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作者：Levinson, Jake; Purbhoo, Kevin
作者单位：Simon Fraser University; University of Waterloo
摘要：We prove a generalization of the Shapiro-Shapiro conjecture on Wronskians of polynomials, allowing the Wronskian to have complex conjugate roots. We decompose the real Schubert cell according to the number of real roots of the Wronski map, and define an orientation of each connected component. For each part of this decomposition, we prove that the topological degree of the restricted Wronski map is given as an evaluation of a symmetric group character. In the case where all roots are real, thi...
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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：Kurinczuk, Robert; Skodlerack, Daniel; Stevens, Shaun
作者单位：Imperial College London; ShanghaiTech University; University of East Anglia
摘要：For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field C of characteristic different from p, intertwine if and only if they are conjugate. This completes work of the first and third authors who showed that every irreducible cuspidal C-representation of a classical group is compactly induced from a cuspidal type. We generalize Bushnell and Henniart's notion of endo-equivalence to sem...
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作者：Chang, Chieh-Yu; Mishiba, Yoshinori
作者单位：National Tsing Hua University; University of the Ryukyus
摘要：In the classical theory of multiple zeta values (MZV's), Furusho pro-posed a conjecture asserting that the p-adic MZV's satisfy the same Q-linear relations that their corresponding real-valued MZV counterparts satisfy. In this paper, we verify a stronger version of a function field analogue of Furusho's conjecture in the sense that we are able to deal with all linear relations over an algebraic closure of the given rational function field, not just the rational linear relations. To each tuple ...
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作者：Gekhtman, Ilya; Gerasimov, Victor; Potyagailo, Leonid; Yang, Wenyuan
作者单位：Technion Israel Institute of Technology; Universidade Federal de Minas Gerais; Universite de Lille; Peking University
摘要：For a random walk on a finitely generated group G we obtain a generalization of a classical inequality of Ancona. We deduce as a corollary that the identity map on G extends to a continuous equivariant surjection from the Martin boundary to the Floyd boundary, with preimages of conical points being singletons. This provides new results for Martin compactifications of relatively hyperbolic groups.
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作者：Ibarlucia, Tomas
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
摘要：We show that all groups of a distinguished class of large topological groups, that of Roelcke precompact Polish groups, have Kazhdan's Property (T). This answers a question of Tsankov and generalizes previous results by Bekka (for the infinite-dimensional unitary group) and by Evans and Tsankov (for oligomorphic groups). Further examples include the group Aut(mu) of measure-preserving transformations of the unit interval and the group Aut * (mu) of non-singular transformations of the unit inte...
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作者：Budzinski, Thomas; Louf, Baptiste
作者单位：University of British Columbia; Universite Paris Cite
摘要：We prove a conjecture of Benjamini and Curien stating that the local limits of uniform random triangulations whose genus is proportional to the number of faces are the planar stochastic hyperbolic triangulations (PSHT) defined in Curien (Probab Theory Relat Fields 165(3):509-540, 2016). The proof relies on a combinatorial argument and the Goulden-Jackson recurrence relation to obtain tightness, and probabilistic arguments showing the uniqueness of the limit. As a consequence, we obtain asympto...
