{"title":"Introduction to a provisional mathematical\u0000 definition of Coulomb branches of 3-dimesional\u0000 𝒩=4","authors":"H. Nakajima","doi":"10.1090/pspum/099/07","DOIUrl":"https://doi.org/10.1090/pspum/099/07","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133729000","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":"Descendants for stable pairs on\u0000 3-folds","authors":"R. Pandharipande","doi":"10.1090/pspum/099/09","DOIUrl":"https://doi.org/10.1090/pspum/099/09","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"523 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115629420","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":"Toward an algebraic Donaldson-Floer\u0000 theory","authors":"Jun Li","doi":"10.1090/PSPUM/099/01740","DOIUrl":"https://doi.org/10.1090/PSPUM/099/01740","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122599543","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}
Around 1988, Floer introduced two important theories: instanton Floer homology as invariants of 3-manifolds and Lagrangian Floer homology as invariants of pairs of Lagrangians in symplectic manifolds. Soon after that, Atiyah conjectured that the two theories should be related to each other and Lagrangian Floer homology of certain Lagrangians in the moduli space of flat connections on Riemann surfaces should recover instanton Floer homology. However, the space of flat connections on a Riemann surface is singular and the first step to address this conjecture is to make sense of Lagrangian Floer homology on this space. In this note, we formulate a possible approach to resolve this issue. A strategy to construct the desired isomorphism in the Atiyah-Floer conjecture is also sketched. We also use the language of A∞categories to state generalizations of the Atiyah-Floer conjecture.
{"title":"Atiyah-Floer conjecture: A formulation, a\u0000 strategy of proof and generalizations","authors":"A. Daemi, K. Fukaya","doi":"10.1090/PSPUM/099/01736","DOIUrl":"https://doi.org/10.1090/PSPUM/099/01736","url":null,"abstract":"Around 1988, Floer introduced two important theories: instanton Floer homology as invariants of 3-manifolds and Lagrangian Floer homology as invariants of pairs of Lagrangians in symplectic manifolds. Soon after that, Atiyah conjectured that the two theories should be related to each other and Lagrangian Floer homology of certain Lagrangians in the moduli space of flat connections on Riemann surfaces should recover instanton Floer homology. However, the space of flat connections on a Riemann surface is singular and the first step to address this conjecture is to make sense of Lagrangian Floer homology on this space. In this note, we formulate a possible approach to resolve this issue. A strategy to construct the desired isomorphism in the Atiyah-Floer conjecture is also sketched. We also use the language of A∞categories to state generalizations of the Atiyah-Floer conjecture.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131451561","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}
This is a one-year graduate-level introduction to modern geometry, what follows is a highly tentative syllabus. We'll see how much of this there is actually time for. For the first part of the course, two textbooks that cover this material at a similar level are:
{"title":"Modern Geometry","authors":"V. Muñoz, I. Smith, Richard P. Thomas","doi":"10.1090/pspum/099","DOIUrl":"https://doi.org/10.1090/pspum/099","url":null,"abstract":"This is a one-year graduate-level introduction to modern geometry, what follows is a highly tentative syllabus. We'll see how much of this there is actually time for. For the first part of the course, two textbooks that cover this material at a similar level are:","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121623154","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}
We discuss a number of open problems about mapping class groups of surfaces. In particular, we discuss problems related to linearity, congruence subgroups, cohomology, pseudo-Anosov stretch factors, Torelli subgroups, and normal subgroups.
{"title":"Problems, questions, and conjectures about\u0000 mapping class groups","authors":"D. Margalit","doi":"10.1090/pspum/102/12","DOIUrl":"https://doi.org/10.1090/pspum/102/12","url":null,"abstract":"We discuss a number of open problems about mapping class groups of surfaces. In particular, we discuss problems related to linearity, congruence subgroups, cohomology, pseudo-Anosov stretch factors, Torelli subgroups, and normal subgroups.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130696357","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":"Three-dimensional 𝒩=4 gauge theories in omega\u0000 background","authors":"Mathew Bullimore","doi":"10.1090/pspum/098/01","DOIUrl":"https://doi.org/10.1090/pspum/098/01","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127116832","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}
A. Kashani-Poor, R. Minasian, N. Nekrasov, B. Pioline
{"title":"String-Math 2016","authors":"A. Kashani-Poor, R. Minasian, N. Nekrasov, B. Pioline","doi":"10.1090/pspum/098","DOIUrl":"https://doi.org/10.1090/pspum/098","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126040034","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}
In this short note, we give an explicit construction of inequivalent Lefschetz pencils and fibrations of same genera on blow-ups of all rational and ruled surfaces. This complements our earlier results, concluding that every symplectic 4-manifold, after sufficiently many blow-ups, admits inequivalent Lefschetz pencils and fibrations, which cannot be obtained from one another even via any sequence of fibered Luttinger surgeries.
{"title":"Inequivalent Lefschetz fibrations on rational\u0000 and ruled surfaces","authors":"R. Baykur","doi":"10.1090/pspum/102/02","DOIUrl":"https://doi.org/10.1090/pspum/102/02","url":null,"abstract":"In this short note, we give an explicit construction of inequivalent Lefschetz pencils and fibrations of same genera on blow-ups of all rational and ruled surfaces. This complements our earlier results, concluding that every symplectic 4-manifold, after sufficiently many blow-ups, admits inequivalent Lefschetz pencils and fibrations, which cannot be obtained from one another even via any sequence of fibered Luttinger surgeries.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115996211","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}
We review the description of three-dimensional gauge theories with N = 4 supersymmetry in the presence of an omega background as an N = 4 supersymmetric quantum mechanics. We will focus throughout on a simple abelian example. The Hilbert space of supersymmetric ground states is populated by generalized vortex congurations, while half-BPS monopole operators act on the Hilbert space by creating and annihilating vortices, furnishing it with the structure of a Verma module for the quantized Coulomb branch chiral ring. Furthermore, by introducing two-dimensional N = (2; 2) boundary conditions, we nd a nite version of the AGT correspondence between vortex partition functions and overlaps of Whittaker vectors for quantized Coulomb branch chiral rings.
{"title":"Three-dimensional cN=4 gauge theories in\u0000 omega background","authors":"Mathew Bullimore","doi":"10.1090/PSPUM/098/01729","DOIUrl":"https://doi.org/10.1090/PSPUM/098/01729","url":null,"abstract":"We review the description of three-dimensional gauge theories with N = 4 supersymmetry in the presence of an omega background as an N = 4 supersymmetric quantum mechanics. We will focus throughout on a simple abelian example. The Hilbert space of supersymmetric ground states is populated by generalized vortex congurations, while half-BPS monopole operators act on the Hilbert space by creating and annihilating vortices, furnishing it with the structure of a Verma module for the quantized Coulomb branch chiral ring. Furthermore, by introducing two-dimensional N = (2; 2) boundary conditions, we nd a nite version of the AGT correspondence between vortex partition functions and overlaps of Whittaker vectors for quantized Coulomb branch chiral rings.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122293584","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}
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