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Conformal Killing forms in Kähler geometry 保角杀伤形式Kähler几何
IF 0.6
Illinois Journal of Mathematics Pub Date : 2020-03-20 DOI: 10.1215/00192082-10088173
P. Nagy, U. Semmelmann
{"title":"Conformal Killing forms in Kähler geometry","authors":"P. Nagy, U. Semmelmann","doi":"10.1215/00192082-10088173","DOIUrl":"https://doi.org/10.1215/00192082-10088173","url":null,"abstract":"For Kaehler manifolds we explicitly determine the solution to the conformal Killing form equation in middle degree. In particular, we complete the classification of conformal Killing forms on compact Kaehler manifolds. We give the first examples of conformal Killing forms on Kaehler manifolds not coming from Hamiltonian 2-forms. These are supported by Calabi type manifolds over a Kaehler Einstein base. In this set up we also give structure results and examples for the closely related class of Hermitian Killing forms.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45025509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On stability of the Erdős–Rademacher problem 关于Erdös–Rademacher问题的稳定性
IF 0.6
Illinois Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1215/00192082-10429321
J. Balogh, F. Clemen
{"title":"On stability of the Erdős–Rademacher problem","authors":"J. Balogh, F. Clemen","doi":"10.1215/00192082-10429321","DOIUrl":"https://doi.org/10.1215/00192082-10429321","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49294599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Subsets of rectifiable curves in Banach spaces I: Sharp exponents in traveling salesman theorems Banach空间I中可整流曲线的子集:旅行推销员定理中的锐指数
IF 0.6
Illinois Journal of Mathematics Pub Date : 2020-02-27 DOI: 10.1215/00192082-10592363
Matthew Badger, Sean McCurdy
{"title":"Subsets of rectifiable curves in Banach spaces I: Sharp exponents in traveling salesman theorems","authors":"Matthew Badger, Sean McCurdy","doi":"10.1215/00192082-10592363","DOIUrl":"https://doi.org/10.1215/00192082-10592363","url":null,"abstract":"The Analyst's Traveling Salesman Problem is to find a characterization of subsets of rectifiable curves in a metric space. This problem was introduced and solved in the plane by Jones in 1990 and subsequently solved in higher-dimensional Euclidean spaces by Okikiolu in 1992 and in the infinite-dimensional Hilbert space $ell_2$ by Schul in 2007. In this paper, we establish sharp extensions of Schul's necessary and sufficient conditions for a bounded set $Esubsetell_p$ to be contained in a rectifiable curve from $p=2$ to $1<p<infty$. While the necessary and sufficient conditions coincide when $p=2$, we demonstrate that there is a strict gap between the necessary condition and sufficient condition when $pneq 2$. We also identify and correct technical errors in the proof by Schul. This investigation is partly motivated by recent work of Edelen, Naber, and Valtorta on Reifenberg-type theorems in Banach spaces and complements work of Hahlomaa and recent work of David and Schul on the Analyst's TSP in general metric spaces.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41565970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Phi, primorials, and Poisson ，原始函数和泊松函数
IF 0.6
Illinois Journal of Mathematics Pub Date : 2020-01-18 DOI: 10.1215/00192082-8591576
P. Pollack, C. Pomerance
{"title":"Phi, primorials, and Poisson","authors":"P. Pollack, C. Pomerance","doi":"10.1215/00192082-8591576","DOIUrl":"https://doi.org/10.1215/00192082-8591576","url":null,"abstract":"The primorial $p#$ of a prime $p$ is the product of all primes $qle p$. Let pr$(n)$ denote the largest prime $p$ with $p# mid phi(n)$, where $phi$ is Euler's totient function. We show that the normal order of pr$(n)$ is $loglog n/logloglog n$. That is, pr$(n) sim loglog n/logloglog n$ as $ntoinfty$ on a set of integers of asymptotic density 1. In fact we show there is an asymptotic secondary term and, on a tertiary level, there is an asymptotic Poisson distribution. We also show an analogous result for the largest integer $k$ with $k!mid phi(n)$.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46393296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Baum–Connes and the Fourier–Mukai transform Baum-Connes和Fourier-Mukai变换
IF 0.6
Illinois Journal of Mathematics Pub Date : 2020-01-17 DOI: 10.1215/00192082-9725548
Heath Emerson, Dan Hudson
{"title":"Baum–Connes and the Fourier–Mukai transform","authors":"Heath Emerson, Dan Hudson","doi":"10.1215/00192082-9725548","DOIUrl":"https://doi.org/10.1215/00192082-9725548","url":null,"abstract":"The Baum-Connes map for finitely generated free abelian groups is a K-theoretic analogue of the Fourier-Mukai transform from algebraic geometry. We describe this K-theoretic transform in the language of topological correspondences, and compute its action on K-theory (of tori) described geometrically in terms of Baum-Douglas cocycles, showing that the Fourier-Mukai transform maps the class of a subtorus to the class of a suitably defined dual torus. We deduce the Fourier-Mukai inversion formula. We use these results to give a purely geometric description of the Baum-Connes assembly map for free abelian groups.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44867343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Decoding pluripotency: Genetic screens to interrogate the acquisition, maintenance, and exit of pluripotency. 解码多能性：通过基因筛选来探究多能性的获得、维持和退出。
IF 7.9
Illinois Journal of Mathematics Pub Date : 2020-01-01 Epub Date: 2019-08-13 DOI: 10.1002/wsbm.1464
Qing V Li, Bess P Rosen, Danwei Huangfu
