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作者：Aspero, David; Schindler, Ralf
摘要：We show that Martin's Maximum(++) implies Woodin's P-max axiom (*). This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply that there are aleph(2) many real numbers.
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作者：Leuzinger, Enrico; Young, Robert
摘要：The Dehn function and its higher-dimensional generalizations measure the difficulty of filling a sphere in a space by a ball. In nonpositively curved spaces, one can construct fillings using geodesics, but fillings become more complicated in subsets of nonpositively curved spaces, such as lattices in symmetric spaces. In this paper, we prove sharp filling inequalities for (arithmetic) lattices in higher rank semisimple Lie groups. When n is less than the rank of the associated symmetric space,...
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作者：Elgindi, Tarek M.
摘要：It has been known since work of Lichtenstein and Gunther in the 1920s that the 3D incompressible Euler equation is locally well-posed in the class of velocity fields with Ho center dot lder continuous gradient and suitable decay at infinity. It is shown here that these local solutions can develop singularities in finite time, even for some of the simplest three-dimensional flows.
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作者：Fresan, Javier; Jossen, Peter
摘要：We answer in the negative Siegel's question whether all E-functions are polynomial expressions in hypergeometric E-functions. Namely, we show that if an irreducible differential operator of order three annihilates an E-function in the hypergeometric class, then the singularities of its Fourier transform are constrained to satisfy a symmetry property that generically does not hold. The proof relies on Andre ''s theory of E-operators and Katz's computation of the Galois group of hypergeometric d...
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作者：Bader, Uri; Fisher, David; Miller, Nicholas; Stover, Matthew
摘要：Let Gamma be a lattice in SO0(n, 1). We prove that if the associated locally symmetric space contains infinitely many maximal totally geodesic subspaces of dimension at least 2, then Gamma is arithmetic. This answers a question of Reid for hyperbolic n-manifolds and, independently, McMullen for hyperbolic 3-manifolds. We prove these results by proving a superrigidity theorem for certain representations of such lattices. The proof of our superrigidity theorem uses results on equidistribution fr...
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作者：Zhang, W.
摘要：We study a partially linearized version of the relative trace formula for the arithmetic Gan-Gross-Prasad conjecture for the unitary group U(V). The linear factor in this relative trace formula provides an SL2-symmetry which allows us to prove by induction the arithmetic fundamental lemma over Q(p) when p is odd and p >= dim V.
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作者：Birkar, Caucher
摘要：We study log canonical thresholds (also called global log canonical threshold or alpha-invariant) of R-linear systems. We prove existence of positive lower bounds in different settings, in particular, proving a conjecture of Ambro. We then show that the Borisov-Alexeev-Borisov conjecture holds; that is, given a natural number d and a positive real number epsilon, the set of Fano varieties of dimension d with epsilon-log canonical singularities forms a bounded family. This implies that biration...
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作者：Harvey, David; van der Hoeven, Joris
摘要：We present an algorithm that computes the product of two n-bit integers in O (n log n) bit operations, thus confirming a conjecture of Schonhage and Strassen from 1971. Our complexity analysis takes place in the multitape Turing machine model, with integers encoded in the usual binary representation. Central to the new algorithm is a novel Gaussian resampling technique that enables us to reduce the integer multiplication problem to a collection of multidimensional discrete Fourier transforms o...
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作者：Beuzart-Plessis, Raphael; Liu, Yifeng; Zhang, Wei; Zhu, Xinwen
摘要：We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet-Rallis relative trace formula, we complete the proof of the global Gan-Gross-Prasad conjecture and its refinement Ichino-Ikeda conjecture for U(n) x U(n + 1) in the stable case.
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作者：Oh, Sung-Jin; Tataru, Daniel
摘要：This article represents the fourth and final part of a four-paper sequence whose aim is to prove the Threshold Conjecture as well as the more general Dichotomy Theorem for the energy critical 4 + 1-dimensional hyperbolic Yang Mills equation. The Threshold Theorem asserts that topologically trivial solutions with energy below twice the ground state energy are global and scatter. The Dichotomy Theorem applies to solutions in arbitrary topological class with large energy, and provides two exclusi...
