-
作者：Kato, Syu
作者单位：Kyoto University
摘要：We explain that the Pontryagin product structure on the equivariant K-group of an affine Grassmannian considered in [Lam-Schilling-Shimozono, Compos. Math. 146 (2010)] coincides with the tensor structure on the equivariant K-group of a semi-infinite flag manifold considered in [K-Naito-Sagaki, Duke Math. 169 (2020)]. Then, we construct an explicit isomorphism between the equivariant K-group of a semi-infinite flag manifold and a suitably localized equivariant quantum K-group of the correspondi...
-
作者：Eberle, Simon; Figalli, Alessio; Weiss, Georg s.
作者单位：Basque Center for Applied Mathematics (BCAM); Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Duisburg Essen
摘要：The characterization of global solutions to the obstacle problems in RN, or equivalently of null quadrature domains, has been studied for more than 90 years. In this paper, we give a conclusive answer to this problem by proving the following long-standing conjecture: The coincidence set of a global solution to the obstacle problem is either a half-space, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base.
-
作者：Betts, L. alexander; Stix, Jakob
作者单位：Cornell University; Goethe University Frankfurt
摘要：Let K be a number field not containing a CM subfield. For any smooth projective curve Y/K of genus >= 2, we prove that the image of the Selmer part of Grothendieck's section set inside the Kv-rational points Y (Kv) is finite for every finite place v. This gives an unconditional verification of a prediction of Grothendieck's section conjecture. In the process of proving our main result, we also refine and extend the method of Lawrence and Venkatesh, with potential consequences for explicit comp...
-
作者：Bhattacharya, Prasit; Kitchloo, Nitu
作者单位：New Mexico State University; Johns Hopkins University
-
作者：Shankar, Ravi; Yuan, Yu
作者单位：Princeton University; University of Washington; University of Washington Seattle
摘要：We derive a priori interior Hessian estimates and interior regularity for the sigma 2 equation in dimension four. Our method provides both a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher (n >= 5) dimensions.
-
作者：Haim-Kislev, Pazit; Ostrover, Yaron
作者单位：Institute for Advanced Study - USA; Tel Aviv University
摘要：We present a counterexample to Viterbo's volume-capacity conjecture. This implies, in particular, that in contrast with a well-known conjecture, symplectic capacities do not coincide on the class of convex domains in the classical phase space.
-
作者：Bishop, Christopher J.
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：This paper gives geometric characterizations of the Weil-Petersson class of rectifiable quasicircles, i.e., the closure of the smooth planar curves in the Weil-Petersson metric on universal Teichmuller space defined by Takhtajan and Teo. Although motivated by the planar case, many of our characterizations make sense for curves in Rn and remain equivalent in all dimensions. We prove that Gamma is Weil-Petersson if and only if it is well approximated by polygons in a precise sense, has finite Mo...
-
作者：Burungale, Ashay A.; Tian, Ye
作者单位：California Institute of Technology; University of Texas System; University of Texas Austin; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
摘要：Let E be a CM elliptic curve defined over Q and p a prime. We show that corankZp Selp infinity (E/Q) = 0 =double right arrow ords=1L(s, E/Q) = 0 for the p infinity- Selmer group Selp infinity(E/Q) and the complex L-function L(s, E/Q). Along with Smith's work on the distribution of 2 infinity-Selmer groups, this leads to the first instance of the even parity Goldfeld conjecture: For 50% of the positive square-free integers n, we have ords=1L(s, E/Q(n)) = 0, where E(n) : ny2 = x3-x is a quadrati...
-
作者：Gowers, W. T.; Green, Ben; Manners, Freddie; Tao, Terence
作者单位：Universite PSL; College de France; University of Cambridge; University of Oxford; University of California System; University of California San Diego; University of California System; University of California Los Angeles
摘要：We prove a conjecture of K. Marton, widely known as the polynomial Freiman-Ruzsa conjecture, in characteristic 2. The argument extends to odd characteristic, with details to follow in a subsequent paper.
-
作者：Heikkila, Susanna; Pankka, Pekka
作者单位：University of Jyvaskyla; University of Helsinki
摘要：We show that, if a closed, connected, and oriented Riemannian n-manifold N admits a non-constant quasiregular mapping from the Euclidean nspace Rn, then the de Rham cohomology algebra H & lowast;dR(N) of N embeds into the exterior algebra n & lowast;Rn. As a consequence, we obtain a homeomorphic classification of closed simply connected quasiregularly elliptic 4-manifolds.
