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作者：Linares, Pablo; Otto, Felix; Tempelmayr, Markus; Tsatsoulis, Pavlos
作者单位：Imperial College London; Max Planck Society; University of Munster; University of Bielefeld
摘要：In this paper, we explore the version of Hairer's regularity structures based on a greedier index set than trees, as introduced in (Otto et al. in A priori bounds for quasi-linear SPDEs in the full sub-critical regime, 2021, arXiv:2103.11039) and algebraically characterized in (Linares et al. in Comm. Am. Math. Soc. 3:1-64, 2023). More precisely, we construct and stochastically estimate the renormalized model postulated in (Otto et al. in A priori bounds for quasi-linear SPDEs in the full sub-...
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作者：Ben-Zvi, David; Chen, Harrison; Helm, David; Nadler, David
作者单位：University of Texas System; University of Texas Austin; Academia Sinica - Taiwan; Imperial College London; University of California System; University of California Berkeley
摘要：Kazhdan and Lusztig identified the affine Hecke algebra H with an equivariant K-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of irreducible representations of reductive groups over nonarchimedean local fields F with an Iwahori-fixed vector. We apply techniques from derived algebraic geometry to pass from K-theory to Hochschild homology and thereby identify H with the endomorphisms of a coherent sheaf on th...
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作者：Blasiak, Jonah; Morse, Jennifer; Pun, Anna
作者单位：Drexel University; University of Virginia; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：Catalan functions, the graded Euler characteristics of certain vector bundles on the flag variety, are a rich class of symmetric functions which include k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$k$\end{document}-Schur functions and parabolic Hall-Littlewood polynomials. We prove that Catalan functions indexed...
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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...
