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作者：Alper, Jarod; Hall, Jack; Rydh, David
摘要：We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is (tale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin's algebraization theorem proved in the appendix. We provide numerous applications of the main theorems.
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作者：Petrow, Ian; Young, Matthew P.
摘要：We prove a Weyl-exponent subconvex bound for any Dirichlet L-function of cube-free conductor. We also show a bound of the same strength for certain L-functions of self-dual GL(2) automorphic forms that arise as twists of forms of smaller conductor.
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作者：Judge, Chris; Mondal, Sugata
摘要：We show that a second Neumann eigenfunction u of a Euclidean triangle has at most one (non-vertex) critical point p, and if p exists, then it is a non-degenerate critical point of Morse index 1. Using this we deduce that (1) the extremal values of u are only achieved at a vertex of the triangle, and (2) a generic acute triangle has exactly one (non-vertex) critical point and that each obtuse triangle has no (non-vertex) critical points. This settles the hot spots conjecture for triangles in th...
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作者：Branden, Petter; Huh, June
摘要：We study the class of Lorentzian polynomials. The class contains homogeneous stable polynomials as well as volume polynomials of convex bodies and projective varieties. We prove that the Hessian of a nonzero Lorentzian polynomial has exactly one positive eigenvalue at any point on the positive orthant. This property can be seen as an analog of the Hodge-Riemann relations for Lorentzian polynomials. Lorentzian polynomials are intimately connected to matroid theory and negative dependence proper...
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作者：Angenent, Sigurd; Daskalopoulos, Panagiota; Sesum, Natasa
摘要：In this paper we consider the classification of closed non-collapsed ancient solutions to the Mean Curvature Flow (n >= 2) that are uniformly two-convex. We prove that they are either contracting spheres or they must coincide up to translations and scaling with the rotationally symmetric closed ancient non-collapsed solution first constructed by Brian White, and later by Robert Haslhofer and Or Hershkovits.
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作者：Guth, Larry; Wang, Hong; Zhang, Ruixiang
摘要：We prove a sharp square function estimate for the cone in R-3 and consequently the local smoothing conjecture for the wave equation in 2 + 1 dimensions.
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作者：Koukoulopoulos, Dimitris; Maynard, James
摘要：Let psi : N -> R->= 0 be an arbitrary function from the positive integers to the non-negative reals. Consider the set A of real numbers a for which there are infinitely many reduced fractions a/q such that vertical bar alpha-a/q vertical bar <= psi(q)/q. If Sigma(infinity)(q=1) psi(q)phi(q)/q = infinity, we show that A has full Lebesgue measure. This answers a question of Duffin and Schaeffer. As a corollary, we also establish a conjecture due to Catlin regarding non-reduced solutions to the i...
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作者：DeMarco, Laura; Krieger, Holly; Ye, Hexi
摘要：We introduce a general strategy for proving quantitative and uniform bounds on the number of common points of height zero for a pair of inequivalent height functions on P-1((Q) over bar). We apply this strategy to prove a conjecture of Bogomolov, Fu, and Tschinkel asserting uniform bounds on the number of common torsion points of elliptic curves in the case of two Legendre curves over C. As a consequence, we obtain two uniform bounds for a two-dimensional family of genus 2 curves: a uniform Ma...
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作者：Goette, S.; Kerin, M.; Shankar, K.
摘要：In this article, a six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO(3)-invariant metric of non-negative curvature.
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作者：Rizzardo, Alice; Van den Bergh, Michel
摘要：In this paper we give an example of a triangulated category, linear over a field of characteristic zero, which does not carry a DG-enhancement. The only previous examples of triangulated categories without a model have been constructed by Muro, Schwede and Strickland. These examples are however not linear over a field.
