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...
AbstractThis talk proposes a construction of C^r conforming finite element spaces with arbitrary r in any dimension. It is shown that if k ≥ 2^dr + 1 the space P_k of polynomials of degree ≤ k can be taken as the shape function space of Cr finite element spaces in d dimensions. This is the first work on constructing such C^r conforming finite elements in any dimension in a unified way.胡俊北...
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