Conference on Homological Mirror Symmetry

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This award supports participation in a conference on Homological Mirror Symmetry to be held at the University of Miami from January 27 through February 31, 2020. Mirror symmetry originated in physics as a duality between superconformal quantum field theories. This duality has been interpreted in a consistent, powerful mathematical framework called Homological Mirror Symmetry (HMS) that has led to dramatic developments in how the mathematical community approaches ideas from theoretical physics, and indeed our conception of space itself. Today HMS is established as one of the most powerful frameworks for building bridges between seemingly unrelated parts of modern geometry. Traditionally HMS has been incredibly successful in discovering novel phenomena and proving unexpected results in symplectic and contact topology informed by algebraic geometry. The goal of this conference is to highlight the flow of ideas in the opposite direction: from symplectic to complex geometry. The conference will summarize recently developed connections between Hodge Theory and HMS which have striking algebraic applications and give new insights into rationality problems. In particular, the conference will focus on new cutting-edge directions of investigation: (1) birational invariants and gluing of D-modules; (2) extending the scope of Homological Mirror Symmetry; (3) categorical Kaehler geometry; and (4) topological recursion. The conference website is https://schms.math.berkeley.edu/events/miami2020/.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.