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作者：Dai, Irving; Kang, Sungkyung; Mallick, Abhishek; Park, Junghwan; Stoffregen, Matthew
作者单位：University of Texas System; University of Texas Austin; University of Oxford; Rutgers University System; Rutgers University New Brunswick; Korea Advanced Institute of Science & Technology (KAIST); Michigan State University
摘要：We prove that the (2,1)-cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.
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作者：Vishik, Alexander
作者单位：University of Nottingham
摘要：In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with F p \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Bbb {F}}_{p}$\end{document} -coefficients). This shows that Isotropic Chow motives coincide with Numerical Chow motives. In...
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作者：Kashiwara, Masaki; Kim, Myungho; Oh, Se-jin; Park, Euiyong
作者单位：Kyoto University; Korea Institute for Advanced Study (KIAS); Kyung Hee University; Sungkyunkwan University (SKKU); University of Seoul
摘要：We introduce a new family of real simple modules over the quantum affine algebras, called the affine determinantial modules, which contains the Kirillov-Reshetikhin (KR)-modules as a special subfamily, and then prove T-systems among them which generalize the T-systems among KR-modules and unipotent quantum minors in the quantum unipotent coordinate algebras simultaneously. We develop new combinatorial tools: admissible chains of i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{w...
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作者：Ai, Albert; Ifrim, Mihaela; Tataru, Daniel
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
摘要：It has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly improved compared to the sharp results of Smith-Tataru for the generic case. The aim of this article is to prove the first result in this direction, namely for the time-like minimal surface equation in the Minkowski space-time. Further, our improvement is substantial, namely by 3/8 derivatives in two space dimensions a...
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作者：Guo, Shaoming; Wang, Hong; Zhang, Ruixiang
作者单位：Nankai University; University of Wisconsin System; University of Wisconsin Madison; New York University; University of California System; University of California Los Angeles; University of California System; University of California Berkeley
摘要：In this paper, we first generalize the work of Bourgain (Geom. Funct. Anal. 1(4):321-374, 1991) and state a curvature condition for H & ouml;rmander-type oscillatory integral operators, which we call Bourgain's condition. This condition is notably satisfied by the phase functions for the Fourier restriction problem and the Bochner-Riesz problem. We conjecture that for H & ouml;rmander-type oscillatory integral operators satisfying Bourgain's condition, they satisfy the same L-p bounds as in th...
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作者：Eckhardt, Jonathan; Kostenko, Aleksey
作者单位：Loughborough University; University of Ljubljana; University of Vienna; Technische Universitat Wien
摘要：Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2\times 2$\end{document} canonical systems). We prove a number of Szeg & odblac;-type theorems for...
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作者：Kottke, Chris; Rochon, Frederic
作者单位：State University System of Florida; New College Florida; University of Quebec; University of Quebec Montreal
摘要：We develop new techniques to compute the weighted L-2-cohomology of quasi-fibered boundary metrics (QFB-metrics). Combined with the decay of L-2-harmonic forms obtained in a companion paper, this allows us to compute the reduced L-2-cohomology for various classes of QFB-metrics. Our results applies in particular to the Nakajima metric on the Hilbert scheme of n points on C-2 , for which we can show that the Vafa-Witten conjecture holds. Using the compactification of the monopole moduli space a...
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作者：Maldague, Dominique
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove a sharp (up to C epsilon R epsilon) L-7 square function estimate for the moment curve in R-3.
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作者：Chodosh, Otis; Choi, Kyeongsu; Mantoulidis, Christos; Schulze, Felix
作者单位：Stanford University; Korea Institute for Advanced Study (KIAS); Rice University; University of Warwick
摘要：We show that the mean curvature flow of generic closed surfaces in R 3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}<^>{3}$\end{document} avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in R 4 \d...
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作者：Hafner, Dietrich; Hintz, Peter; Vasy, Andras
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Swiss Federal Institutes of Technology Domain; ETH Zurich; Stanford University
