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Events happening on March 14, 2017

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Mar. 14, 2017 12:10pm (MATH …	Kempner Mark Behrens (Notre Dame) X In physics, the detection of certain particles has required working at increasingly high energy. These accelerator experiments have required increasingly elaborate detectors and data analysis to reconstruct events from the production of dozens, sometimes hundreds of resulting particles. I will use this analogy to discuss the increasingly elaborate "detectors" used in homotopy theory to probe the stable homotopy groups of spheres in increasingly large dimensions. These "detectors" are versions of the Adams spectral sequence. To maximize the accessibility of this talk, I will avoid using the language of spectral sequences. Detectors in homotopy theory
Mar. 14, 2017 2pm (Math 220)	Peter Jipsen (Chapman University) X The study of Boolean algebras with operators dates back to Jónsson and Tarski’s seminal 1951-52 papers, and has many applications in the theory of relation algebras, modal logic and computer science. It was generalized to distributive lattices with operators by Gehrke and Jonsson in 1994, and to lattices with operators by Gehrke and Harding in 2001. In this talk we consider Heyting algebras with operators, with applications to residuated Heyting algebras and intuitionistic relation algebras. We define weakening relation algebras as division-conuclear images of relation algebras, and show that they are distributive involutive residuated lattices with a Heyting implication. The class of representable weakening relation algebras is not finitely based, but all members are downset-algebras of partially ordered Brandt groupoids. Furthermore we prove that downset algebras of po-groupoids are cyclic involutive residuated Heyting algebras, and we calculate the Gumm-Ursini ideal terms that describe congruences of residuated Heyting algebras. This is joint research with Nick Galatos from the University of Denver. Residuated Heyting algebras and intuitionistic relation algebras
Mar. 14, 2017 2pm (MATH 350)	Lie Theory Sarah Wolff (Denison University) X The (classical) Fast Fourier Transform remains among the most important algorithms in information processing. It is in fact not one algorithm, but a family of algorithms that together effect the efficient computation of the discrete Fourier transform (DFT). We take an algebraic point of view and cast the DFT as a change of basis in the complex group algebra of the cyclic group of order n. This in turn gives rise to a more general notion of the DFT on an arbitrary finite group or semisimple algebra, with concomitant questions of algorithmic efficiency. We will present a diagrammatic approach using Bratteli diagrams to construct efficient algorithms for computing these transforms, and will then discuss a random walk application Fourier Analysis on Groups and Algebras: an Algorithm and a Walk Sponsored by the Meyer Fund
Mar. 14, 2017 3pm (MATH 350)	Topology Mark Behrens (University of Notre Dame) X Quillen-Sullivan theory encodes a rational homotopy type in either a differential graded rational Lie algebra, or a differential graded rational commutative algebra. The first encodes the rational homotopy groups, with its Whitehead products, and the second encodes the rational cohomology groups, with its cup products. I will describe a generalization of this theory, joint with Charles Rezk, where "rational homotopy theory" is replaced with "unstable v_n-periodic homotopy theory. A generalization of Quillen-Sullivan rational homotopy theory Sponsored by the Meyer Fund
Mar. 14, 2017 4pm (MATH 350)	Topology Xiang Tang (Washington University at St. Louis) X A G-gerbe is a principal BG bundle, where BG is the classifying space of G. In this talk, we will explain what they are, and introduce a Leray-Hirsch principle to study the geometry of G gerbes on orbifolds. The key ingredient in our development is the Mackey machine for the restriction of a representation. We will aim to make the talk accessible to graduate students. A Leray-Hirsch Principle for Gerbes on Orbifolds Sponsored by the Meyer Fund

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