Project MUSE®: American Journal of Mathematics - Latest Articles
https://muse.jhu.edu/journals/american_journal_of_mathematics
Project MUSE®: Latest articles in American Journal of Mathematics.daily12015-07-07T04:00:29-05:00text/htmlen-USThe Johns Hopkins University PressVol. 118 (1996) through current issueLatest Articles: American Journal of MathematicsMathematicsTWOProject MUSE®American Journal of Mathematics1080-63770002-9327Latest articles in American Journal of Mathematics. Feed provided by Project MUSE®Semiclassical completely integrable systems: long-time dynamics and observability via two-microlocal Wigner measures
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.anantharaman.html
<p>By Nalini Anantharaman, Clotilde Fermanian-Kammerer, Fabricio MaciĆ </p>
We look at the long-time behavior of solutions to a semi-classical Schr\"odinger equation on the torus. We consider time scales which go to infinity when the semi-classical parameter goes to zero and we associate with each time-scale the set of semi-classical measures associated with all possible choices of initial data. On each classical invariant torus, the structure of semi-classical measures is described in terms of two-microlocal measures, obeying explicit propagation laws. We apply this construction in two directions. We first analyze the regularity of semi-classical measures, and we emphasize the existence of a threshold: for time-scales below this threshold, the set of semi-classical measures contains ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.anantharaman.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgSemiclassical completely integrable systems: long-time dynamics and observability via two-microlocal Wigner measures2015-05-28text/htmlen-USThe Johns Hopkins University PressSemiclassical completely integrable systems: long-time dynamics and observability via two-microlocal Wigner measures2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28Complex multiplication cycles and Kudla-Rapoport divisors, II
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.howard.html
<p>By Benjamin Howard</p>
This paper is about the arithmetic of {\it Kudla-Rapoport divisors} on Shimura varieties of type ${\rm GU}(n-1,1)$. In the first part of the paper we construct a toroidal compactification of N.~Kr\"amer's integral model of the Shimura variety. This extends work of K.-W.~Lan, who constructed a compactification at unramified primes. In the second, and main, part of the paper we use ideas of Kudla to construct Green functions for the Kudla-Rapoport divisors on the open Shimura variety, and analyze the behavior of these functions near the boundary of the compactification. The Green functions turn out to have logarithmic singularities along certain components of the boundary, up to log-log error terms. Thus, by ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.howard.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgComplex multiplication cycles and Kudla-Rapoport divisors, II2015-05-28text/htmlen-USThe Johns Hopkins University PressComplex multiplication cycles and Kudla-Rapoport divisors, II2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28Integrals of ψ-classes over double ramification cycles
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.buryak.html
<p>By A. Buryak, S. Shadrin, L. Spitz, D. Zvonkine</p>
A double ramification cycle, or DR-cycle, is a codimension $g$ cycle in the moduli space $\overline{\scr{M}}_{g,n}$ of stable curves. Roughly speaking, given a list of integers $(a_1,\ldots,a_n)$, the DR-cycle ${\rm DR}_g(a_1,\ldots,a_n) \subset\overline{\scr{M}}_{g,n}$ is the locus of curves $(C,x_1,\ldots,x_n)$ such that the divisor $\sum a_ix_i$ is principal. We compute the intersection numbers of DR-cycles with all monomials in ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.buryak.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgIntegrals of ψ-classes over double ramification cycles2015-05-28text/htmlen-USThe Johns Hopkins University PressIntegrals of ψ-classes over double ramification cycles2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28Counting rank two local systems with at most one, unipotent, monodromy
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.flicker.html
<p>By Yuval Z. Flicker</p>
The number of rank two $\overline{\Bbb{Q}}_\ell$-local systems, or $\overline{\Bbb{Q}}_\ell$-smooth sheaves, on $(X-\{u\})\otimes_{\Bbb{F}_q}\Bbb{F}$, where $X$ is a smooth projective absolutely irreducible curve over $\Bbb{F}_q$, $\Bbb{F}$ an algebraic closure of $\Bbb{F}_q$ and $u$ is a closed point of $X$, with principal unipotent monodromy at $u$, and fixed by ${\rm Gal}(\Bbb{F}/\Bbb{F}_q)$, is computed. It is expressed as the trace of the Frobenius on the virtual $\overline{\Bbb{Q}}_\ell$-smooth sheaf found in the author's work with Deligne on the moduli stack of curves with \'etale divisors of degree $M\ge 1$. This completes the work with Deligne in rank two. This number is the same as that of ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.flicker.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgCounting rank two local systems with at most one, unipotent, monodromy2015-05-28text/htmlen-USThe Johns Hopkins University PressCounting rank two local systems with at most one, unipotent, monodromyDifferential equations2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28On the Coble quartic
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.grushevsky.html
<p>By Samuel Grushevsky, Riccardo Salvati Manni</p>
