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作者：Wendl, Chris
摘要：We develop new techniques to study regularity questions for moduli spaces of pseudoholomorphic curves that are multiply covered. Among the main results, we show that unbranched multiple covers of closed holomor-phic curves are generically regular, and simple index 0 curves in dimen-sions greater than four are generically super-rigid, implying, e.g., that the Gromov-Witten invariants of Calabi-Yau 3-folds reduce to sums of local in-variants for finite sets of embedded curves. We also establish ...
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作者：Chifan, Ionut; Ioana, Adrian; Osin, Denis; Sun, Bin
摘要：We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have Kazhdan's property (T). In this paper, we prove that any group G in a natural family of wreath-like products with property (T) is W*-superrigid: the group von Neumann algebra L(G) remembers the isomorphism class of G. This allows us to ...
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作者：Matomaeki, Kaisa; Radziwill, Maksym; Tao, Terence; Teraevaeinen, Joni; Ziegler, Tamar
摘要：Let lambda denote the Liouville function. We show that, as X-+ oo,2X Zsup X P(Y)ER[Y] degP 0 < theta < 1 fiixed but arbitrarily small. Previously this was only established for k < 1. We obtain this result as a special case of the corresponding statement for (non-pretentious) 1 -bounded multiplicative functions that we prove.In fact, we are able to replace the polynomial phases e(-P (n)) by degree k nilsequences F(g(n)Gamma). By the inverse theory for the Gowers norms this implies the higher or...
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作者：Yuan, Xinyi; Zhang, Shou-Wu
摘要：We will fix an error in our paper on the average Colmez conjecture by proving a slightly weaker statement than Theorem 2.7, which is sufficient for application to the main results.
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作者：Browning, Tim; Le Boudec, Pierre; Sawin, Will
摘要：It is known that the Brauer-Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general con-jecture of Colliot-The ' le`ne that the Brauer-Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hy-persurfaces of fixed degree and dimension by height, we p...
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作者：Song, Antoine
摘要：Using min-max theory, we show that in any closed Riemannian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds on the methods developed by F. C. Marques and A. Neves.
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作者：Dasgupta, Samit; Kakde, Mahesh
摘要：Let H/F be a finite abelian extension of number fields with F totally real and H a CM field. Let S and T be disjoint finite sets of places of F satisfying the standard conditions. The Brumer-Stark conjecture states that the Stickelberger element Theta H/F S,T annihilates the T-smoothed class group ClT (H). We prove this conjecture away from p = 2, that is, after tensoring with Z[1/2]. We prove a stronger version of this result conjectured by Kurihara that gives a formula for the 0th Fitting id...
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作者：Simon, Leon
摘要：With respect to a C infinity metric which is close to the standard Euclidean metric on RN+1+e, where N > 7 and $ > 1 are given, we construct a class of embedded (N + )-dimensional pound hypersurfaces (without boundary) which are minimal and strictly stable, and which have singular set equal to an arbitrary preassigned closed subset K C {0} x Re. Thus the question is settled, with a strong affirmative, as to whether there can be gaps or even fractional dimensional parts in the singular set. Suc...
