Pub Date : 2020-01-29DOI: 10.1007/s11537-019-1566-3
J. Demailly
{"title":"Recent results on the Kobayashi and Green-Griffiths-Lang conjectures","authors":"J. Demailly","doi":"10.1007/s11537-019-1566-3","DOIUrl":"https://doi.org/10.1007/s11537-019-1566-3","url":null,"abstract":"","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11537-019-1566-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53190012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-18DOI: 10.1007/s11537-019-1650-8
Bảo Châu Ngô
This is a survey on recent works of Langlands’s work on functoriality conjectures and related works including the works of Braverman and Kazhdan on the functional equation of automorphic L-functions. Efforts have been made to carry out in complete generality the construction of the L-monoid, and certain a kernel which is, we believe, related to the elusive Hankel kernel.
{"title":"Hankel transform, Langlands functoriality and functional equation of automorphic L -functions","authors":"Bảo Châu Ngô","doi":"10.1007/s11537-019-1650-8","DOIUrl":"https://doi.org/10.1007/s11537-019-1650-8","url":null,"abstract":"This is a survey on recent works of Langlands’s work on functoriality conjectures and related works including the works of Braverman and Kazhdan on the functional equation of automorphic <i>L</i>-functions. Efforts have been made to carry out in complete generality the construction of the <i>L</i>-monoid, and certain a kernel which is, we believe, related to the elusive Hankel kernel.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-28DOI: 10.1007/s11537-019-1912-5
M. Nazarov
{"title":"Double Yangian and the universal R-matrix","authors":"M. Nazarov","doi":"10.1007/s11537-019-1912-5","DOIUrl":"https://doi.org/10.1007/s11537-019-1912-5","url":null,"abstract":"","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11537-019-1912-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53190597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-21DOI: 10.1007/s11537-019-1837-z
James Maynard
The Twin Prime Conjecture asserts that there should be infinitely many pairs of primes which differ by 2. Unfortunately this long-standing conjecture remains open, but recently there has been several dramatic developments making partial progress. We survey the key ideas behind proofs of bounded gaps between primes (due to Zhang, Tao and the author) and developments on Chowla's conjecture (due to Matomäki, Radziwiłł and Tao).
{"title":"The twin prime conjecture","authors":"James Maynard","doi":"10.1007/s11537-019-1837-z","DOIUrl":"https://doi.org/10.1007/s11537-019-1837-z","url":null,"abstract":"The Twin Prime Conjecture asserts that there should be infinitely many pairs of primes which differ by 2. Unfortunately this long-standing conjecture remains open, but recently there has been several dramatic developments making partial progress. We survey the key ideas behind proofs of bounded gaps between primes (due to Zhang, Tao and the author) and developments on Chowla's conjecture (due to Matomäki, Radziwiłł and Tao).","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-21DOI: 10.1007/s11537-019-1839-x
F. C. Marques
{"title":"Abundance of minimal surfaces","authors":"F. C. Marques","doi":"10.1007/s11537-019-1839-x","DOIUrl":"https://doi.org/10.1007/s11537-019-1839-x","url":null,"abstract":"","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11537-019-1839-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48071123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-21DOI: 10.1007/s11537-019-1825-3
B. Bakalov, Alberto De Sole, Reimundo Heluani, V. Kac
{"title":"An operadic approach to vertex algebra and Poisson vertex algebra cohomology","authors":"B. Bakalov, Alberto De Sole, Reimundo Heluani, V. Kac","doi":"10.1007/s11537-019-1825-3","DOIUrl":"https://doi.org/10.1007/s11537-019-1825-3","url":null,"abstract":"","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11537-019-1825-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53190082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-30DOI: 10.1007/s11537-019-1840-4
Y. André
{"title":"Singularities in mixed characteristic. The perfectoid approach","authors":"Y. André","doi":"10.1007/s11537-019-1840-4","DOIUrl":"https://doi.org/10.1007/s11537-019-1840-4","url":null,"abstract":"","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11537-019-1840-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53190183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-03-05DOI: 10.1007/s11537-018-1727-9
Mark Braverman
This paper is a lecture note accompanying the 19th Takagi Lectures lectures in July 2017 at Kyoto University.We give a high-level overview of information complexity theory and its connections to communication complexity.We then discuss some fundamental properties of information complexity, and applications to direct sum theorems and to exact communication bounds. We conclude with some open questions and directions.
{"title":"Information complexity and applications","authors":"Mark Braverman","doi":"10.1007/s11537-018-1727-9","DOIUrl":"https://doi.org/10.1007/s11537-018-1727-9","url":null,"abstract":"This paper is a lecture note accompanying the 19th Takagi Lectures lectures in July 2017 at Kyoto University.We give a high-level overview of information complexity theory and its connections to communication complexity.We then discuss some fundamental properties of information complexity, and applications to direct sum theorems and to exact communication bounds. We conclude with some open questions and directions.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-02-18DOI: 10.1007/s11537-018-1744-8
Andrei Okounkov
These are introductory notes on Donaldson–Thomas counts of curves in threefolds and their connections with other branches of mathematics and mathematical physics. They are based on my 2018 Takagi Lectures at The University of Tokyo.
{"title":"Takagi Lectures on Donaldson–Thomas theory","authors":"Andrei Okounkov","doi":"10.1007/s11537-018-1744-8","DOIUrl":"https://doi.org/10.1007/s11537-018-1744-8","url":null,"abstract":"These are introductory notes on Donaldson–Thomas counts of curves in threefolds and their connections with other branches of mathematics and mathematical physics. They are based on my 2018 Takagi Lectures at The University of Tokyo.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-28DOI: 10.1007/s11537-018-1726-x
Hugo Duminil-Copin
This text describes the content of the Takagi Lectures given by the author in Kyoto in 2017. The lectures present some aspects of the theory of sharp thresholds for Boolean functions and its application to the study of phase transitions in statistical physics.
{"title":"Sharp threshold phenomena in statistical physics","authors":"Hugo Duminil-Copin","doi":"10.1007/s11537-018-1726-x","DOIUrl":"https://doi.org/10.1007/s11537-018-1726-x","url":null,"abstract":"This text describes the content of the Takagi Lectures given by the author in Kyoto in 2017. The lectures present some aspects of the theory of sharp thresholds for Boolean functions and its application to the study of phase transitions in statistical physics.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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