Conference: Geometry and Physics---Deformations, Homotopy Algebras, and Higher Structures

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This award provides financial support for U.S.-based participants in two international summer schools in Geometry and Physics (GAP): GAP XVII (2022) to be held at the Pacific Institute for Mathematical Science in Vancouver, Canada during the week May 16-20, 2022 and GAP XVIII (2023) to be held at the Institut Henri Poincaré, in Paris, France during the week May 22-26, 2023. The twofold purpose of the proposed activities are to gather leading experts and early-career researchers working in rapidly developing subjects, and to foster interaction between groups of mathematicians and physicists working on different aspects of related problems; this will facilitate cross-fertilization between different fields and disseminate the most recent results of current research. GAP XVII and GAP XVIII will allow earlier-career mathematicians to disseminate their ideas and to broaden their perspective, both mathematically and internationally. Both summer schools, which will provide the opportunity for researchers to exchange ideas with foreign peers and launch collaborations, will include a poster session for individuals to present their recent work. The theme of both schools is "Higher Structures: Deformations and Homotopy Algebras". GAP XVII (2022) will be devoted to "Deformations" and GAP XVIII (2023) to "Homotopy Algebras". Higher structures has emerged as a new field in mathematics, as well as in mathematical and theoretical physics. Covering many different topics, this field encompasses deformation theory, quantization, homotopy algebras, derived geometry, enumerative geometry, representation theory, Poisson geometry, mirror symmetry, noncommutative algebraic geometry, string theory, and quantum field theory. The event will be devoted to bringing together different aspects of higher structures, in particular deformations and homotopy algebras, as well as identifying new emerging directions of investigation. Deformation theory has become an important area of mathematics. Deformation quantization lies on the boundary between classical and quantum mechanics. Roughly speaking, it is the study and prediction of quantum phenomena, which are normally described by noncommutative associative algebras, from the geometry of their underlying classical counterparts. Homotopy algebras provide a powerful machinery for studying many interconnected questions in different areas of contemporary mathematics and mathematical physics. This award will allow US scholars to abroad to attend these impactful events. For more information on the conference series, see http://www.geometryandphysics.org/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.