# Colloquia

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## Henry Riely – Washington State University

#### Monday, September 10, 2018 at 3:00 p.m. in Math 103 Refreshments at 4:00 p.m. in Math Lounge 109

October 22 – FEC meeting

### Available Dates

August 27
September 17, 24
October 1, 8, 15, 29
November 5, 19, 26
December 3

## Ricela Feliciano-SemideiUniversity of Montana – PhD Candidate

### Understanding Conditional Probability with the Monty Hall Problem

Conditional probability is an important concept that is widely used in social sciences, natural sciences, health sciences and business. There is a high need to understand how students learn conditional probability and to develop effective teaching interventions to improve their learning experiences. This study developed a teaching intervention that incorporated the Monty Hall problem into a game learning model. Through the implementation of the teaching intervention in a statistics introductory course at college level, researchers investigated students’ conceptions on conditional probability. The impact of the teaching module on students’ learning was examined through pretest and posttest. Researchers identified the Law of Large Numbers as a key concept required prior to learning conditional probability. Findings from the study had implications to improve the teaching and learning of conditional probability.

## Michael Dorff – Brigham Young University

### Analytic functions, harmonic functions, and minimal surfaces

Complex-valued harmonic mappings can be regarded as generalizations of analytic functions and are related to minimal surfaces which are beautiful geometric shapes with intriguing properties. In this talk we will provide background material about these harmonic mappings, discuss the relationship between them and minimal surfaces, present some new results, and pose a few open problems.

## Vanni Noferini – University of Essex

### Localization results for indefinite eigenvalue problems

Sylvester's law of inertia states that the number of positive, zero or negative eigenvalues of a matrix is invariant under congruence, and the same is true for pencils when at least one matrix is definite (and both are allowed to undergo independent congruences). Nothing was known thus far for indefinite pencils, and almost nothing for nonlinear problems. I will present new results of ours in this area, including inertia-based lower and upper bounds for the number of eigenvalues in a real interval. This talk is based on joint work with Yuji Nakatsukasa (University of Oxford).

## Matthias Chung – Department of Mathematics at Virginia Tech.

### Computational Challenges of Inverse Problems

Inverse problems are omnipresent in many scientific fields such as systems biology, engineering, medical imaging, and geophysics. The main challenges toward obtaining meaningful real-time solutions to large, data-intensive inverse problems are ill-posedness of the problem, large parameter dimensions, and/or complex model constraints. This talk discusses computational challenges of inverse problems by exploiting a combination of tools from applied linear algebra, parameter estimation and optimization, and statistics. For instance, for large scale ill-posed inverse problems, approximate solutions are computed using a regularization method that solves a nearby well-posed problem.  Oftentimes, the selection of a proper regularization parameter is the most critical and computationally intensive task and may hinder real-time computations of the solution. We present a new framework for solving ill-posed inverse problems by computing optimal regularized inverse matrices. We further discuss randomized Newton and randomized quasi-Newton approaches to efficiently solve large linear least-squares problems, where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In this framework, randomness is introduced as a means to overcome computational limitations, and probability distributions that can exploit structure and/or sparsity are considered. We will present numerical examples, from deblurring, tomography, and machine learning to illustrate the challenges and our proposed methods.

## Zhuang Niu – University of Wyoming

### The classification of C*-algebras

A C*-algebra is an algebra of bounded linear operators acting on a Hilbert space, closed under adjoint operation and closed under the norm topology. Prototype examples include the algebra of n by n matrices and the algebra of continuous function on a compact Hausdorff space, and in general, C*-algebras arise naturally in the studies of dynamical systems, mathematical physics, group theory, and representation theory, etc. In this talk, I will give an overview of the recent progress on the classification of C*-algebras using the K-theory information.

## Dr. Edray H Goins – Purdue UniversityColloquium & Reception honoring Dr. Gloria Hewitt

### Yes, Even You Can Bend It Like Beckham

In the 2002 film by Gurinder Chadha, character Jesminder 'Jess' Bhamra states "No one can cross a ball or bend it like Beckham'' in a reference to the international soccer star's ability to cause the ball to swerve. In 2010, French researchers Guillaume Dupeux, Anne Le Goff, David Quere and Christophe Clanet published a paper in the New Journal of Physics detailing both experimental and mathematical analyses of a spinning ball in a fluid to show that it must follow a spiral.

In this talk, we give an overview of their discussion by reviewing the Navier-Stokes equation in a Serret-Frenet coordinate system. This talk is dedicated to the memory of Angela Grant and her love of mathematics in sports.

## Wend Werner – University of Muenster in Germany

### Algebraic composition with more than two ingredients

Are we biologically biased towards thinking that products, sums and the like always require the contribution of exactly two agents in order to spawn a third one? We will survey some sample theories where ternary (and higher) algebraic operations show up and see that sometimes, there is a binary structure governing these somewhat exotic structures and that on other occasions, this is less true.

### Teacher Learning in a Professional Learning Community (PLC) in The Netherlands

In 2013, the Dutch government started funding for professional learning communities (PLC’s) in The Netherlands. Aim of this funding was to do research about ways to improve mathematics teaching by teachers involved in these PLC’s. Radboud Teachers Academy started a PLC with 12 mathematics teachers from 11 different middle schools and high schools, starting from the idea of Lesson Study, a Japanese method for teacher development. As a result, teachers reported that they were inspired and that their teaching skills increased. However, the intended shift from instruction centred teaching to attention on student learning proved hard to realize.

## Nhan NguyenUniversity of Montana – PhD Candidate

### Kummer subspaces of generic abelian crossed products(And other things I learned during a PhD here)

An element $$x$$ of a central simple algebra is called $$\textit{p-central}$$ if $$x$$ is central or $$x^p$$ is central but $$x^{p'}$$ is not for any $$1\leq p'<p$$. $$p$$-central elements play an important role in the structure and presentations of central simple algebras. In this talk we discuss abelian crossed products (to be defined), their $$p$$-central subspaces, and present some open problems in regarding them.

## Atish Mitra – Montana Tech

### Extension Theory: Large Scale vs Small Scale

Classical extension theory deals with extensions of continuous functions between topological spaces. In this talk we will discuss progress made in the extension theory of morphisms in various large scale categories, and will compare the results and techniques with that of classical extension theory. We will also outline an axiomatic viewpoint that unifies a classical extension result in topology with recent results in the coarse category.

## Ellie Bayat MokhtariUniversity of Montana – PhD Candidate

### Information Processing in Hippocampal Interneuron Synapses

Understanding of the brain as an extremely sophisticated information processing system has gained tremendous momentum in the past few decades and it continues to advance.

Information theory  proposed by Shannon in 1948 provides primary tools to uncover how the central nervous system (CNS) acquires, transforms, stores, and uses information to control the body in a complex environment. In this talk I will provide a brief overview of the basics of information theoretic functionals and describe how these concepts are applied to estimate the information transfer in  both deterministic and stochastic models of hippocampal synapses. The Stochastic model can be used to simulate the main sources of variability in synaptic transmission. In addition, we assume that a synapse serves as a dynamic memory buffer that can store and transfer information. However, it is clear that it cannot carry infinite amount of information about the temporal activity of presynaptic neuron. We address the question of how much further back in time a synapse can store and transmit information; in other words what is the capacity of a particular synapse in the transmission information.

### Department Picnic & Softball game

Friday, May 4, 5:00 p.m.
Bonner Park Band Shelter