# Maseeh Mathematics & Statistics Colloquium Series

## (Location: Urban Center Building room 204, except on March 8.)

# The upcoming colloquium:

### 3:15PM Friday, February 1, 2019

Bernardo Cockburn, University of Minnesota

*TBA*

**Abstract:**TBA.

# The 2018-2019 Colloquium Series:

### 3:15PM Friday, October 5, 2018:

Marilyn Carlson, Arizona State University*A research-based approach for improving precalculus teaching and learning*

view abstract view talk

### 3:15PM Friday, October 12, 2018:

Meir Pachter, Air Force Institute of Technology*Many-on-one pursuit*

view abstract view slides view talk

### 3:15PM Friday, October 19, 2018:

Ksenija Simic-Muller, Pacific Lutheran University*Teaching mathematics for social justice: the promise and practice*

view abstract view talk

### 3:15PM Friday, November 2, 2018:

Lalit Jain, University of Washington*Ordinal embedding*

view abstract view slides view talk

### 3:15PM Friday, November 16, 2018:

Luka Grubišić, University of Zagreb*Constrained PDE models on metric graphs: should we let the linear algebra solver do the heavy lifting?*

view abstract view talk

### 3:15PM Friday, February 1, 2019:

Bernardo Cockburn, University of Minnesota*TBA*

view abstract

### 3:15PM Friday, February 22, 2019:

Alexandre Tartakovsky, Pacific Northwest National Laboratory*TBA*

view abstract

### 3:15PM Friday, March 8, 2019, in **Market Center Building 316**:

Martin Levin, The Bridges Organization*The Platonic solids: geometric sculptures as an accessible introduction to group theory and projective geometry*

view abstract

### 3:15PM Friday, March 15, 2019:

Jyotishka Datta, University of Arkansas*TBA*

view abstract

### 3:15PM Friday, April 12, 2019:

Alan Demlow, Texas A&M University*TBA*

view abstract

### 3:15PM Friday, May 10, 2019:

Tavis Abrahamsen, Duke University*TBA*

view abstract

### 3:15PM Friday, May 31, 2019:

Neha Prabhu, Queen's University*TBA*

view abstract

### 3:15PM Friday, June 7, 2019:

Andrew Womack, Indiana University–Bloomington*Horseshoes with heavy tails*

view abstract

# Abstracts:

### October 5, 2018 (return)

Marilyn Carlson, Arizona State University*A research-based approach for improving precalculus teaching and learning*_{ }

The function concept is a central idea of precalculus and beginning calculus and is used for modeling in the sciences and engineering, yet many students complete courses in precalculus and calculus with weak understandings of this concept. Students who are unable to construct meaningful function formulas to relate two varying quantities have little chance of responding to novel applied problems, or understanding key ideas of calculus such as derivative, accumulation and the Fundamental Theorem of Calculus. I will share data that reveals how students might construct these and other critical reasoning abilities and understandings for learning calculus. I will share the research developed *Pathways Precalculus* student materials and teacher resources that provide the context for this research, and are resulting in large gains in student learning of the function concept and other foundational ideas for learning calculus. Results from using Pathways materials at 5 large universities will be shared and contrasted with other popular approaches to teaching precalculus mathematics.

### October 12, 2018 (return)

Meir Pachter, Air Force Institute of Technology*Many-on-one pursuit*_{ }

We consider swarm pursuit-evasion dierential games in the Euclidean plane where an evader is engaged by multiple pursuers and point capture is required. All the players have simple motion à la Isaacs and the pursuers are faster than the evader. It is shown that in group/swarm pursuit, when the players are in general position, capture is eected by one, two, or by three critical pursuers, and this irrespective of the size *N* (> 3) of the pursuit pack. Thus, group pursuit devolves into pure pursuit by one of the pursuers, into a pincer movement pursuit by two pursuers, or cornering by three pursuers, who isochronously capture the evader, a mènage à trois. The solution of the Game of Kind is obtained and critical pursuers are identified. Concerning the Game of Degree, the players' state feedback optimal strategies are synthesized and the Value of the game is derived.

