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作者：Venerucci, Rodolfo
作者单位：University of Duisburg Essen
摘要：Let A/Q be an elliptic curve with split multiplicative reduction at a prime p. We prove (an analogue of) a conjecture of Perrin-Riou, relating p-adic Beilinson-Kato elements to Heegner points in A(Q), and a large part of the rank-one case of the Mazur-Tate-Teitelbaum exceptional zero conjecture for the cyclotomic p-adic L-function of A. More generally, let f be the weight-two newform associated with A, let f(infinity) be the Hida family of f, and let L p(f(infinity), k, s) be the Mazur-Kitagaw...
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作者：Carlotto, Alessandro; Chodosh, Otis; Eichmair, Michael
作者单位：University of Cambridge; University of Vienna
摘要：The study of stable minimal surfaces in Riemannian 3-manifolds (M, g) with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when (M, g) is asymptotically flat and has horizon boundary. As a consequence, we obtain an effective version of the positive mass theorem in terms of isoperimetric or, more generally, closed volume-preserving stable CMC surfaces that is appealing from both a physical and a purely geometric point of view. We also include ...
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作者：Aka, Menny; Einsiedler, Manfred; Shapira, Uri
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Technion Israel Institute of Technology
摘要：Linnik proved in the late 1950's the equidistribution of integer points on large spheres under a congruence condition. The congruence condition was lifted in 1988 by Duke (building on a break-through by Iwaniec) using completely different techniques. We conjecture that this equidistribution result also extends to the pairs consisting of a vector on the sphere and the shape of the lattice in its orthogonal complement. We use a joining result for higher rank diagonalizable actions to obtain this...
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作者：Liu, Yifeng
作者单位：Northwestern University
摘要：Let E be an elliptic curve over and A another elliptic curve over a real quadratic number field. We construct a -motive of rank 8, together with a distinguished class in the associated Bloch-Kato Selmer group, using Hirzebruch-Zagier cycles, that is, graphs of Hirzebruch-Zagier morphisms. We show that, under certain assumptions on E and A, the non-vanishing of the central critical value of the (twisted) triple product L-function attached to (E, A) implies that the dimension of the associated B...
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作者：Guardia, Marcel; Martin, Pau; Seara, Tere M.
作者单位：Universitat Politecnica de Catalunya; Universitat Politecnica de Catalunya
摘要：The restricted three body problem models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. When they move along circular Keplerian orbits and the third body moves in the same plane, one has the restricted planar circular three body problem (RPC3BP). In suitable coordinates, it is a Hamiltonian system of two degrees of freedom. The conserved energy is usually called the Jacobi constant. Llibre and Sim [Math An...
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作者：Farkas, Gavril; Kemeny, Michael
作者单位：Humboldt University of Berlin
摘要：Using lattice theory on special surfaces, calculations on moduli stacks of pointed curves and Voisin's proof of Green's Conjecture on syzygies of canonical curves, we prove the Prym-Green Conjecture on the naturality of the resolution of a general Prym-canonical curve of odd genus, as well as (many cases of) the Green-Lazarsfeld Secant Conjecture on syzygies of non-special line bundles on general curves.
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作者：Alekseev, Anton; Rossi, Carlo A.; Torossian, Charles; Willwacher, Thomas
作者单位：University of Geneva; Universite Paris Cite; University of Zurich
摘要：We prove the statement/conjecture of M. Kontsevich on the existence of the logarithmic formality morphism . This question was open since 1999, and the main obstacle was the presence of dr / r type singularities near the boundary in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise to a version of Stokes' formula for differential forms with singularities at ...
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作者：Davini, Andrea; Fathi, Albert; Iturriaga, Renato; Zavidovique, Maxime
作者单位：Sapienza University Rome; Ecole Normale Superieure de Lyon (ENS de LYON); CIMAT - Centro de Investigacion en Matematicas; Sorbonne Universite
摘要：We consider a continuous coercive Hamiltonian H on the cotangent bundle of the compact connected manifold M which is convex in the momentum. If is the viscosity solution of the discounted equation where c(H) is the critical value, we prove that converges uniformly, as , to a specific solution of the critical equation We characterize in terms of Peierls barrier and projected Mather measures. As a corollary, we infer that the ergodic approximation, as introduced by Lions, Papanicolaou and Varadh...
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作者：Andersson, John
作者单位：Royal Institute of Technology
摘要：We will show optimal regularity for minimizers of the Signorini problem for the Lame system. In particular if u = (u(1), u(2), ..., u(n)) is an element of W-1,W-2(B-1(+) : R-n) minimizes J (u) = integral(B1+) vertical bar del u+del(perpendicular to)vertical bar(2) + lambda div(u)(2) in the convex set K = {u = (u(1), u(2), ... , u(n)) is an element of W-1,W-2 (B-1(+) : R-n); u(n) = 0 on Pi, u = f is an element of C-infinity(partial derivative B-1) on (partial derivative B-1)(+)}, where lambda >...
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作者：Maulik, Davesh
作者单位：Columbia University
摘要：Given a planar curve singularity, we prove a conjecture of Oblomkov-Shende, relating the geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated algebraic link. More generally, we prove an extension of this conjecture, due to Diaconescu-Hua-Soibelman, relating stable pair invariants on the conifold to the colored HOMFLY polynomial of the algebraic link. Our proof uses wall-crossing techniques to prove a blowup identity on the algebro-geometric side. We prove a match...
