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作者：Braun, Lukas
作者单位：University of Freiburg
摘要：We prove a conjecture of Kollar stating that the local fundamental group of a klt singularity x is finite. In fact, we prove a stronger statement, namely that the fundamental group of the smooth locus of a neighbourhood of x is finite. We call this the regional fundamental group. As the proof goes via a local-to-global induction, we simultaneously confirm finiteness of the orbifold fundamental group of the smooth locus of a weakly Fano pair.
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作者：Chen, Qile; Janda, Felix; Ruan, Yongbin
作者单位：Boston College; University of Notre Dame; Zhejiang University
摘要：We introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and reduced) are constructed for these moduli stacks. The main results are two comparison theorems relating the reduced virtual cycle to the cosection localized virtual cycle, as well as the reduced virtual cycle to the canonical virtual cycle. This sets the foundation of a new technique for computing higher genus Gromov-...
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作者：Liedtke, Christian
作者单位：Technical University of Munich
摘要：As was pointed out by Bragg and Lieblich
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作者：Ren, Haojie; Shen, Weixiao
作者单位：Fudan University; Fudan University
摘要：For a real analytic periodic function phi : R -> R, an integer b >= 2 and lambda is an element of (1/b, 1), we prove the following dichotomy for the Weierstrass-type function W(x) = Sigma(n >=)0 lambda(n)phi(b(n)x): Either W(x) is real analytic, or the Hausdorff dimension of its graph is equal to 2 + log(b) lambda. Furthermore, given b and phi, the former alternative only happens for finitely many lambda unless phi is constant.
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作者：Benedikter, Niels; Nam, Phan Thanh; Porta, Marcello; Schlein, Benjamin; Seiringer, Robert
作者单位：University of Milan; University of Munich; International School for Advanced Studies (SISSA); University of Zurich; Institute of Science & Technology - Austria
摘要：We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state, while showing that gapless and non-collective excitations have only a ne...
