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Events happening on October 4, 2016

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Oct. 04, 2016 10am (MATH 350)	PDE/Analysis Jae Min Lee (CUNY Graduate Center) X In this talk, we will study the local well-posedness of the Camassa-Holm equation on the real line. That is, we will show the local existence and uniqueness of the solution, and the continuous dependence of the solution on the initial data. The main idea is to use the Lagrangian flow to rewrite the PDE as a smooth ODE on a Banach Space. We will also show that the group of diffeomorphisms is a topological group, which is necessary to prove the smoothness of the equation and continuous dependence. Local Well-posedness of the Camassa-Holm equation on the real line
Oct. 04, 2016 10am (MATH 220)	Number Theory Stefan Erickson (Colorado College) X Leavitt path algebras are algebraic structures associated with a given directed graph. A natural question is to study the structure of these algebras, including the Grothendieck group generated by the Leavitt path algebras of certain Cayley graphs. As finite abelian groups, they have a canonical cyclic group decomposition. Studying the cyclic components leads to interesting divisibility relations between certain sequences of numbers. After a brief introduction to Leavitt path algebras, we will present some number theoretic results related to groups arising from a class of "almost" cyclic graphs. This is ongoing work with Gene Abrams at UCCS and Cristobal Gil at University of Malaga. Divisibility Sequences Arising from Leavitt Path Algebras
Oct. 04, 2016 12:10pm (MATH …	Kempner Joe Auslander (University of Maryland) X A flow is a jointly continuous action of a topological group on a compact Hausdorff space . The flow is minimal if every orbit is dense. The flow is said to be equicontinuous if the maps defined by form an equicontinuous family, in which case the action can be embedded in a compact group. Distality is a generalization of equicontinuity, and the structure of distal minimal flows is provided by a deep theorem of Hillel Furstenberg which says that an arbitrary distal minimal flow can be obtained from the trivial one point flow by a (possibly transfinite) sequence of “equicontinuous extensions”. Given an arbitrary flow, there are distal and equicontinuous structure relations–closed invariant equivalence relations such that the factor flow is, respectively distal or equicontinuous. These relations are generated, respectively, by the proximal and regionally proximal relations. For a minimal flow in many cases (including when is abelian) surprisingly the latter coincides with a smaller relation due to Veech. Structure and homomorphisms of minimal flows
Oct. 04, 2016 2pm (MATH 220)	Mark Pullins (CU) X Morley rank is a model-theoretic generalization of dimension, and interest in groups of finite Morley rank traces its origins to a conjecture due to Gregory Cherlin (1979) and Boris Zilber (1977) that all infinite -stable simple groups are algebraic groups over algebraically closed fields. This has not yet been proven even for groups of finite Morley rank, which is a subclass of the class of -stable groups. A purely-model theoretic approach appears insufficient to answer this question and, over the years, techniques inspired by finite group theory and intuition from algebraic geometry have played a role in the study of groups of finite Morley rank. In this talk, we will introduce an axiomatic approach to Morley rank and examine the basic properties of rank. From there, we can begin to discuss the structure of groups of finite Morley rank. An Introduction to Groups of Finite Morley Rank, 1
Oct. 04, 2016 2pm (MATH 350)	Lie Theory Shawn Burkett (CU) X Normal subgroups play a central role in the study of finite groups and their irreducible characters. Many times, one may stitch together information about a normal subgroup and its quotient to learn a tremendous amount about about the original group and its representation theory. For example, if a group is a semidirect product the structure of the is determined by and and the way they interact. In certain situations (i.e. direct products), the irreducible characters of can be completely determined by knowing the irreducible characters of both and its quotient . Not surprisingly, normal subgroups also play a central role in the study of supercharacter theories of a finite group. In this talk, we will explore some of the ways that normal subgroups can be used to understand the supercharacter theories of a finite group. Normal Subgroups and Supercharacter Theory
Oct. 04, 2016 3pm (MATH 350)	Topology Sarah Yeakel (U Maryland) X Goodwillie's calculus of functors is a method of approximating a homotopy functor with easier "polynomial" functors, building a Taylor tower where the homogeneous pieces are classified by certain spectra, called the derivatives of the functor. It is known that the derivatives of the identity functor of spaces form an operad and composable functors have a chain rule. We will discuss a general framework for these results and the extra structure that the derivatives possess. During the introductory talk, we will review the theory of functor calculus and why operads show up. Derivatives in Goodwillie Calculus

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