# Undergraduate Colloquia

**Math Club/Department Socials**

#### Fridays Fall 2021, 3-5pm (4-5pm on Colloquium Fridays)

#### Durham Science Center Room 164

UNO’s math socials are not just for math people to talk about math. They are for everyone to have a chance to get away from classes and socialize. For the fall 2021 semester they will be held on Fridays from 3-5pm. On the weeks of Colloquium Fridays, the time will be from 4-5pm. The events will be held outside the south entrance of Durham Science Center for the early part of fall where we will be playing a plethora of outdoor games such as yard bowling, corn hole, frisbee and much more! The first social will be held on September 17.

We would love for you to join the Math Club and Math Department for a gathering. This is a great opportunity to meet fellow students, discuss life and math, chat with professors, and meet the colloquium speakers. All are welcome to join!

## Fall 2021

*This colloquium series is aimed at undergraduate students who are in calculus or higher mathematics courses.*

#### Friday, October 22nd, 3:00-4:00 pm in DSC 115**, or available via Zoom**

**Dr. Margaret Doig, Creighton University**

**Title: Typical Knots: a story about your shoelaces (and DNA and quantum cryptography)**

**Abstract:** Knots appear everywhere in life - most familiarly, on shoelaces and ropes and jewelry, but they also hide in our DNA and lie behind some very interesting science in areas like polymer physics and quantum cryptography. We can study the knot as a mathematical object and ask all sorts of interesting questions about it. Sometimes we want to classify knots: If I draw a knot, and you draw a knot, when should we say they’re the same? If they’re different, how do we prove that? Can I list all the knots, at least all the ones that are “kind of small” (whatever that means)? Often we define and study things called “invariants”, numbers or polynomials or other things that we can calculate for a knot and which help us predict their properties or distinguish them from one another. Occasionally we’re more interested in the effects of the knots on whatever is being knotted: If your DNA is twisted up like the knot I just drew, will that affect your gene expression? Or, if I pick the wrong knot when I engage my quantum cryptographic security, will you be able to read my email? Finally, sometimes, we just want to know how common a knot is, or how likely it is to have certain properties, which can have far-reaching implications for how useful some of these properties are or how the knotted things in the world behave.

We’ll take a brief trip through knot theory and talk about all of these questions, culminating in a quick look at a basic example: if I randomly draw a knot, how many separate pieces of string will it have? (The experts might rightly object to this extremely casual terminology; a more precise way to phrase it could be: We’ll derive a generating function describing the distribution of the number of components of a randomly generated link grid diagram.)

**Bio:** Dr. Margaret Doig is an Assistant Professor at Creighton University. Her research interests focus on low-dimensional topology and have recently included studying the typical behavior of knots, understanding grid Floer homology, and bounding the Randic index of a graph. She lives in Omaha, NE, with her husband and three children. In her spare time, she volunteers with aviation emergency services, is a flight instructor, and owns an airplane.

#### Friday, October 8th, 3:00-4:00 pm in DSC 115**, or available via Zoom**

**Dr. Fabio Vitor, University of Nebraska - Omaha**

**Title: Let's talk about operations research, its impact, and some advancements in multidimensional search methods for optimization.**

**Abstract: **Operations research, also known as OR, have been used for decades to help organizations make better and smarter decisions. Operations research uses analytical methods to determine the most effective way to design and operate a system, usually, under conditions requiring the allocation of scarce resources. Most operations research models are categorized in the class of prescriptive analytics. During this talk, I will discuss some successful applications using operations research models and methods as well as the impact these applications have in our society. I will also briefly discuss some advancements in the class of multidimensional search algorithms to solve optimization models. Traditionally, optimization methods seek for an optimal solution by following a single search direction and solving a one-dimensional subspace problem at each step. In contrast, multidimensional search algorithms consider multiple search directions and solve a multidimensional subspace problem at each iteration.

