Speaker: Tibor Marcinek

Title: Designing and Studying Interpretation Tasks in Mathematics Content Courses for Elementary Teachers

Abstract: Mathematics content courses for teachers are often specifically designed to go beyond common knowledge of mathematics and expose students to the multifaceted nature of mathematics for teaching. In the presentation, we will explain how one such facet is studied in our mathematics courses for elementary teachers. We will describe activities that facilitate students’ involvement in interpreting and responding to the mathematical ideas and thinking of others (their peers) and how such activities are studied and evaluated. This presentation will also bring up the importance of practitioner knowledge in mathematics education and a fuzzy borderline that separates it from the research knowledge.

Speaker: Christine Phelps

Title: Using a Discussion Board to Support Prospective Teachers in Analyzing a Lesson

Abstract: I present the results on an online discussion board intervention designed to help prospective teachers (PTs) learn to systematically analyze student thinking and mathematics teaching. Findings suggest that the intervention helped PTs to look past surface features of the lesson and focus on students' mathematical thinking, although gaps remained in their analysis skills. Results of this work can help improve teacher education.

It was in 2010 when Bennett, Cochran, Safnuk, and Woskoff used the non-degeneracy of $\Omega$, and the fact that the top-dimensional cells of $\mathrm{RG}_{g,n}$ have all trivalent vertices, to calculate the symplectic volume of $\mathrm{RG}_{g,n}$. Creating a hamiltonian torus action on the top-dimension of $\mathrm{RG}_{g,n}$, they use symplectic reduction techniques to create a recursive formula for the volume.

In this talk, I discuss my dissertation research which extends the work done by Bennett et al. I define the sub-complexes $\overline{\mathrm{RG}}_{g,n}^{(\alpha_1, \alpha_2, \ldots)}$ of $\overline{\mathrm{RG}}_{g,n}$ which, roughly, is the ribbon graph complex cosisting of ribbon graphs with exactly $\alpha_i$ vertices of degree $2i+3$. I pay particular attention to $\overline{\mathrm{RG}}_{g,n}^{(1,0,0,\ldots)}$, finding a hamiltonian torus action on the top-dimensional cells and using symplectic reduction to recursively calculate its volume.

We hope to see you there!

Speaker: Debraj Chakrabarti

Title: Several Complex Variables Are Better Than Just One

Abstract: In this talk we discuss how the properties of holomorphic functions of several complex variables differ from those of one complex variable. In particular, we discuss the Hartogs phenomenon, an extension phenomenon for holomorphic functions of several variables which has no analog in one variable.

Speaker: Ben Salisbury

Title: Introduction to Crystals and an Application

Abstract: In this short talk, we will quickly introduce crystal bases in a combinatorial way, and overview a very recent application of the theory of crystal bases to the field of automorphic forms.

Speaker: Mohamed Amezziane

Title: Function Estimation Using Shrinkage Techniques

Abstract: This talk introduces the concept of estimating a function (as opposed to estimating a function's parameters) and its connection to the problem of estimating the means of several Normal random variables. This connection enables the use of shrinkage techniques to obtain several types of function estimators with nice asymptotic optimality properties. These types of estimators, like any other nonparametric estimators, are plagued by the curse of dimensionality, i.e., the degradation of the estimator's accuracy as the dimension of the data increases. To curb the effect of this curse, shrinkage techniques are used to propose new classes of semiparametric estimators.

Speaker: Mingan Yang

Title: Bayesian Variable Selection For Mixed Effects Models

Abstract: Recently, variable selection has drawn great attention and a vast number of penalized regression approaches with shrinkage estimation have been developed for general linear models. Correspondingly, the Bayesian alternative approaches have also been proposed. However, it gains little attention for the linear mixed effects model.

For linear mixed effects model, generally, it is a common practice to assume that the random effects follow a parametric distribution, for example, a normal distribution. However, substantial violation of the normality assumption might potentially impact the subset selection of variables in the models. Potentially, one might propose a nonparametric random effect model. The challenge is that the random effects generally have a none-zero mean, which causes identifiability and complicates interpretation for variable selection, in the nonparametric random effect model. I propose a shrinkage approach on a nonparametric centered random effects models and consider some possible extensions.

We hope to see you there!

This talk will be accessible to all graduate students.