中国科学院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人： 赵禹 博士
（Institute for the Physics and Mathematics of the Universe, University of Tokyo）
题  目：Derived Birational Geometry of Nested Quiver Varieties
时  间：2023.08.21（星期一），09:00-10:00
地  点：数学院南楼N913
摘  要：Given a complex smooth surface, Negut constructed an action of the quantum toroidal algebra on the Grothendieck group of moduli space of stable sheaves, which generalized the construction of Nakajima, Grojnowski, Baranovsky in cohomology. In this talk, we will obtain a weak categorification of Negut's action, by constructing explicit natural transformations and compute the categorical commutators of the positive and negative part. Moreover, we will generalize this categorification to any Nakajima quiver varieties.
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报告人： 赵禹 博士
（Institute for the Physics and Mathematics of the Universe, University of Tokyo）
题  目：Categorical Resolution of the Diagonal
时  间：2023.08.21（星期一），10:00-11:00
地  点：数学院南楼N913
摘  要：In this talk, we will apply the generalized vanishing theorem we discuss to the diagonal of several morphisms, including the projectivization of two term complexes, the blow up of smooth varieties and root stacks. We will give a explicit resolution of the diagonal and give a new proof the semi orthogonal decomposition in those situations.