À¶Ý®ÊÓƵ

Yash Singh, University of À¶Ý®ÊÓƵ

Vector Bundles on Toric Stacks

We give moduli interpretations of toric vector bundles and generalize this approach to a classification of bundles on arbitrary toric stacks.

MC 5403

Sean Lee, University of À¶Ý®ÊÓƵ

Topological dynamics of the Rado graph

We introduce some concepts from topological dynamics, in particular the universal minimal flow, with the goal of showing that the universal minimal flow of the automorphism group of the Rado graph is the space of linear orders of the Rado graph.

MC 5417

Faisal Romshoo, University of À¶Ý®ÊÓƵ

Constructing calibrated submanifolds through evolution equations

I will talk about how we can construct examples of calibrated submanifolds using the techniques of evolution equations. We will begin by defining the ideas involved in coming up with these evolution equations and then look at some of the examples of calibrated submanifolds that are constructed this way, following arXiv:math/0008021, arXiv:math/0008155, arXiv:math/0010036 and arXiv:math/0401123.

MC 5403

Xuemiao Chen, University of À¶Ý®ÊÓƵ

On the space of lines

I will make a story about the space of oriented lines in the three dimensional Euclidean space.

MC 5403

Jiahao Hu, Yau Mathematical Sciences Center, Tsinghua University

Homotopy theoretical holomorphic invariants of complex manifolds

In this talk, I will begin by presenting a method for extracting new holomorphic invariants of a complex manifold from its de Rham algebra of complex-valued differential forms. These invariants can be seen as refined versions of the complexified homotopy groups. I will then explore their potential connections with Hermitian geometry. Specifically: (1) the non-abelian part (refined fundamental group) should be related to a generalization of Higgs bundle; (2) the abelian part (refined higher homotopy) may provide new tools for studying the geometry of holomorphic mappings.

MC 5417