{"title":"Decoding pluripotency: Genetic screens to interrogate the acquisition, maintenance, and exit of pluripotency.","authors":"Qing V Li, Bess P Rosen, Danwei Huangfu","doi":"10.1002/wsbm.1464","DOIUrl":"10.1002/wsbm.1464","url":null,"abstract":"<p><p>Pluripotent stem cells have the ability to unlimitedly self-renew and differentiate to any somatic cell lineage. A number of systems biology approaches have been used to define this pluripotent state. Complementary to systems level characterization, genetic screens offer a unique avenue to functionally interrogate the pluripotent state and identify the key players in pluripotency acquisition and maintenance, exit of pluripotency, and lineage differentiation. Here we review how genetic screens have helped us decode pluripotency regulation. We will summarize results from RNA interference (RNAi) based screens, discuss recent advances in CRISPR/Cas-based genetic perturbation methods, and how these advances have made it possible to more comprehensively interrogate pluripotency and differentiation through genetic screens. Such investigations will not only provide a better understanding of this unique developmental state, but may enhance our ability to use pluripotent stem cells as an experimental model to study human development and disease progression. Functional interrogation of pluripotency also provides a valuable roadmap for utilizing genetic perturbation to gain systems level understanding of additional cellular states, from later stages of development to pathological disease states. This article is categorized under: Developmental Biology > Stem Cell Biology and Regeneration Developmental Biology > Developmental Processes in Health and Disease Biological Mechanisms > Cell Fates.</p>","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"55 1","pages":"e1464"},"PeriodicalIF":7.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6898739/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88172083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simple factor dressings and Bianchi–Bäcklund transformations 简单因子敷料和Bianchi–Bäcklund变换
IF 0.6
Illinois Journal of Mathematics Pub Date : 2019-12-01 DOI: 10.1215/00192082-7988989
Joseph Cho, Yuta Ogata
{"title":"Simple factor dressings and Bianchi–Bäcklund transformations","authors":"Joseph Cho, Yuta Ogata","doi":"10.1215/00192082-7988989","DOIUrl":"https://doi.org/10.1215/00192082-7988989","url":null,"abstract":"In this paper, we directly show the known equivalence of simple factor dressings of extended frames and the classical Bianchi–Backlund transformations for constant mean curvature surfaces. In doing so, we show how the parameters of classical Bianchi–Backlund transformations can be incorporated into the simple factor dressings method.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44208032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The zero sets of ℓAp are nested l_ap的零集是嵌套的
IF 0.6
Illinois Journal of Mathematics Pub Date : 2019-12-01 DOI: 10.1215/00192082-7937310
R. Cheng
{"title":"The zero sets of ℓAp are nested","authors":"R. Cheng","doi":"10.1215/00192082-7937310","DOIUrl":"https://doi.org/10.1215/00192082-7937310","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"63 1","pages":"601-618"},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46808485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Hausdorff measures, dyadic approximations, and the Dobiński set 豪斯多夫测度，二进逼近和Dobiński集
IF 0.6
Illinois Journal of Mathematics Pub Date : 2019-11-14 DOI: 10.1215/00192082-9082098
Alberto Dayan, Jos'e L. Fern'andez, Mar'ia J. Gonz'alez
{"title":"Hausdorff measures, dyadic approximations, and the Dobiński set","authors":"Alberto Dayan, Jos'e L. Fern'andez, Mar'ia J. Gonz'alez","doi":"10.1215/00192082-9082098","DOIUrl":"https://doi.org/10.1215/00192082-9082098","url":null,"abstract":"Dobinski set $mathcal{D}$ is an exceptional set for a certain infinite product identity, whose points are characterized as having exceedingly good approximations by dyadic rationals. We study the Hausdorff dimension and logarithmic measure of $mathcal{D}$ by means of the Mass Transference Principle and by the construction of certain appropriate Cantor-like sets, termed willow sets, contained in $mathcal{D}$.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44191373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Space curves on surfaces with ordinary singularities 具有普通奇异点的曲面上的空间曲线
IF 0.6
Illinois Journal of Mathematics Pub Date : 2019-10-18 DOI: 10.1215/00192082-9753971
Mengyuan Zhang
{"title":"Space curves on surfaces with ordinary singularities","authors":"Mengyuan Zhang","doi":"10.1215/00192082-9753971","DOIUrl":"https://doi.org/10.1215/00192082-9753971","url":null,"abstract":"We show that smooth curves in the same biliaison class on a hypersurface in $mathbf{P}^3$ with ordinary singularities are linearly equivalent. We compute the invariants $h^0(mathscr{I}_C(d))$, $h^1(mathscr{I}_C(d))$ and $h^1(mathscr{O}_C(d))$ of a curve $C$ on such a surface $X$ in terms of the cohomologies of divisors on the normalization of $X$. We then study general projections in $mathbf{P}^3$ of curves lying on the rational normal scroll $S(a,b)subsetmathbf{P}^{a+b+1}$. If we vary the curves in a linear system on $S(a,b)$ as well as the projections, we obtain a family of curves in $mathbf{P}^3$. We compute the dimension of the space of deformations of these curves in $mathbf{P}^3$ as well as the dimension of the family. We show that the difference is a linear function in $a$ and $b$ which does not depend on the linear system. Finally, we classify maximal rank curves on ruled cubic surfaces in $mathbf{P}^3$. We prove that the general projections of all but finitely many classes of projectively normal curves on $S(1,2)subsetmathbf{P}^4$ fail to have maximal rank in $mathbf{P}^3$. These give infinitely many classes of counter-examples to a question of Hartshorne.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46067879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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