connection between point-counting over finite fields and weight 4 modular forms. Gain insights into cutting-edge research in algebraic geometry and number theory through this collaborative work presented by Jim Bryan from the University of British Columbia.

Syllabus

Jim Bryan - The geometry and arithmetic of banana nano-manifolds


Taught by

M-Seminar, Kansas State University

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