中科院数学与系统科学研究院

数学研究所

中科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： 白少云 博士（Simons Center for Geometry and Physics）
题  目：Integral counts of pseudo-holomorphic curves and beyond
时  间：2023.08.03（星期四），09:00-10:00
地  点：数学院南楼N913
摘  要：As discussed in my previous lecture back in April, the resolution of the Arnold conjecture over integers crucially depends on defining a version of Hamiltonian Floer homology with integral coefficients. In this lecture, I will discuss an abstract algebra-topological setup which suitably captures essential features of moduli spaces of pseudo-holomorphic curves, and sketch how ideas from representation theory and algebraic geometry can be incorporated to define integral counts from these moduli spaces. Time permitting, I will speculate the possibility of defining complex cobordism valued Gromov-Witten invariants.
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报告人： 白少云 博士（Simons Center for Geometry and Physics）
题  目：A generalization of Franks’ theorem to toric symplectic manifolds
时  间：2023.08.03（星期四），14:00-15:00
地  点：数学院南楼N913
摘  要：I will discuss a recent result which shows that any Hamiltonian diffeomorphism of any compact toric symplectic manifolds admits infinitely many simple periodic points if it has more fixed points than the total Betti number of the ambient manifold. This generalizes a renowned result of Franks for the two-sphere, widely known as the two or infinity dichotomy. Gauged linear sigma model plays an essential role in the proof. This is joint work with Guangbo Xu.