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作者：Lapid, Erez; Minguez, Alberto
作者单位：Weizmann Institute of Science; University of Vienna
摘要：In 1980 Zelevinsky introduced certain commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate geometric conditions for certain triples of such components and conjecture that these conditions are related to irreducibility of parabolic induction. The conditions are in the spirit of the Geiss-Leclerc-Schroer condition that occurs in the conjectural...
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作者：Yang, Pengyu
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the general problem of equidistribution of expanding translates of an analytic curve by an algebraic diagonal flow on the homogeneous space G/Gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G/\Gamma $$\end{document} of a semisimple algebraic group G. We define two families of algebraic subvarieties of...
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作者：Guth, Larry; Iosevich, Alex; Ou, Yumeng; Wang, Hong
作者单位：Massachusetts Institute of Technology (MIT); University of Rochester; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：If E subset of R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E \subset \mathbb {R}<^>2$$\end{document} is a compact set of Hausdorff dimension greater than 5 / 4, we prove that there is a point x is an element of E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \use...
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作者：Kielak, Dawid
作者单位：University of Bielefeld
摘要：We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal differences of two polytopes); this result can be seen as analogous to the fact that determinants of matrices over commutative Laurent polynomial rings are themselves polynomials, rather than rational functions. We also exhibit a relationship between the Newton polytopes and invertibility of the matrices...
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作者：Lawrence, Brian; Venkatesh, Akshay
作者单位：University of Chicago; Institute for Advanced Study - USA
摘要：We give an alternative proof of Faltings's theorem (Mordell's conjecture): a curve of genus at least two over a number field has finitely many rational points. Our argument utilizes the set-up of Faltings's original proof, but is in spirit closer to the methods of Chabauty and Kim: we replace the use of abelian varieties by a more detailed analysis of the variation of p-adic Galois representations in a family of algebraic varieties. The key inputs into this analysis are the comparison theorems...
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作者：Chaika, Jon; Masur, Howard
作者单位：Utah System of Higher Education; University of Utah; University of Chicago
摘要：We show that the set of not uniquely ergodic d-IETs with permutation in the Rauzy class of the hyperelliptic permutation has Hausdorff dimension d - 3/2 [in the (d - 1)-dimension space of d-IETs] for d >= 5. For d = 4 this was shown by Athreya-Chaika and for d is an element of {2, 3} the set is known to have dimension d - 2. This provides lower bounds on the Hausdorff dimension of non-weakly mixing IETs and, with input from Al-Saqban et al. (Exceptional directions for the Teichmuller geodesic ...
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作者：Erschler, Anna; Zheng, Tianyi
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); University of California System; University of California San Diego
摘要：On torsion Grigorchuk groups we construct random walks of finite entropy and power-law tail decay with non-trivial Poisson boundary. Such random walks provide near optimal volume lower estimates for these groups. In particular, for the first Grigorchuk group G we show that its growth vG,S(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-...
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作者：Behrens, Mark; Rezk, Charles
作者单位：University of Notre Dame; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological Andre-Quillen cohomology of the K(n)-local Spanier-Whitehead dual of the space, and show that the map is an equivalence in the case where the space is a sphere. This results in a method for computing unstable v(n)-periodic homotopy groups of spheres from their Morava E-cohomology (as modules over the Dyer-Lashof algebra of Morava E-theory). We relate the resulting algebraic computation...
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作者：Conca, Aldo; Varbaro, Matteo
作者单位：University of Genoa
摘要：Let I be a homogeneous ideal of S = K[x(1), ..., x(n)] and let J be an initial ideal of I with respect to a term order. We prove that if J is radical then the Hilbert functions of the local cohomology modules supported at the homogeneous maximal ideal of S/I and S/J coincide. In particular, depth(S/I) = depth(S/J) and reg(S/I) = reg(S/J).
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作者：Atobe, Hiraku
作者单位：Hokkaido University
摘要：In this paper, we explicitly compute the semisimplifications of all Jacquet modules of irreducible representations with generic L-parameters of p-adic split odd special orthogonal groups or symplectic groups. Our computation represents them in terms of linear combinations of standard modules with rational coefficients. The main ingredient of this computation is to apply M oe glin's explicit construction of local A-packets to tempered L-packets. Finally, we study the derivatives introduced by M...
