Çağatay Kutluhan, G. Matić, Jeremy Van Horn-Morris, Andy Wand
{"title":"A Heegaard Floer analog of algebraic\u0000 torsion","authors":"Çağatay Kutluhan, G. Matić, Jeremy Van Horn-Morris, Andy Wand","doi":"10.1090/PSPUM/102/10","DOIUrl":"https://doi.org/10.1090/PSPUM/102/10","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133755998","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":"Breadth in Contemporary Topology","authors":"Weiwei Wu","doi":"10.1090/pspum/102","DOIUrl":"https://doi.org/10.1090/pspum/102","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133589032","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}
Complex representations of reductive groups over different fields. [Course 80759-I changed the topic] Sundays 11.30-13.15 This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Q p and F q ((s))]. In this part I'll closely follow the notes of the course of J.Bernstein. Moreover I'll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Q p ((s))]. In the first part we explain the basics of a) induction from parabolic and parahoric subgroups, b) Jacquet functors, c) cuspidal representations d) the second adjointness and e) Affine Hecke algebras. In the second we discuss the generalization these concepts to the case of representations of reductive groups over 2-dimensional local fields. Prerequisites. The familiarity with the following subjects will be helpful. a) P-adic numbers, [see first few chapters of the book " p-adic numbers , p-adic analysis, and zeta-functions " by N.Koblitz or sections 4-5 in the book " Number theory " of Borevich and Shafarevich]. b) Basics of the theory of split reductive groups G [Bruhat decomposition , Weyl groups, parabolic and Levi subgroups] of reductive groups, [ One who does not know this this theory can restrict oneself to the case when G = GL(n) when Bruhat decomposition= Gauss decomposition.] c) Basics of the category theory: adjoint functors, Abelian categories. [ see the chapter 2 of book " Methods of homological algebra " 1
{"title":"Representations of Reductive Groups","authors":"David Vogan","doi":"10.1090/pspum/101","DOIUrl":"https://doi.org/10.1090/pspum/101","url":null,"abstract":"Complex representations of reductive groups over different fields. [Course 80759-I changed the topic] Sundays 11.30-13.15 This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Q p and F q ((s))]. In this part I'll closely follow the notes of the course of J.Bernstein. Moreover I'll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Q p ((s))]. In the first part we explain the basics of a) induction from parabolic and parahoric subgroups, b) Jacquet functors, c) cuspidal representations d) the second adjointness and e) Affine Hecke algebras. In the second we discuss the generalization these concepts to the case of representations of reductive groups over 2-dimensional local fields. Prerequisites. The familiarity with the following subjects will be helpful. a) P-adic numbers, [see first few chapters of the book \" p-adic numbers , p-adic analysis, and zeta-functions \" by N.Koblitz or sections 4-5 in the book \" Number theory \" of Borevich and Shafarevich]. b) Basics of the theory of split reductive groups G [Bruhat decomposition , Weyl groups, parabolic and Levi subgroups] of reductive groups, [ One who does not know this this theory can restrict oneself to the case when G = GL(n) when Bruhat decomposition= Gauss decomposition.] c) Basics of the category theory: adjoint functors, Abelian categories. [ see the chapter 2 of book \" Methods of homological algebra \" 1","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127159595","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":"Totally disconnected groups (not) acting on\u0000 two-manifolds","authors":"J. Pardon","doi":"10.1090/pspum/102/13","DOIUrl":"https://doi.org/10.1090/pspum/102/13","url":null,"abstract":"We briefly survey the Hilbert--Smith Conjecture, and we include a proof of it in dimension two (where it is originally due to Montgomery--Zippin).","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115944330","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 recursion and Givental’s\u0000 formalism: Spectral curves for Gromov-Witten\u0000 theories","authors":"P. Dunin-Barkowski","doi":"10.1090/PSPUM/100/01773","DOIUrl":"https://doi.org/10.1090/PSPUM/100/01773","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122475249","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}
The BKMP Remodeling Conjecture cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion cite{EO07} on its mirror curve. The proof of the Remodeling Conjecture by the authors cite{FLZ1,FLZ3} relies on comparing two Feynman-type graph sums in both A and B-models. In this paper, we will survey these graph sum formulae and discuss their roles in the proof of the conjecture.
