Proceedings of Symposia in Pure Mathematics最新文献

{"title":"A note on knot concordance and involutive\u0000 knot Floer homology","authors":"Kristen Hendricks, Jennifer Hom","doi":"10.1090/pspum/102/09","DOIUrl":"https://doi.org/10.1090/pspum/102/09","url":null,"abstract":"We prove that if two knots are concordant, their involutive knot Floer complexes satisfy a certain type of stable equivalence.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115447968","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":"Weinstein manifolds revisited","authors":"Y. Eliashberg","doi":"10.1090/PSPUM/099/01737","DOIUrl":"https://doi.org/10.1090/PSPUM/099/01737","url":null,"abstract":"This is a very biased and incomplete survey of some basic notions, old and new results, as well as open problems concerning Weinstein symplectic manifolds.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124383555","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":"An overview of knot Floer homology","authors":"P. Ozsváth, Z. Szabó","doi":"10.1090/PSPUM/099/01742","DOIUrl":"https://doi.org/10.1090/PSPUM/099/01742","url":null,"abstract":"Knot Floer homology is an invariant for knots discovered by the authors and, independently, Jacob Rasmussen. The discovery of this invariant grew naturally out of studying how a certain three-manifold invariant, Heegaard Floer homology, changes as the three-manifold undergoes Dehn surgery along a knot. Since its original definition, thanks to the contributions of many researchers, knot Floer homology has emerged as a useful tool for studying knots in its own right. We give here a few selected highlights of this theory, and then move on to some new algebraic developments in the computation of knot Floer homology.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128744134","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":"Pure 𝑆𝑈(2) gauge theory partition function\u0000 and generalized Bessel kernel","authors":"P. Gavrylenko, O. Lisovyy","doi":"10.1090/PSPUM/098/01727","DOIUrl":"https://doi.org/10.1090/PSPUM/098/01727","url":null,"abstract":"We show that the dual partition function of the pure $mathcal N=2$ $SU(2)$ gauge theory in the self-dual $Omega$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painleve III equation of type $D_8$ (radial sine-Gordon equation). In particular, the principal minor expansion of the Fredholm determinant yields Nekrasov combinatorial sums over pairs of Young diagrams.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124464288","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":"On ELSV-type formulae, Hurwitz numbers and\u0000 topological recursion","authors":"D. Lewanski","doi":"10.1090/PSPUM/100/01764","DOIUrl":"https://doi.org/10.1090/PSPUM/100/01764","url":null,"abstract":"We present several recent developments on ELSV-type formulae and topological recursion concerning Chiodo classes and several kind of Hurwitz numbers. The main results appeared in D. Lewanski, A. Popolitov, S. Shadrin, D. Zvonkine, \"Chiodo formulas for the r-th roots and topological recursion\", Lett. Math. Phys. (2016).","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124602349","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":"Graded linearisations","authors":"Gergely B'erczi, B. Doran, F. Kirwan","doi":"10.1090/pspum/099/01","DOIUrl":"https://doi.org/10.1090/pspum/099/01","url":null,"abstract":"When the action of a reductive group on a projective variety has a suitable linearisation, Mumford’s geometric invariant theory (GIT) can be used to construct and study an associated quotient variety. In this article we describe how Mumford’s GIT can be extended effectively to suitable actions of linear algebraic groups which are not necessarily reductive, with the extra data of a graded linearisation for the action. Any linearisation in the traditional sense for a reductive group action induces a graded linearisation in a natural way. The classical examples of moduli spaces which can be constructed using Mumford’s GIT are moduli spaces of stable curves and of (semi)stable bundles over a fixed nonsingular curve. This more general construction can be used to construct moduli spaces of unstable objects, such as unstable curves or unstable bundles (with suitable fixed discrete invariants in each case, related to their singularities or Harder–Narasimhan type). In algebraic geometry it is often useful to be able to construct quotients of algebraic varieties by linear algebraic group actions; in particular moduli spaces (or stacks) can be constructed in this way. When the linear algebraic group is reductive, and we have a suitable linearisation for its action on a projective variety, we can use Mumford’s geometric invariant theory (GIT) to construct and study such quotient varieties [32]. The aim of this article is to describe how Mumford’s GIT can be extended effectively to actions of a large family of linear algebraic groups which are not necessarily reductive, with the extra data of a graded linearisation for the action. Any linearisation in the traditional sense for a reductive group action can be regarded as a graded linearisation in a natural way. When a linear algebraic group