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Dynamical Systems
 Kesong Yan, MSU and Guangxi University of Finance and Economics
 Entropy and Complexity of topological dynamical systems
 12/04/2018
 3:00 PM  4:00 PM
 C304 Wells Hall
Abstract: In this talk, we will review some results about the topological entropy and complexity for topological dynamical systems.
This is a continuation of the talk given in the last week.

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Informal Geometric Analysis Seminar
 Thomas Walpuski, MSU
 Quantitative Stratification and the Regularity of Harmonic Maps (part II)
 12/05/2018
 2:00 PM  3:30 PM
 C304 Wells Hall
Continuation of last week's talk.
Student Geometry/Topology
 Zhe Zhang
 Bott's paper about geometric quantization
 12/05/2018
 4:10 PM  5:00 PM
 A202 Wells Hall
Raoul Bott  "On some recent interactions between mathematics and physics" (1985).
It is a mathematical point of view about how quantum phenomena naturally arises when we use Feynman’s idea of path integral and try to give a rigorous definition of the electromagnetic potential. This in turn gives us a new interpretation of a symplectic manifold as space of flat connections over a Riemann surface.

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Geometry and Topology
 Lev TovstopyatNelip , Boston College
 The transverse invariant and braid dynamics
 12/06/2018
 2:00 PM  2:50 PM
 C304 Wells Hall
Let K be a link braided about an open book (B,p) supporting a contact manifold (Y,x). K and B are naturally transverse links. We prove that the hat version of the transverse link invariant defined by Baldwin, VelaVick and Vertesi is nonzero for the union of K with B. As an application, we prove that the transverse invariant of any braid having fractional Dehn twist coefficient greater than one is nonzero. We discuss geometric consequences and future directions.
Seminar in Cluster algebras
 Daping Weng, MSU
 More on Scattering Diagram and Theta Functions
 12/06/2018
 3:00 PM  4:00 PM
 C117 Wells Hall
I will continue the discussion on scattering diagram and theta functions and relate them to the classical cluster theories. I will sketch GrossHackingKeelKontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.

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CoIntegrate Mathematics
 Corey Drake and Kimberly Jansen, MSU and University of Virginia
 Novice Elementary Teachers’ Enactment of Ambitious Instruction in Mathematics: Challenges and Responses
 12/07/2018
 12:00 PM  1:00 PM
 133F Erick
Substantial work in teacher education over the past several years has focused on elaborating and understanding the construct of ambitious instruction. While research on ambitious instruction has included detailed descriptions of ambitious teaching practices and the ways in which teacher education experiences are intended to promote the development of these practices, less research has investigated the conditions under which teachers, particularly novice teachers, are more or less likely to enact ambitious instruction (though Thompson, Windschitl, & Braaten, 2013, provide an exception). In this presentation, we will share the challenges to ambitious instruction identified by a group of 61 novice elementary teachers from four different teacher preparation programs. We will also share four types of responses novices had to these challenges and the implications of these responses for the enactment of ambitious instruction.
Thompson, J., Windschitl, M., & Braaten, M. (2013). Developing a theory of ambitious earlycareer teacher practice. American Education Research Journal, 50(3), 574615.
Applied Mathematics
 Ming Tse Paul Laiu, Oak Ridge National Laboratory
 A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations
 12/07/2018
 4:10 PM  5:00 PM
 1502 Engineering Building
We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering.
The proposed scheme is developed using a standard spectral angular discretization and a classical micromacro decomposition.
The three main ingredients are a semiimplicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization.
Under mild assumptions, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering crosssection tends to infinity.
The scheme also preserves positivity of the particle concentration on the spacetime mesh and therefore fixes a common defect of spectral angular discretizations.
The scheme is tested on wellknown benchmark problems and gives promising results.

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