Speaker: Kesong Yan, MSU and Guangxi University of Finance and Economics

Title: Entropy and Complexity of topological dynamical systems

Date: 12/04/2018

Time: 3:00 PM - 4:00 PM

Place: 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.

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.

Title: The transverse invariant and braid dynamics

Date: 12/06/2018

Time: 2:00 PM - 2:50 PM

Place: 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, Vela-Vick and Vertesi is non-zero 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 non-zero. We discuss geometric consequences and future directions.

Title: More on Scattering Diagram and Theta Functions

Date: 12/06/2018

Time: 3:00 PM - 4:00 PM

Place: 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 Gross-Hacking-Keel-Kontsevich’s proofs of positive Laurent phenomenon, sign coherence, and a weak version of the cluster duality conjecture.

Speaker: Corey Drake and Kimberly Jansen, MSU and University of Virginia

Title: Novice Elementary Teachers’ Enactment of Ambitious Instruction in Mathematics: Challenges and Responses

Date: 12/07/2018

Time: 12:00 PM - 1:00 PM

Place: 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 early-career teacher practice. American Education Research Journal, 50(3), 574-615.

Speaker: Ming Tse Paul Laiu, Oak Ridge National Laboratory

Title: A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations

Date: 12/07/2018

Time: 4:10 PM - 5:00 PM

Place: 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 micro-macro decomposition.
The three main ingredients are a semi-implicit 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 cross-section tends to infinity.
The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations.
The scheme is tested on well-known benchmark problems and gives promising results.