Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques最新文献

{"title":"Vertices of the Harder and Narasimhan polygons and the laws of large numbers","authors":"Nathan Grieve","doi":"10.4153/S000843952200039X","DOIUrl":"https://doi.org/10.4153/S000843952200039X","url":null,"abstract":"Abstract We build on the recent techniques of Codogni and Patakfalvi (2021, Inventiones Mathematicae 223, 811–894), which were used to establish theorems about semi-positivity of the Chow Mumford line bundles for families of \u0000$mathrm {K}$\u0000 -semistable Fano varieties. Here, we apply the Central Limit Theorem to ascertain the asymptotic probabilistic nature of the vertices of the Harder and Narasimhan polygons. As an application of our main result, we use it to establish a filtered vector space analogue of the main technical result of Codogni and Patakfalvi (2021, Inventiones Mathematicae 223, 811–894). In doing so, we expand upon the slope stability theory, for filtered vector spaces, that was initiated by Faltings and Wüstholz (1994, Inventiones Mathematicae 116, 109–138). One source of inspiration for our abstract study of Harder and Narasimhan data, which is a concept that we define here, is the lattice reduction methods of Grayson (1984, Commentarii Mathematici Helvetic 59, 600–634). Another is the work of Faltings and Wüstholz (1994, Inventiones Mathematicae 116, 109–138), and Evertse and Ferretti (2013, Annals of Mathematics 177, 513–590), which is within the context of Diophantine approximation for projective varieties.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"66 1","pages":"340 - 357"},"PeriodicalIF":0.6,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45132044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Arithmetically equivalent fields in a Galois extension with Frobenius Galois group of 2-power degree","authors":"Masanari Kida","doi":"10.4153/S0008439522000388","DOIUrl":"https://doi.org/10.4153/S0008439522000388","url":null,"abstract":"Abstract Let \u0000$F_{2^n}$\u0000 be the Frobenius group of degree \u0000$2^n$\u0000 and of order \u0000$2^n ( 2^n-1)$\u0000 with \u0000$n ge 4$\u0000 . We show that if \u0000$K/mathbb {Q} $\u0000 is a Galois extension whose Galois group is isomorphic to \u0000$F_{2^n}$\u0000 , then there are \u0000$dfrac {2^{n-1} +(-1)^n }{3}$\u0000 intermediate fields of \u0000$K/mathbb {Q} $\u0000 of degree \u0000$4 (2^n-1)$\u0000 such that they are not conjugate over \u0000$mathbb {Q}$\u0000 but arithmetically equivalent over \u0000$mathbb {Q}$\u0000 . We also give an explicit method to construct these arithmetically equivalent fields.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"66 1","pages":"380 - 394"},"PeriodicalIF":0.6,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44014000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Magnitude and Holmes–Thompson intrinsic volumes of convex bodies","authors":"M. Meckes","doi":"10.4153/S0008439522000728","DOIUrl":"https://doi.org/10.4153/S0008439522000728","url":null,"abstract":"Abstract Magnitude is a numerical invariant of compact metric spaces, originally inspired by category theory and now known to be related to myriad other geometric quantities. Generalizing earlier results in \u0000$ell _1^n$\u0000 and Euclidean space, we prove an upper bound for the magnitude of a convex body in a hypermetric normed space in terms of its Holmes–Thompson intrinsic volumes. As applications of this bound, we give short new proofs of Mahler’s conjecture in the case of a zonoid and Sudakov’s minoration inequality.