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作者：Pigati, Alessandro; Stern, Daniel
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Princeton University
摘要：Given a Hermitian line bundle L -> M over a closed, oriented Riemannian manifoldM, we study the asymptotic behavior, as epsilon -> 0, of couples(u(epsilon), del(epsilon)) critical for the rescalings E epsilon(u, del)= (M)integral(vertical bar del u vertical bar(2)+epsilon(2)vertical bar F-del vertical bar(2)+1/4 epsilon(2)(1-vertical bar u vertical bar(2))(2)) of the self-dual Yang-Mills-Higgs energy, whereuis a section of Land del is a Hermitian connection on L with curvature F-del. Under the...
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作者：Daskalopoulos, Georgios; Mese, Chikako
作者单位：Brown University; Johns Hopkins University
摘要：We prove the holomorphic rigidity conjecture of Teichmuller space which loosely speaking states that the action of the mapping class group uniquely determines theTeichmuller space as a complex manifold. The method of proof is through harmonicmaps. We prove that the singular set of a harmonic map from a smooth n-dimensional Riemannian domain to theWeil-Petersson completion T of Teichmuller space has Hausdorff dimension at most n - 2, and moreover, u has certain decay near the singular set. Comb...
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作者：Avramidi, Grigori; Okun, Boris; Schreve, Kevin
作者单位：Max Planck Society; University of Wisconsin System; University of Wisconsin Milwaukee; University of Chicago
摘要：We compute the mod p homology growth of residual sequences of finite index normal subgroups of right-angled Artin groups. We find examples where this differs from the rational homology growth, which implies the homology of subgroups in the sequence has lots of torsion. More precisely, the homology torsion grows exponentially in the index of the subgroup. For odd primes p, we construct closed locally CAT(0) manifolds with nonzero mod p homology growth outside the middle dimension. These example...
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作者：Davison, Ben; Mandel, Travis
作者单位：University of Edinburgh; University of Oklahoma System; University of Oklahoma - Norman
摘要：We construct quantum theta bases, extending the set of quantum cluster monomials, for various versions of skew-symmetric quantum cluster algebras. These bases consist precisely of the indecomposable universally positive elements of the algebras they generate, and the structure constants for their multiplication are Laurent polynomials in the quantum parameter with non-negative integer coefficients, proving the quantum strong cluster positivity conjecture for these algebras. The classical limit...
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作者：Larson, Hannah K.
摘要：Let f : C -> P-1 be a degree k genus g cover. The stratification of line bundles L is an element of Pic(d) (C) by the splitting type of f(*)L is a refinement of the stratification by Brill-Noether loci W-d(r) (C). We prove that for general degree k covers, these strata are smooth of the expected dimension. In particular, this determines the dimensions of all irreducible components of W-d(r)(C) for a general k-gonal curve (there are often components of different dimensions), extending results o...
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作者：Fraczyk, Mikolaj
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：We show that every sequence of torsion-free arithmetic congruence lattices in PGL(2, R) or PGL(2, C) satisfies a strong quantitative version of the limit multiplicity property. We deduce that for R > 0 in certain range, growing linearly in the degree of the invariant trace field, the volume of the R-thin part of any congruence arithmetic hyperbolic surface or congruence arithmetic hyperbolic 3-manifold M is of order at most Vol(M)(11/12). As an application we prove Gelander's conjecture on hom...
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作者：Bartholdi, Laurent; Dudko, Dzmitry
作者单位：University of Gottingen; Universite PSL; Ecole Normale Superieure (ENS); State University of New York (SUNY) System; Stony Brook University
摘要：We considerThurston maps: branched self-coverings of the sphere with ultimately periodic critical points, and prove that the Thurston equivalence problem between them (continuous deformation of maps along with their critical orbits) is decidable. More precisely, we consider the action of mapping class groups, by pre- and post-composition, on branched coverings, and encode them algebraically asmapping class bisets. We show how the mapping class biset of maps preserving a multicurve decomposes i...
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作者：Klingler, B.; Otwinowska, A.
作者单位：Humboldt University of Berlin
摘要：Given V a polarizable variation of Z-Hodge structures on a smooth connected complex quasi-projective variety S, the Hodge locus for V-circle times is the set of closed points s of S where the fiber V-s has more Hodge tensors than the very general one. A classical result of Cattani, Deligne and Kaplan states that the Hodge locus for V-circle times is a countable union of closed irreducible algebraic subvarieties of S, called the special subvarieties of S for V. Under the assumption that the adj...
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作者：Buckmaster, T.; Germain, P.; Hani, Z.; Shatah, J.
作者单位：Princeton University; University of Michigan System; University of Michigan
摘要：Consider the cubic nonlinear Schrodinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the Fourier coefficients is governed by the so-called wave kinetic equation, predicted in wave turbulence theory, on a nontrivial timescale.
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作者：Ding, Jian; Xia, Jiaming
作者单位：University of Pennsylvania
摘要：We study the random field Ising model on Z(2) where the external field is given by i.i.d. Gaussian variables with mean zero and positive variance. We show that the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary.
