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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 co-operations (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 high-energy 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 low-energy. A tell-tale 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 "ten-fold way" was explained by Kitaev using K-theory. And Kitaev's 16 types of vortex-fermion 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 Chern--Simons anomaly comes from the fourth cohomology class of a compact Lie group and the 5-brane 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 non-abelian 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 Yang--Mills 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.

The foundations of quantum mechanics have been revitalized in the past few decades by three developments:  (i) the influence of quantum computation and quantum information theory (ii) studies of the interplay between quantum theory and relativity particularly the analysis of indefinite causal structure and (iii) proposals to reconstruct quantum theory from basic axioms.  There have also been very interesting developments in understanding and classifying no=locality and contextuality using tools from sheaf theory and cohomology as well as operator algebras and category theory. The International Congress of Mathematical Physics is a natural forum for the discussion of these topics.  In the past there have been satellite workshops on topics like Operator algebras and quantum statistical mechanics which also address fundamental issues.  The modern study of quantum foundations is very much influenced and informed by mathematics:  sheaf theory and cohomology category theory information theory convex analysis in addition to the continuing interest in operator algebras and functional analysis. The aim of the workshop is to bring together researchers who have made substantial contribution to the recent developments.  The workshop will be held at Perimeter Institute over a five day period from July 30