Proceedings of Symposia in Pure Mathematics最新文献_第6页

Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras Jordan颤振规范理论的量子化库仑分支与分环有理Cherednik代数

Proceedings of Symposia in Pure Mathematics Pub Date : 2016-08-02 DOI: 10.1090/PSPUM/098/01720

R. Kodera, H. Nakajima

引用次数: 45

Primary invariants of Hurwitz Frobenius manifolds Hurwitz Frobenius流形的初等不变量

Proceedings of Symposia in Pure Mathematics Pub Date : 2016-05-24 DOI: 10.1090/pspum/100/01768

P. Dunin-Barkowski, Paul T. Norbury, N. Orantin, A. Popolitov, S. Shadrin

引用次数: 15

Two lectures on gauge theory and Khovanov homology 两节课讲规范论和Khovanov同调

Proceedings of Symposia in Pure Mathematics Pub Date : 2016-03-12 DOI: 10.1090/PSPUM/099/01747

E. Witten

引用次数: 20

Modular functors, cohomological field theories, and topological recursion 模函子，上同调场论，和拓扑递归

Proceedings of Symposia in Pure Mathematics Pub Date : 2015-09-04 DOI: 10.1090/PSPUM/100/01772

J. Andersen, G. Borot, N. Orantin

{"title":"Modular functors, cohomological field\u0000 theories, and topological recursion","authors":"J. Andersen, G. Borot, N. Orantin","doi":"10.1090/PSPUM/100/01772","DOIUrl":"https://doi.org/10.1090/PSPUM/100/01772","url":null,"abstract":"Given a topological modular functor $mathcal{V}$ in the sense of Walker cite{Walker}, we construct vector bundles over $bar{mathcal{M}}_{g,n}$, whose Chern classes define semi-simple cohomological field theories. This construction depends on a determination of the logarithm of the eigenvalues of the Dehn twist and central element actions. We show that the intersection of the Chern class with the $psi$-classes in $bar{mathcal{M}}_{g,n}$ is computed by the topological recursion of cite{EOFg}, for a local spectral curve that we describe. In particular, we show how the Verlinde formula for the dimensions $D_{vec{lambda}}(mathbf{Sigma}_{g,n}) = dim mathcal{V}_{vec{lambda}}(mathbf{Sigma}_{g,n})$ is retrieved from the topological recursion. We analyze the consequences of our result on two examples: modular functors associated to a finite group $G$ (for which $D_{vec{lambda}}(mathbf{Sigma}_{g,n})$ enumerates certain $G$-principle bundles over a genus $g$ surface with $n$ boundary conditions specified by $vec{lambda}$), and the modular functor obtained from Wess-Zumino-Witten conformal field theory associated to a simple, simply-connected Lie group $G$ (for which $mathcal{V}_{vec{lambda}}(mathbf{Sigma}_{g,n})$ is the Verlinde bundle).","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"141 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134465566","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}

引用次数: 10

Spectral theory and mirror symmetry 光谱理论和镜像对称

Proceedings of Symposia in Pure Mathematics Pub Date : 2015-06-25 DOI: 10.1090/PSPUM/098/01722

M. Mariño

引用次数: 50

A remark on the geography problem in Heegaard Floer homology 论《赫加德花》同源性中的地理问题

Proceedings of Symposia in Pure Mathematics Pub Date : 2015-06-16 DOI: 10.1090/pspum/102/08

J. Hanselman, Çağatay Kutluhan, Tye Lidman

引用次数: 4

The hybrid Landau–Ginzburg models of Calabi–Yau complete intersections Calabi-Yau完全交叉口的Landau-Ginzburg混合模型

Proceedings of Symposia in Pure Mathematics Pub Date : 2015-06-09 DOI: 10.1090/PSPUM/100/01760

A. Chiodo, J. Nagel

引用次数: 14

Quantization of spectral curves for meromorphic Higgs bundles through topological recursion 亚纯希格斯束谱曲线的拓扑递推量化

Proceedings of Symposia in Pure Mathematics Pub Date : 2014-11-04 DOI: 10.1090/PSPUM/100/01780

Olivia Dumitrescu, M. Mulase

{"title":"Quantization of spectral curves for\u0000 meromorphic Higgs bundles through topological\u0000 recursion","authors":"Olivia Dumitrescu, M. Mulase","doi":"10.1090/PSPUM/100/01780","DOIUrl":"https://doi.org/10.1090/PSPUM/100/01780","url":null,"abstract":"A geometric quantization using the topological recursion is established for the compactified cotangent bundle of a smooth projective curve of an arbitrary genus. In this quantization, the Hitchin spectral curve of a rank $2$ meromorphic Higgs bundle on the base curve corresponds to a quantum curve, which is a Rees $D$-module on the base. The topological recursion then gives an all-order asymptotic expansion of its solution, thus determining a state vector corresponding to the spectral curve as a meromorphic Lagrangian. We establish a generalization of the topological recursion for a singular spectral curve. We show that the partial differential equation version of the topological recursion automatically selects the normal ordering of the canonical coordinates, and determines the unique quantization of the spectral curve. The quantum curve thus constructed has the semi-classical limit that agrees with the original spectral curve. Typical examples of our construction includes classical differential equations, such as Airy, Hermite, and Gaus hypergeometric equations. The topological recursion gives an asymptotic expansion of solutions to these equations at their singular points, relating Higgs bundles and various quantum invariants.","PeriodicalId":384712,"journal":{"name":"Proceedings of Symposia in Pure\n Mathematics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122791468","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}

引用次数: 25

Quantum curves for simple Hurwitz numbers of an arbitrary base curve 简单赫尔维茨数的任意基曲线的量子曲线

Proceedings of Symposia in Pure Mathematics Pub Date : 2013-03-29 DOI: 10.1090/PSPUM/100/01769

Xiaojun Liu, M. Mulase, Adam J. Sorkin

引用次数: 10