{"title":"Generalized Ricci Flow","authors":"M. Garcia‐Fernandez, J. Streets","doi":"10.1090/ulect/076","DOIUrl":"https://doi.org/10.1090/ulect/076","url":null,"abstract":"This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and K\"ahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as `canonical metrics' in generalized Riemannian and complex geometry. The generalized Ricci flow is introduced as a tool for constructing such metrics, and extensions of the fundamental Hamilton/Perelman regularity theory of Ricci flow are proved. These results are refined in the setting of generalized complex geometry, where the generalized Ricci flow is shown to preserve various integrability conditions, taking the form of pluriclosed flow and generalized K\"ahler-Ricci flow. This leads to global convergence results, and applications to complex geometry. A purely mathematical introduction to the physical idea of T-duality is given, and a discussion of its relationship to generalized Ricci flow.","PeriodicalId":210073,"journal":{"name":"University Lecture Series","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127209014","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}
{"title":"Quantum Field Theory: Batalin–Vilkovisky\u0000 Formalism and Its Applications","authors":"P. Mnev","doi":"10.1090/ulect/072","DOIUrl":"https://doi.org/10.1090/ulect/072","url":null,"abstract":"","PeriodicalId":210073,"journal":{"name":"University Lecture Series","volume":"145 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124660405","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}
L. Beresford, Jesse Liu, L. Harland–Lang, V. Khoze
{"title":"Feynman diagrams","authors":"L. Beresford, Jesse Liu, L. Harland–Lang, V. Khoze","doi":"10.1090/ulect/072/03","DOIUrl":"https://doi.org/10.1090/ulect/072/03","url":null,"abstract":"Precision measurements of electromagnetic couplings are fundamental tests of quantum electrodynamics (QED) and powerful probes of new physics beyond the Standard Model (BSM). The electron anomalous magnetic moment ae = 1 2 (ge 2) is among the most precisely measured observables in nature [1, 2]. The muon counterpart aμ is measured to 1 part in 107 [3] and reports a longstanding 3 4 deviation from the SM prediction, which may be a harbinger of new physics.","PeriodicalId":210073,"journal":{"name":"University Lecture Series","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116516716","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}
{"title":"Topological Persistence in Geometry and\u0000 Analysis","authors":"L. Polterovich, D. Rosen, K. Samvelyan, Jun Zhang","doi":"10.1090/ULECT/074","DOIUrl":"https://doi.org/10.1090/ULECT/074","url":null,"abstract":"The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions with geometry and analysis. In particular, we present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, we discuss topological function theory which provides a new insight on oscillation of functions. The material should be accessible to readers with a basic background in algebraic and differential topology.","PeriodicalId":210073,"journal":{"name":"University Lecture Series","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130371471","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}
{"title":"Introduction to Analysis on Graphs","authors":"A. Grigor’yan","doi":"10.1090/ULECT/071","DOIUrl":"https://doi.org/10.1090/ULECT/071","url":null,"abstract":"","PeriodicalId":210073,"journal":{"name":"University Lecture Series","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121824495","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}
J. Hough, Manjunath Krishnapur, Y. Peres, B. Virág
{"title":"Zeros of Gaussian Analytic Functions and Determinantal Point Processes","authors":"J. Hough, Manjunath Krishnapur, Y. Peres, B. Virág","doi":"10.1090/ULECT/051","DOIUrl":"https://doi.org/10.1090/ULECT/051","url":null,"abstract":"The book examines in some depth two important classes of point processes, determinantal processes and 'Gaussian zeros', i.e., zeros of random analytic functions with Gaussian coefficients. These processes share a property of 'point-repulsion', where distinct points are less likely to fall close to each other than in processes, such as the Poisson process, that arise from independent sampling. Nevertheless, the treatment in the book emphasizes the use of independence: for random power series, the independence of coefficients is key; for determinantal processes, the number of points in a domain is a sum of independent indicators, and this yields a satisfying explanation of the central limit theorem (CLT) for this point count. Another unifying theme of the book is invariance of considered point processes under natural transformation groups. The book strives for balance between general theory and concrete examples. On the one hand, it presents a primer on modern techniques on the interface of probability and analysis. On the other hand, a wealth of determinantal processes of intrinsic interest are analyzed; these arise from random spanning trees and eigenvalues of random matrices, as well as from special power series with determinantal zeros. The material in the book formed the basis of a graduate course given at the IAS-Park City Summer School in 2007; the only background knowledge assumed can be acquired in first-year graduate courses in analysis and probability.","PeriodicalId":210073,"journal":{"name":"University Lecture Series","volume":"2 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128691672","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
