Higher algebra has become important throughout mathematics physics and mathematical physics and this conference will bring together leading experts in higher algebra and its mathematical physics applications. In physics the term algebra is used quite broadly any time you can take two operators or fields multiply them and write the answer in some standard form a physicist will be happy to call this an algebra. Higher algebra is characterized by the appearance of a hierarchy of multilinear operations (e.g. A_infty and L_infty algebras). These structures can be higher categorical in nature (e.g. derived categories cosmology theories) and can involve mixtures of operations and cooperations (Hopf algebras Frobenius algebras etc.). Some of these notions are purely algebraic (e.g. algebra objects in a category) while others are quite geometric (e.g. shifted symplectic structures). An early manifestation of higher algebra in highenergy physics was supersymmetry. Supersymmetry makes quantum field theory richer and thus more complicated but at the same time many aspects become more tractable and many problems become exactly solvable. Since then higher algebra has made numerous appearances in mathematical physics both high and lowenergy. A telltale sign of the occurrence of higher structures is when classification results involve cohomology. Group cohomology appeared in the classification of condensed matter systems by the results of Wen and collaborators. Altland and Zirnbauer s "tenfold way" was explained by Kitaev using Ktheory. And Kitaev's 16 types of vortexfermion statistics were classified by spin modular categories. All these results were recently enhanced by the work of Freed and Hopkins based on cobordism theory. In high energy physics cohomology appears most visibly in the form of "anomalies". The ChernSimons anomaly comes from the fourth cohomology class of a compact Lie group and the 5brane anomaly is related to a certain cohomology class of the Spin group. The classification of conformal field theories involves the computation of all algebras objects in certain monoidal categories which is a type of nonabelian cohomology. Yet another important role for higher algebra in mathematical physics has been in the famous Langlands duality. Langlands duality began in number theory and then became geometry. It turned into physics when Kapustin and Witten realized geometric Langlands as an electromagnetic duality in cN=4 super YangMills theory. Derived algebra higher categories shifted symplectic geometry cohomology and supersymmetry all appear in Langlands duality. The conference speakers and participants drawn from both sides of the Atlantic and connected by live video streams will explore these myriad aspects of higher algebra in mathematical physics.
Format results

Welcome and Opening Remarks

Theo JohnsonFreyd Dalhousie University

Andre Henriques University of Oxford
PIRSA:18080042 

N=1 supersymmetric vertex algebras of small index
Davide Gaiotto Perimeter Institute for Theoretical Physics

Geometric Langlands: Comparing the views from CFT and TQFT
Joerg Teschner Deutsches ElektronenSynchrotron DESY

Cutting and gluing branes
David Nadler University of California, Berkeley

The lowenergy TQFT of the generalized double semion model
Arun Debray University of Texas  Austin


Moduli of connexions on open varieties
Bertrand Toen Paul Sabatier University

The Duistermaat–Heckman distribution for the based loop group
Lisa Jeffrey University of Toronto

Vertex models and Enalgebras
Damien Calaque University of Montpellier


Higher operations in supersymmetric ﬁeld theory
Andrew Neitzke The University of Texas at Austin

Homotopy types and geometries below Spec(Z)
Matilde Marcolli University of Toronto