{"title":"Graph sums in the remodeling\u0000 conjecture","authors":"Bohan Fang, Zhengyu Zong","doi":"10.1090/pspum/100/01767","DOIUrl":"https://doi.org/10.1090/pspum/100/01767","url":null,"abstract":"The BKMP Remodeling Conjecture cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion cite{EO07} on its mirror curve. The proof of the Remodeling Conjecture by the authors cite{FLZ1,FLZ3} relies on comparing two Feynman-type graph sums in both A and B-models. In this paper, we will survey these graph sum formulae and discuss their roles in the proof of the conjecture.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115619007","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 Recursion and its Influence in\u0000 Analysis, Geometry, and Topology","authors":"Chiu-Chu Melissa Liu, M. Mulase","doi":"10.1090/pspum/100","DOIUrl":"https://doi.org/10.1090/pspum/100","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131165775","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":"Bouchard-Klemm-Marino-Pasquetti conjecture\u0000 for ℂ³","authors":"Lin Chen","doi":"10.1090/PSPUM/100/01771","DOIUrl":"https://doi.org/10.1090/PSPUM/100/01771","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124678392","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}
Single Hurwitz numbers enumerate branched covers of the Riemann sphere with specified genus, prescribed ramification over infinity, and simple branching elsewhere. They exhibit a remarkably rich structure. In particular, they arise as intersection numbers on moduli spaces of curves and are governed by the topological recursion of Chekhov, Eynard and Orantin. Double Hurwitz numbers are defined analogously, but with prescribed ramification over both zero and infinity. Goulden, Jackson and Vakil have conjectured that double Hurwitz numbers also arise as intersection numbers on moduli spaces. In this paper, we repackage double Hurwitz numbers as enumerations of branched covers weighted by certain monomials and conjecture that they are governed by the topological recursion. Evidence is provided in the form of the associated quantum curve and low genus calculations. We furthermore reduce the conjecture to a weaker one, concerning a certain polynomial structure of double Hurwitz numbers. Via the topological recursion framework, our main conjecture should lead to a direct connection to enumerative geometry, thus shedding light on the aforementioned conjecture of Goulden, Jackson and Vakil.
{"title":"Towards the topological recursion for double\u0000 Hurwitz numbers","authors":"N. Do, M. Karev","doi":"10.1090/PSPUM/100/01761","DOIUrl":"https://doi.org/10.1090/PSPUM/100/01761","url":null,"abstract":"Single Hurwitz numbers enumerate branched covers of the Riemann sphere with specified genus, prescribed ramification over infinity, and simple branching elsewhere. They exhibit a remarkably rich structure. In particular, they arise as intersection numbers on moduli spaces of curves and are governed by the topological recursion of Chekhov, Eynard and Orantin. Double Hurwitz numbers are defined analogously, but with prescribed ramification over both zero and infinity. Goulden, Jackson and Vakil have conjectured that double Hurwitz numbers also arise as intersection numbers on moduli spaces. \u0000In this paper, we repackage double Hurwitz numbers as enumerations of branched covers weighted by certain monomials and conjecture that they are governed by the topological recursion. Evidence is provided in the form of the associated quantum curve and low genus calculations. We furthermore reduce the conjecture to a weaker one, concerning a certain polynomial structure of double Hurwitz numbers. Via the topological recursion framework, our main conjecture should lead to a direct connection to enumerative geometry, thus shedding light on the aforementioned conjecture of Goulden, Jackson and Vakil.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"354 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115931004","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":"Donaldson theory in non-Kählerian\u0000 geometry","authors":"A. Teleman","doi":"10.1090/PSPUM/099/12","DOIUrl":"https://doi.org/10.1090/PSPUM/099/12","url":null,"abstract":"","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"115 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":"132160604","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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