over an algebraically closed field k of characteristic 0 is a semidirect productH = U ⋊R of its unipotent radical U and a reductive subgroupR ∼= H/U which contains a central one-parameter subgroup λ : Gm → Rwhose adjoint action on the Lie algebra of U has only strictly positive weights, we will see that any linearisation for an action of H on a projective variety X becomes graded if it is twisted by an appropriate (rational) character, and then many of the good properties of Mumford’s GIT hold. Many non-reductive linear algebraic group actions arising in algebraic geometry are actions of groups of this form: for example, any parabolic subgroup of a reductive group has this form, as does the automorphism group of any complete simplicial toric variety [11], and the group of k-jets of germs of biholomorphisms of (C, 0) for any positive integers k and p [6]. Example 0.1. The automorphism group of the weighted projective plane P(1, 1, 2) with weights 1,1 and 2 is Aut(P(1, 1, 2)) ∼= R⋉ U where R ∼= (GL(2)×Gm)/Gm ∼= GL(2) is reductive and U ∼= (k+)3 is unipotent with elements given by (x, y, z) 7→ (x, y, z + λx2 + μxy + νy2) for (λ, μ, ν) ∈ k3. Early work on this project was suppo","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"265 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127547421","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":"Descendents for stable pairs on\u0000 3-folds","authors":"R. Pandharipande","doi":"10.1090/PSPUM/099/01743","DOIUrl":"https://doi.org/10.1090/PSPUM/099/01743","url":null,"abstract":"We survey here the construction and the basic properties of descendent invariants in the theory of stable pairs on nonsingular projective 3-folds. The main topics covered are the rationality of the generating series, the functional equation, the Gromov-Witten/Pairs correspondence for descendents, the Virasoro constraints, and the connection to the virtual fundamental class of the stable pairs moduli space in algebraic cobordism. In all of these directions, the proven results constitute only a small part of the conjectural framework. A central goal of the article is to introduce the open questions as simply and directly as possible.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121227268","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":"Supersymmetric field theories and geometric\u0000 Langlands: The other side of the coin","authors":"A. Balasubramanian, J. Teschner","doi":"10.1090/PSPUM/098/01723","DOIUrl":"https://doi.org/10.1090/PSPUM/098/01723","url":null,"abstract":"This note announces results on the relations between the approach of Beilinson and Drinfeld to the geometric Langlands correspondence based on conformal field theory, the approach of Kapustin and Witten based on $N=4$ SYM, and the AGT-correspondence. The geometric Langlands correspondence is described as the Nekrasov-Shatashvili limit of a generalisation of the AGT-correspondence in the presence of surface operators. Following the approaches of Kapustin - Witten and Nekrasov - Witten we interpret some aspects of the resulting picture using an effective description in terms of two-dimensional sigma models having Hitchin's moduli spaces as target-manifold.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116664955","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":"Periods of meromorphic quadratic\u0000 differentials and Goldman bracket","authors":"D. Korotkin","doi":"10.1090/PSPUM/100/01763","DOIUrl":"https://doi.org/10.1090/PSPUM/100/01763","url":null,"abstract":"We study symplectic properties of monodromy map for second order linear equation with meromorphic potential having only simple poles on a Riemann surface. We show that the canonical symplectic structure on the cotangent bundle $T^*M_{g,n}$ implies the Goldman bracket on the corresponding character variety under the monodromy map, thereby extending the recent results of the paper of M.Bertola, C.Norton and the author from the case of holomorphic to meromorphic potentials with simple poles.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134226983","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":"Airy structures and symplectic geometry of\u0000 topological recursion","authors":"M. Kontsevich, Y. Soibelman","doi":"10.1090/PSPUM/100/01765","DOIUrl":"https://doi.org/10.1090/PSPUM/100/01765","url":null,"abstract":"We propose a new approach to the topological recursion of Eynard-Orantin based on the notion of Airy structure, which we introduce in the paper. We explain why Airy structure is a more fundamental object than the one of the spectral curve. We explain how the concept of quantization of Airy structure leads naturally to the formulas of topological recursion as well as their generalizations. The notion of spectral curve is also considered in a more general framework of Poisson surfaces endowed with foliation. We explain how the deformation theory of spectral curves is related to Airy structures. Few other topics (e.g. the Holomorphic Anomaly Equation) are also discussed from the general point of view of Airy structures.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125503842","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}