Homeomorphisms of Euclidean space

Abstract：The topological group of homeomorphisms of d-dimensional Euclidean space is a basic object in geometric topology, closely related to understanding the difference between diffeomorphisms and homeomorphisms of all d-dimensional manifolds (except when d=4). I will explain some methods that have been used for studying the algebraic topology of this group, and report on a recently obtained...

Reporter：Prof.Oscar Randal-Williams（University of Cambridge）

Non-abelian Hodge theory and higher Teichmüller spaces

Abstract: Non-abelian Hodge theory relates representations of the fundamental group of a compact Riemann surface X into a Lie group G with holomorphic objects on X known as Higgs bundles, introduced by Hitchin more than 35 years ago. Starting with the case in which G is the circle, and the 19th century Abel-Jacobi's theory, we will move to the case of G=SL(2,R) and the relation to Teichmüller t...

Reporter：Prof. Oscar García-Prada (Instituto de Ciencias Matemáticas)

Perverse sheaves on affine flag varieties and coherent sheaves on the dual Steinberg variety

Abstract: We will report on an ongoing project with R. Bezrukavnikov and L. Rider which aims at constructing an equivalence of categories lifting to the categorical level the comparison between the two natural geometric realizations of the affine Hecke algebra of a reductive group: one in terms of constructible sheaves on the associated affine flag variety, and one in terms of coherent sheaves ...

Reporter：Prof. Simon Riche (Université Clermont Auvergne）

Data-driven optimization --- Integrating data sampling, learning, and optimization

Abstract:Traditionally machine learning and optimization are two different branches in computer science. They need to accomplish two different types of tasks, and they are studied by two different sets of domain experts. Machine learning is the task of extracting a model from the data, while optimization is to find the optimal solutions from the learned model. In the current era of big data and...

Reporter：Prof.Wei Chen (Microsoft Research Asia)

Model Selection for Optimal Regression Learning

In statistical learning, various mathematical optimalities are used to characterize performances of different learning methods. They include minimax optimality from a worst-case standpoint and asymptotic efficiency from a rosy view that the regression function to be learned sits there to be discovered. When multiple models, e.g., trees, neural networks and support vector machines, are considere...

Reporter：Prof.Yuhong Yang(University of Minnesota)