报告题目: 2-representations and 2-vector bundles
报告人：郇真(华中科技大学)
时间： 2023-08-30 15:30-17:00
地点: 数学学院425
邀请人：孙鹏
报告摘要: An elliptic cohomology theory is an even periodic multiplicative generalized cohomology theory whose associated formal group is the formal completion of an elliptic curve. It is at the intersection of a variety of areas in mathematics, including algebraic topology, algebraic geometry, mathematical physics, representation theory and number theory. From different perspectives we have different interpretations of elliptic cohomology, which gives us different ways to study it.
One approach is via a representing object of elliptic cohomology. Other than elliptic spectrum, a good choice is its geometric object. For example, the geometric object of K-theory is vector bundle. As a higher version of K-theory, the geometric object of elliptic cohomology should be “2-vector bundle”. Analogous to the relation between vector bundles and group representations, a 2-representation of a 2-group is a 2-vector bundle at a point. We glue the local (equivariant) 2-vector bundles together by higher sheafification and obtain the 2-stack of (equivariant) 2-vector bundles. Currently I'm exploring further the relation between this model of 2-vector bundles and elliptic cohomology.
报告人简介：郇真的主要研究方向是代数拓扑，代数几何和数学物理。2006年本科毕业于北京大学数学学院，2017年博士毕业于伊利诺伊大学厄巴纳-香槟分校，现任华中科技大学数学中心副研究员。郇真的主要研究对象是椭圆上同调。博士期间她构造了一个闭路空间（现被称为Huan’s Inertia orbifold），在高阶几何领域具有启发意义。该闭路空间的K-理论和椭圆上同调关系紧密，被称为拟椭圆上同调。另外，除了通过代数拓扑领域的正交等变谱，郇真也在尝试从高阶几何的角度构造椭圆上同调的表示物，即2-向量丛。该项工作仍在进一步发展完善中。
