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Events happening on September 12, 2017

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Sep. 12, 2017 10am (Math 350)	Functional Analysis Andrzej Sitarz (Institute of Physics, Jagiellonian University in Krak�w, Poland) X Quotient spaces of actions of finite groups on tori provide interesting examples of flat manifolds and orbifolds. In some cases, actions can also be defined on non-commutative tori, and the fixed-point sub-algebras give their non-commutative counterparts. I�ll discuss three-dimensional examples (non-commutative Bieberbach manifolds) and two-dimensional (the non-commutative pillow), addressing the question of whether the resulting objects are manifolds or orbifolds. Based on joint work with P. Olczykowski (Bieberbach manifolds) and T. Brzezinski (the non-commutative pillow). Quotients of Non-Commutative Tori
Sep. 12, 2017 1pm (MATH 220)	Grad Algebra/Logic Peter Mayr (CU Boulder) X In combinatorial group theory the Reidemeister-Schreier Theorem (1927) asserts that a subgroup of finite index in a finitely presented group is itself finitely presented. Similar results exist for semigroups (Campbell, et al., 1996) and associative algebras over fields (Voden, 2009) for the appropriate interpretation of ``finite index''.� We show a version for rings: let $B$ be a subring of a finitely presented ring $A$ such that $A/B$ is finitely generated as a group. Then $B$ is finitely presented. This is joint work with Nik Ruskuc (University of St. Andrews). Reidemeister-Schreier for rings 1
Sep. 12, 2017 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (CU) X The maps from symmetric functions to Q functions and from quasi-symmetric functions to peak algebra, called Theta maps, are combinatorial Hopf morphisms and have their own interests. We are going to develop a general theory for theta maps for many families of combinatorial Hopf algebras. In particular, we will describe theta maps for the Malvenuto-Reutenaur Hopf algebra whose images are potentially generalizations of Q functions and peak algebra. We will also describe a Hopf algebra of permutations, which has a Theta map and the image is exactly the peak algebra. Theta maps for combinatorial Hopf algebras
Sep. 12, 2017 2pm (MATH 220)	Peter Mayr X In combinatorial group theory the Reidemeister-Schreier Theorem (1927) asserts that a subgroup of finite index in a finitely presented group is itself finitely presented. Similar results exist for semigroups (Campbell, et al., 1996) and associative algebras over fields (Voden, 2009) for the appropriate interpretation of ``finite index''. We show a version for rings: let $B$ be a subring of a finitely presented ring $A$ such that $A/B$ is finitely generated as a group. Then $B$ is finitely presented. This is joint work with Nik Ruskuc (University of St. Andrews). Reidemeister-Schreier for rings 2
Sep. 12, 2017 3pm (MATH 350)	Topology Paul Lessard X The talk is comprised of two obvious parts: In the first hour we will abstract the familiar "pasting lemma", defining sheaves, and discovering Grothendieck topologies as a minimal structure upon with a theory of sheaves might me built. In the subsequent hour we will discover how sheaves can be used not only to deal with geometry: structures consisting of continuous functions organized over the topology of the base; but may actually be used to organize and encode axioms about data which are not obviously geometric. In particular we will learn how sheaves with respect to different Grothendieck topologies on Joyal's category \Theta allow us to model a variety of generalizations of a category which are not merely -en vogue-, but at the heart of a new proof of the co-bordism hypothesis due to Ayala and Francis. Reverse Engineering Continuity from Sheaves, and Composition Laws Encoded as Sheaves: From Grothendieck Topologies to Globular Theories

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