We obtain a short explicit expression for the universal Coble quartic whose partial derivatives give the defining equations for the universal family of Kummer threefolds. The Coble quartic was recently determined completely in Ren, Sam, Schrader, and Sturmfels, where (Theorem 7.1a) it was computed explicitly, as a polynomial with 372060 monomials of bidegree $(28,4)$ in theta constants of the second order and theta functions of the second order, respectively. Our expression is in terms of products of theta constants with characteristics corresponding to G\"opel systems, and is a polynomial with 134 terms. Our approach is based on the beautiful geometry studied by Coble and further investigated by Dolgachev and ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.grushevsky.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgOn the Coble quartic2015-05-28text/htmlen-USThe Johns Hopkins University PressOn the Coble quartic2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28The circle method and bounds for L-functions---II: Subconvexity for twists of GL(3) L-functions
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.munshi.html
<p>By Ritabrata Munshi</p>
Let $\pi$ be a ${\rm SL}(3,\Bbb{Z})$ Hecke-Maass cusp form. Let $\chi=\chi_1\chi_2$ be a Dirichlet character with $\chi_i$ primitive modulo $M_i$. Suppose $M_1$, $M_2$ are primes such that $\sqrt{M_2}M^{4\delta}<M_1<M_2M^{-3\delta}$, where $M=M_1M_2$ and $0<\delta<1/28$. In this paper we will prove the following subconvex bound $$ L\left({1\over 2},\pi\otimes\chi\right)\ll_{\pi,\varepsilon} M^{{3\over 4}-\delta+\varepsilon}. ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.munshi.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgThe circle method and bounds for L-functions---II: Subconvexity for twists of GL(3) L-functions2015-05-28text/htmlen-USThe Johns Hopkins University PressThe circle method and bounds for L-functions---II: Subconvexity for twists of GL(3) L-functions2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28Stable categories of Cohen-Macaulay modules and cluster categories Dedicated to Ragnar-Olaf Buchweitz on the occasion of his sixtieth birthday
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.amiot.html
<p>By Claire Amiot, Osamu Iyama, Idun Reiten</p>
By Auslander's algebraic McKay correspondence, the stable category of Cohen-Macaulay modules over a simple singularity is triangle equivalent to the $1$-cluster category of the path algebra of a Dynkin quiver (i.e., the orbit category of the derived category by the action of the Auslander-Reiten translation). In this paper we give a systematic method to construct a similar type of triangle equivalence between the stable category of Cohen-Macaulay modules over a Gorenstein isolated singularity $R$ and the generalized (higher) cluster category of a finite dimensional algebra $\Lambda$. The key role is played by a bimodule Calabi-Yau algebra, which is the higher Auslander algebra of $R$ as well as the higher ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.amiot.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgStable categories of Cohen-Macaulay modules and cluster categories Dedicated to Ragnar-Olaf Buchweitz on the occasion of his sixtieth birthday2015-05-28text/htmlen-USThe Johns Hopkins University PressStable categories of Cohen-Macaulay modules and cluster categories Dedicated to Ragnar-Olaf Buchweitz on the occasion of his sixtieth birthday2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28The Tate Conjecture for a family of surfaces of general type with pg = q = 1 and K2 = 3
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lyons.html
<p>By Christopher Lyons</p>
We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants pg = q = 1 and K2 = 3, that has been introduced by Catanese and Ciliberto. This is accomplished via a careful study of degenerations. As corollaries, when a surface in this family is defined over a finitely generated extension of ℚ, we verify the semisimplicity and Tate conjectures for the Galois representation on the middle ℓ-adic cohomology of the ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lyons.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgThe Tate Conjecture for a family of surfaces of general type with pg = q = 1 and K2 = 32015-04-13text/htmlen-USThe Johns Hopkins University PressThe Tate Conjecture for a family of surfaces of general type with pg = q = 1 and K2 = 32015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13On the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lie.html
<p>By Victor Lie</p>
We are proving L2(ℝ) × L2(ℝ) → L1(ℝ) bounds for the bilinear Hilbert transform HΓ along curves Γ = (t,−γ(t)) with γ being a smooth “non-flat” curve near zero and ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lie.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgOn the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves2015-04-13text/htmlen-USThe Johns Hopkins University PressOn the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13Confluent A-hypergeometric functions and rapid decay homology cycles
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.esterov.html
<p>By Alexander Esterov, Kiyoshi Takeuchi</p>
We study confluent A-hypergeometric functions introduced by Adolphson. In particular, we give their integral representations by using rapid decay homology cycles of Hien. The method of toric compactifications introduced in our previous works will be used to prove our main theorem. Moreover we apply it to obtain a formula for the asymptotic expansions at infinity of confluent A-hypergeometric ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.esterov.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-07-07T04:00:29-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgConfluent A-hypergeometric functions and rapid decay homology cycles2015-04-13text/htmlen-USThe Johns Hopkins University PressConfluent A-hypergeometric functions and rapid decay homology cycles2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13