The Geometry and Arithmetic of Banana Nano-Manifolds

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.