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：郇真 副研究员（华中科技大学数学中心）
题  目：Twisted Real quasi-elliptic cohomology
时  间：2023.03.30（星期四），15:00-17:00
地  点：腾讯会议：831-267-314
摘  要：Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic cohomology theories.  It can be interpreted by orbifold loop spaces and expressed in terms of equivariant K-theories. We formulate the complete power operation of this theory. Applying that we prove the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. In this talk we construct twisted Real quasi-elliptic cohomology as the twisted KR-theory of loop groupoids. The theory systematically incorporates loop rotation and reflection. After establishing basic properties of the theory, we construct Real analogues of the string power operation of quasi-elliptic cohomology. We also explore the relation of the theory to the Tate curve. This is joint work with Matthew Spong and Matthew Young.

-----------------------

报告人：郇真 副研究员（华中科技大学数学中心）
题  目：2-representations and 2-vector bundles
时  间：2023.04.06（星期四），15:00-17:00
地  点：腾讯会议：512-564-929
摘  要：In this talk I will introduce some basic concepts in higher category and some details of the construction in the first talk. I will introduce crossed modules and the example of strict 2-representation via it. And I will present Murray, Roberts and Wockel’s coherent model of string 2-group and its relation with BCSS model. In addition, I will show the relation between 1-representations and 2-representations after introducing the bicategory of bicategories. Moreover, I will introduce a little descent theory, i.e. how we glue in topology and geometry in a nice way. Higher stack is a higher presheaf in which descent theory works.