Speaker: Yingdi Qin (SIMIS)
Time: 2025-06-18 16:00
Location: R1210, SIMIS
Zoom Meeting ID:828 5522 9312 (Passcode:196485)
Abstract:
Condensed mathematics is a framework that aims to provide a more convenient way to treat algebraic objects equipped with topology, such as topological abelian groups or topological vector spaces. It has been developed to combine algebra and topology in a new way, by introducing the abelian category of ‘condensed abelian groups’, which contains (compactly generated) topological abelian groups as a full subcategory. Once playing with the tensor products of condensed modules, one immediately realizes that we need the concept of ‘complete’ condensed modules and ‘complete’ tensor products to produce the desirable results of certain tensor products. For example, the desirable tensor product of function rings on two spaces are supposed to be the function rings on the product of the two spaces. We have several different versions of completeness in condensed mathematics. Among them are solid modules in the non-Archimedean case, and liquid/gaseous modules in the Archimedean case. In this talk I will introduce solid and liquid/gaseous modules in condensed mathematics. And using it to construct an integral form of Sato-Segal-Wilson Grassmannians, which finds applications in integrable systems, moduli of curves/sheaves and geometric representation theory.
About Speaker:
Yingdi Qin is currently a postdoctoral researcher at SIMIS. He completed his PhD at UC Berkeley in 2020, under the supervision of Professor Denis Auroux. Prior to joining SIMIS, he held postdoctoral positions at the University of Pennsylvania and ICMS-Sofia. His main areas of research are symplectic geometry，mirror symmetry, generalized complex geometry, derived geometry and higher geometry.
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