### October 19, 2018 (return)

Ksenija Simic-Muller, Pacific Lutheran University*Teaching mathematics for social justice: the promise and practice*_{ }

Teaching mathematics for social justice centers mathematics as a tool for understanding the sociopolitical forces that shape the world around us. It addresses complex and sometimes controversial real-world issues (especially those related to economic and racial justice) through open-ended investigations. This approach to teaching is sometimes criticized as not being rigorous enough; and some also believe that mathematics is neutral and should not deal with controversial issues. In this talk, I will argue that addressing social justice issues in mathematics courses is timely and important; and that it can be rigorous and result in significant learning both of mathematics and the issues investigated. I will share examples of activities, assignments, and projects I have developed and used, and give some recommendations for beginning and sustaining this work.

### November 2, 2018 (return)

Lalit Jain, University of Washington*Ordinal embedding*_{ }

The standard problem of metric ordinal embedding concerns learning the embedding of *n* objects into a d dimensional Euclidean space by asking questions of the form "Is object *i* closer to object *j* than object *k*?" Ordinal embedding is a classical technique with roots in psychometrics. However, even though it has been in use for over 70 years, the proper theoretical foundations were lacking. In this talk, I'll discuss some recent results, algebraic questions that arise from this problem, various algorithms, and connections to standard matrix completion problems.

### November 16, 2018 (return)

Luka Grubišić, University of Zagreb*Constrained PDE models on metric graphs: should we let the linear algebra solver do the heavy lifting?*_{ }

In this talk we present two 1D models of an endovascular stent. Endovascular stents are biomedical devices made of struts used for treating arterial stenosis. The state of the system in both models is described by a vector valued function on a metric graph which satisfies a system of ODEs and a set of algebraic constraints. Both models are obtained by Γ-convergence from 3D nonlinear elasticity. As a result of asymptotic analysis, solutions are contained in a set of functions which are constrained by a set of algebraic constraints in the nodes of the graph and by requiring that the middle line of a strut does not extend. In the first model we place all constraints in the variational product space and build a finite element approximation there, whereas in the second model we study the problem in a large “free” product space and leave all of the constraints as a part of the system matrix to be removed by a linear algebra solver in a search of the solution. We will present convergence results for both models, but the much more puzzling question is which of the models will yield more efficient numerical methods. Namely, the second model yields a system matrix which is more than three times larger than in the first model. We present results of empirical comparison of the solution methods. We will further also study properties of the eigenvalue and the dynamical problem on a metric graph and discuss the solution methods and their efficiency. Finally, we will present validation experiments for the method by comparing it empirically to the 3D model solved by the standard legacy finite element code. This is a joint work with M. Ljulj, V. Mehrmann and J. Tambaca.

### February 1, 2019 (return)

Bernardo Cockburn, University of Minnesota*TBA*_{ }

TBA.

### February 22, 2019 (return)

Alexandre Tartakovsky, Pacific Northwest National Laboratory*TBA*_{ }

TBA.

### March 8, 2019 (return)

Martin Levin, The Bridges Organization*The Platonic solids: geometric sculptures as an accessible introduction to group theory and projective geometry*_{ }

Although the five Platonic solids may seem quite elementary, as one builds them up in one’s imagination and contemplates them, they become quite captivating. Since they represent all possible finite irreducible rotation groups of 3-space, they are fundamental to the structure of space. This talk will be accompanied by geometric sculptures that explore the relationships between the Platonic solids. They make concepts from group theory and projective geometry understandable by depicting them visually and vividly.

### March 15, 2019 (return)

Jyotishka Datta, University of Arkansas*TBA*_{ }

TBA.

### April 12, 2019 (return)

Alan Demlow, Texas A&M University*TBA*_{ }

TBA.

### May 10, 2019 (return)

Tavis Abrahamsen, Duke University*TBA*_{ }

TBA.

### May 31, 2019 (return)

Neha Prabhu, Queen's University*TBA*_{ }

TBA.

### June 7, 2019 (return)

Andrew Womack, Indiana University–Bloomington*Horseshoes with heavy tails*_{ }

In high dimensional problems, the usual two groups problem of model selection is impossible due to the combinatorial complexity of the model space. In recent years, a set of one group models that approximates the two groups problem have been developed. Of these, the Horseshoe prior is perhaps the most famous and places a Beta(1/2,1/2) prior on the local shrinkage parameters._{ }

There are many modifications and extensions of this framework, and we propose a new modification. Specifically, we model the local shrinkage parameter as a Beta(*p*,1-*p*) for each parameter under consideration in order to mimic the model selection problem. Placing priors on the *p* produces a prior distribution with extremely heavy tails that yields both very strong shrinkage of small signals and unbiased estimation of large signals, having overall better risk behavior. We also consider other prior specifications for *p* that provide superior inference in super-sparse settings.