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"66 1","pages":"854 - 867"},"PeriodicalIF":0.6,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44958529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasisymmetric harmonics of the exterior algebra","authors":"N. Bergeron, K. Chan, F. Soltani, M. Zabrocki","doi":"10.4153/S0008439523000024","DOIUrl":"https://doi.org/10.4153/S0008439523000024","url":null,"abstract":"Abstract We study the ring of quasisymmetric polynomials in n anticommuting (fermionic) variables. Let \u0000$R_n$\u0000 denote the ring of polynomials in n anticommuting variables. The main results of this paper show the following interesting facts about quasisymmetric polynomials in anticommuting variables: (1) The quasisymmetric polynomials in \u0000$R_n$\u0000 form a commutative subalgebra of \u0000$R_n$\u0000 . (2) There is a basis of the quotient of \u0000$R_n$\u0000 by the ideal \u0000$I_n$\u0000 generated by the quasisymmetric polynomials in \u0000$R_n$\u0000 that is indexed by ballot sequences. The Hilbert series of the quotient is given by \u0000$$ begin{align*}text{Hilb}_{R_n/I_n}(q) = sum_{k=0}^{lfloor{n/2}rfloor} f^{(n-k,k)} q^k,,end{align*} $$\u0000 where \u0000$f^{(n-k,k)}$\u0000 is the number of standard tableaux of shape \u0000$(n-k,k)$\u0000 . (3) There is a basis of the ideal generated by quasisymmetric polynomials that is indexed by sequences that break the ballot condition.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"66 1","pages":"997 - 1013"},"PeriodicalIF":0.6,"publicationDate":"2022-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44232527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The error term in the truncated Perron formula for the logarithm of an -function","authors":"S. Garcia, J. Lagarias, Ethan S. Lee","doi":"10.4153/s0008439523000218","DOIUrl":"https://doi.org/10.4153/s0008439523000218","url":null,"abstract":"We improve upon the traditional error term in the truncated Perron formula for the logarithm of an $L$-function. All our constants are explicit.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45387011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Association of Fluid Volatility With Subretinal Hyperreflective Material and Ellipsoid Zone Integrity in Neovascular AMD.","authors":"Justis P Ehlers, Nikhil Patel, Peter K Kaiser, Jeffrey S Heier, David M Brown, Xiangyi Meng, Jamie Reese, Leina Lunasco, Thuy K Le, Ming Hu, Sunil K Srivastava","doi":"10.1167/iovs.63.6.17","DOIUrl":"10.1167/iovs.63.6.17","url":null,"abstract":"<p><strong>Purpose: </strong>To evaluate the association of fluid volatility with ellipsoid zone (EZ) integrity and subretinal hyperreflective material (SHRM) volume during anti-vascular endothelial growth factor (VEGF) therapy in neovascular age-related macular degeneration (nAMD).</p><p><strong>Methods: </strong>This study was a post hoc analysis of the OSPREY study. Retinal volatility was quantified as the standard deviation across weeks 12 to 56 for six optical coherence tomography (OCT) metrics: central subfield thickness (CST), total fluid (TF) volume, subretinal fluid (SRF) volume, intraretinal fluid (IRF) volume, macular total retinal fluid index (TRFI), and central macular TRFI. Eyes with volatility ≤ 25th or ≥ 75th percentile values were compared.</p><p><strong>Results: </strong>Eyes with low volatility in several exudative metrics showed greater change from baseline in SHRM volume at week 12 than eyes with high volatility. During the maintenance phase (weeks 12-56), eyes exhibiting high SRF volatility demonstrated increased SHRM volume compared to eyes with low SRF volatility (P = 0.027). Eyes exhibiting high volatility in CST, TF, and SRF demonstrated less improvement in EZ total attenuation (P < 0.001, P = 0.033, and P = 0.043, respectively) than eyes with low volatility. Early exudative instability (i.e., between weeks 4-8 or weeks 8-12) in multiple parameters (i.e., CST, TF, IRF, macular TRFI, or central macular TRFI) was associated with greater volatility during the maintenance phase (P < 0.05).