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作者：Budur, Nero; van der Veer, Robin; Wu, Lei; Zhou, Peng
作者单位：KU Leuven; Utah System of Higher Education; University of Utah; Universite Paris Saclay
摘要：We prove a conjecture of the first author relating the Bernstein-Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. This generalizes a classical theorem of Malgrange and Kashiwara relating the b-function of a multivariate polynomial with the monodromy eigenvalues on the Milnor fibers cohomology.
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作者：Hedden, Matthew; Pinzon-Caicedo, Juanita
作者单位：Michigan State University; University of Notre Dame
摘要：We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use SO(3) gauge theory to provide a general criterion sufficient for the image of a satellite operation to generate an infinite rank subgroup of the smooth concordance group C. Our criterion applies widely; notably to many unknotted patterns for which the corresponding operators on the topological concordance gro...
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作者：Bezrukavnikov, Roman; Losev, Ivan
作者单位：Massachusetts Institute of Technology (MIT); Yale University
摘要：We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing. We provide an exact count in the case when the quiver is of finite type or is of affine type and the framing is the coordinate vector at the extending vertex. The latter case precisely covers Etingof's conjecture on the number of finite dimensional irreducible representations for Symplectic reflection algebras associ...
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作者：Karpukhin, Mikhail
作者单位：University of California System; University of California Irvine
摘要：In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres Sn. First, we propose a new approach to isoperimetric eigenvalue inequalities based on energy index. Using this approach we show that for any positive k, the k-th non-zero eigenvalue of the Laplacian on the real projective plane endowed with a metric of unit area, is maximized on the sequence of metrics converging to a union of (k - 1) identical copies of round ...
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作者：Blanco, Guillem
作者单位：KU Leuven
摘要：We present a proof of a conjecture proposed by Yano (Sci Rep Saitama Univ Ser 10(2): 21-28, 1982) about the generic b-exponents of irreducible plane curve singularities.
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作者：Beraldo, Dario
作者单位：University of London; University College London
摘要：We characterize the tempered part of the automorphic Langlands category D(Bun(G)) using the geometry of the big cell in the affine Grassmannian. We deduce that, for G non-abelian, tempered D-modules have no de Rham cohomology with compact support. The latter fact boils down to a concrete statement, which we prove using the Ran space and some explicit t-structure estimates: for G non-abelian and Sigma a smooth affine curve, the Borel-Moore homology of the indscheme Maps(Sigma, G) vanishes.
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作者：Sawin, Will
作者单位：Columbia University
摘要：We prove a characteristicpanalogue of a result of Massey which bounds the dimensions of the stalks of a perverse sheaf in terms of certain intersection multiplicities of the characteristic cycle of that sheaf. This uses the construction of the characteristic cycle of a perverse sheaf in characteristicpby Saito. We apply this to prove a conjecture of Shende and Tsimerman on the Betti numbers of the intersections of two translates of theta loci in a hyperelliptic Jacobian. This implies a functio...
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作者：Izumi, Masaki; Matui, Hiroki
作者单位：Kyoto University; Chiba University
摘要：This is the second part of our serial work on the classification of poly-Z group actions on Kirchberg algebras. Based on technical results obtained in our previous work, we completely reduce the problem to the classification of continuous fields of Kirchberg algebras over the classifying spaces. As an application, we determine the number of cocycle conjugacy classes of outer Z(n)-actions on the Cuntz algebras.
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作者：Heuer, Nicolaus; Loeh, Clara
作者单位：University of Cambridge; University of Regensburg
摘要：New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds is dense in R->= 0. In dimension 4 we prove that every non-negative rational number is the simplicial volume of some orientable closed connected 4-manifold. Our group theoretic results relate stable commutator length to the l(1)-semi-norm of certain singula...
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作者：Clausen, Dustin; Mathew, Akhil
作者单位：University of Copenhagen; University of Chicago
摘要：We study the etale sheafification of algebraic K-theory, called etale K-theory. Our main results show that etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories. Consequently, we show that etale K-theory has surprisingly well-behaved properties, integrally and without finiteness assumptions. A key theoretical ingredient is the distinction, which we investigate in detail, between sheaves and hypersheaves of spectra on etal...
