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作者：McMullen, Curtis T.; Mukamel, Ronen E.; Wright, Alex
摘要：In this paper we present the first example of a primitive, totally geodesic subvariety F subset of M-g,M-n with dim(F) > 1. The variety we consider is a surface F subset of M-1,M-3 defined using the projective geometry of plane cubic curves. We also obtain a new series of Teichmuller curves in M-4, and new SL2(R)-invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms.
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作者：Zhu, Xinwen
摘要：We endow the set of lattices in Q(P)(n) with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake equivalence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.
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作者：Naber, Aaron; Valtora, Daniele
摘要：In this paper we study the regularity of stationary and minimizing harmonic maps f: B-2(p) subset of M -> N between Riemannian manifolds. If Sk(f)={x is an element of M: no tangent map at x is k+1-symmetric} is kth-stratum of the singular set of f, then it is well known that dimSk=k, however little else about the structure of Sk(f) is understood in any generality. Our first result is for a general stationary harmonic map, where we prove that Sk(f) is k-rectifiable. In the case of minimizing ha...
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作者：Tikuisis, Aaron; White, Stuart; Winter, Wilhelm
摘要：We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear C*-algebras of finite nuclear dimension which satisfy the UCT is now complete. Secondly, our result links the finite to the general version of the Toms-Winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dim...
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作者：Labourie, Francois
摘要：We prove that given a Hitchin representation in a real split rank 2 group G(0), there exists a unique equivariant minimal surface in the corresponding symmetric space. As a corollary, we obtain a parametrization of the Hitchin components by a Hermitian bundle over Teichm\uller space. The proof goes through introducing holomorphic curves in a suitable bundle over the symmetric space of G(0). Some partial extensions of the construction hold for cyclic bundles in higher rank.
