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Events for June – October

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Thu, Jun. 5 3:30pm (MATH 3…	Functional Analysis PIOTR M. HAJAC (IMPAN, Warsaw, Poland) X Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphims. As both functors are often used at the same time, one needs a new category of graphs that allows a “common denominator” functor unifying the covariant and contravariant constructions. In this talk, I will show how to solve this problem by first introducing the relation category of graphs RG, and then determining the concept of admissible graph relations that yields a subcategory of RG admitting a contravariant functor to k-Alg simultaneously generalizing the aforementioned covariant and contravariant functors. I will illustrate relation morphisms of graphs by many naturally occurring examples, including Cuntz algebras, quantum spheres and quantum balls. Although I will focus on Leavitt path algebras and graph C-algebras, time permitting, I will unravel functors given by path algebras, Cohn path algebras and Toeplitz graph C-algebras from suitable subcategories of RG to k-Alg. Based on joint work with Gilles G. de Castro and Francesco D'Andrea. RELATION MORPHISMS OF DIRECTED GRAPHS
Fri, Jun. 6 2:30pm (Math 2…	Noncomm Geometry Paul Bressler (Universidad de los Andes) X I will describe a construction of a complex associated to a Lie algebroid originally due to V. Schechtman and use it to obtain interesting representatives of a characteristic classes of manifolds. Characteristic classes of natural bundles Sponsored by the Meyer Fund
Thu, Jul. 17 2:30pm (MATH 3…	Lie Theory Robert McRae (Tsinghua University) X This will be an overview talk on braided tensor categories obtained from representation categories of vertex operator algebras. I will describe how the tensor category structure is defined and also discuss what is currently known about examples and further properties (especially rigidity/existence of duals) of this tensor category structure. Tensor categories from vertex operator algebras Sponsored by the Meyer Fund

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