</p><p><strong>Conclusions: </strong>Greater volatility in exudative OCT metrics, particularly SRF volatility, was associated with a greater increase in SHRM and less improvement in EZ integrity, suggesting that volatility is detrimental to multiple anatomic features in nAMD. Early exudative instability during the loading phase of treatment was associated with longer-term volatility in exudation.</p>","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"65 1","pages":"17"},"PeriodicalIF":5.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9206498/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80029691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BCM volume 65 issue 2 Cover and Front matter","authors":"June juin, J. Mashreghi, K. Bringmann, Alessandro Gambini, Remis Tonon","doi":"10.4153/s0008439522000303","DOIUrl":"https://doi.org/10.4153/s0008439522000303","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"65 1","pages":"f1 - f3"},"PeriodicalIF":0.6,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45469943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BCM volume 65 issue 2 Cover and Back matter","authors":"","doi":"10.4153/s0008439522000315","DOIUrl":"https://doi.org/10.4153/s0008439522000315","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":"b1 - b2"},"PeriodicalIF":0.6,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46878938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CONCORDANCE OF SPATIAL GRAPHS","authors":"Egor Lappo","doi":"10.4153/S000843952300019X","DOIUrl":"https://doi.org/10.4153/S000843952300019X","url":null,"abstract":"We define smooth notions of concordance and sliceness for spatial graphs. We prove that sliceness of a spatial graph is equivalent to a condition on a set of linking numbers together with sliceness of a link associated to the graph. This generalizes the result of Taniyama for $theta$-curves.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48785384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Zeros in the character tables of symmetric groups with an \u0000$ell $\u0000 -core index","authors":"Eleanor Mcspirit, K. Ono","doi":"10.4153/S0008439522000443","DOIUrl":"https://doi.org/10.4153/S0008439522000443","url":null,"abstract":"Abstract Let \u0000$mathcal {C}_n =left [chi _{lambda }(mu )right ]_{lambda , mu }$\u0000 be the character table for \u0000$S_n,$\u0000 where the indices \u0000$lambda $\u0000 and \u0000$mu $\u0000 run over the \u0000$p(n)$\u0000 many integer partitions of \u0000$n.$\u0000 In this note, we study \u0000$Z_{ell }(n),$\u0000 the number of zero entries \u0000$chi _{lambda }(mu )$\u0000 in \u0000$mathcal {C}_n,$\u0000 where \u0000$lambda $\u0000 is an \u0000$ell $\u0000 -core partition of \u0000$n.$\u0000 For every prime \u0000$ell geq 5,$\u0000 we prove an asymptotic formula of the form \u0000$$ begin{align*}Z_{ell}(n)sim alpha_{ell}cdot sigma_{ell}(n+delta_{ell})p(n)gg_{ell} n^{frac{ell-5}{2}}e^{pisqrt{2n/3}}, end{align*} $$\u0000 where \u0000$sigma _{ell }(n)$\u0000 is a twisted Legendre symbol divisor function, \u0000$delta _{ell }:=(ell ^2-1)/24,$\u0000 and \u0000$1/alpha _{ell }>0$\u0000 is a normalization of the Dirichlet L-value \u0000$Lleft (left ( frac {cdot }{ell } right ),frac {ell -1}{2}right ).$\u0000 For primes \u0000$ell $\u0000 and \u0000$n>ell ^6/24,$\u0000 we show that \u0000$chi _{lambda }(mu )=0$\u0000 whenever \u0000$lambda $\u0000 and \u0000$mu $\u0000 are both \u0000$ell $\u0000 -cores. Furthermore, if \u0000$Z^*_{ell }(n)$\u0000 is the number of zero entries indexed by two \u0000$ell $\u0000 -cores, then, for \u0000$ell geq 5$\u0000 , we obtain the asymptotic \u0000$$ begin{align*}Z^*_{ell}(n)sim alpha_{ell}^2 cdot sigma_{ell}( n+delta_{ell})^2 gg_{ell} n^{ell-3}. end{align*} $$","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"66 1","pages":"467 - 476"},"PeriodicalIF":0.6,"publicationDate":"2022-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48127336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}