**Bio:** Dr. Fabio Vitor is an Assistant Professor in the department of Mathematics at the University of Nebraska at Omaha. He joined the department and the university in 2019. He received a Ph.D. in Industrial Engineering and a M.S. in Operations Research from Kansas State University, and a B.S. in Industrial Engineering from Maua Institute of Technology, Brazil. Dr. Vitor also has around 10 years of industry experience. He worked for companies such as Monsanto, Kalmar (Cargotec Corporation), and Volkswagen. He also participated in the Google Summer of Code program as a student developer. His research interests include both theoretical and applied topics in operations research. His theoretical research creates algorithms to more quickly solve continuous and discrete optimization problems such as linear, nonlinear, and integer programs. Some of his applied research involves the application of optimization models and other operations research tools to reduce inventory costs, improve delivery routings, optimize nursery planting allocation, improve airport operations, and create strategies to overcome human trafficking. Dr. Vitor is passionate about optimization and eager to share his enthusiasm with his students.

**Friday, September 24th, 3:00-4:00pm in DSC 254, or available via Zoom**

**Title: All about pursuing a PhD in Mathematics: A panel of UNO grads.**

**Abstract:** Ever thought about graduate school in mathematics? Did you know that in mathematics you don't pay to go to graduate school? Graduate schools pay you!

What does the application process look like? What do you take during your first two years? Do you have any time to have fun?

Come participate in a discussion with 4 recent UNO graduates who are pursuing a PhD in a variety of mathematical areas (pure and applied). Sarah McCarty (UNO '20) is at Iowa State, Alex Fish (UNO '19) is at Southern Methodist studying Numerical Analysis, Gage Hoefer (UNO '20) is at Delaware studying operator theory and quantum information theory, and Grant Moles (UNO '20) is at Clemson University studying Commutative Algebra. The panelists will be joining us from their current home university by zoom.

If you can think of any questions ahead of time, please share them by email with Dr Elder elder@unomaha.edu so that he can pass them along.

*Join us immediately afterwards outside the South Entrance of the Durham Science Center for the Math Club Social!*

**Friday, September 10th, 3:00-4:00pm in DSC 115 and Zoom**

**Dr. Nicole Infante, University of Nebraska - Omaha**

**Title: Joy and Curiosity Inspired by Mathematical Media Morsels (View Flyer)**

**Abstract:** We watch movies and television to get away from work and studying. But as mathematics is a part of life, it sometimes creeps into our entertainment escapes. The mathematics may be integral to the plot, maybe a sidenote, or perhaps it's only in the background. How do you react when a bit of mathematics suddenly appears on the screen? When I unexpectedly find mathematics, I experience great joy and curiosity. This joy stems from that moment of revelation - Cool, there's some math! Curiosity takes over with digging deeper: This is math I know! How is it being used? Alternatively, this is math I don't know, I want to learn more! I will share some gems that have crossed my path on my journey as a mathematician that have sparked this joy and curiosity in me.

**Bio****: **Dr. Nicole Infante is the Director of Quantitative Reasoning and an Associate Professor of Mathematics. Her research interests are centered on student success and communication in the undergraduate mathematics classroom, particularly alternative forms of assessment and gesture use. Dr. Infante is very excited about the changes that are being made in first-year mathematics courses at UNO. Outside the classroom, you can find her baking, running, hiking, canoeing, camping, and generally exploring the world.

### Join us in DSC 115 or click here to watch on Zoom!

## Spring 2021

**Friday, April 23rd, 3:00-4:00pm **

##### Sponsors: Department of Mathematics (College of Arts & Sciences), Department of English (College of Arts & Sciences), Writer’s Workshop (College of Communication, Fine Arts and Media)

**Dr. Larry Lesser, The University of Texas at El Paso**

**Poetry and Mathematics**

**Abstract**: In honor of Poetry Month and National Mathematics and Statistics Awareness Month, we will compare, contrast, and integrate the products and processes of these beautiful realms. I’ll overview types of mathematical poetry and share examples written by me or by others. You can browse resources at http://www.ams.org/programs/students/math-poetry.

**Bio**: Dr. Larry Lesser is a UTEP Distinguished Teaching Professor and a Professor in the UTEP Mathematical Sciences Department. Professor Lesser (*hey, that rhymes!*) has degrees in mathematics, statistics, and mathematics education, has taught full-time for mathematics departments at three universities and a high school, worked as a state agency statistician, co-authored a math-for-liberal-arts textbook, won statewide and national teaching awards, won first-place awards in ASA, CAUSE, and MoMath song or poetry contests, won recent NSF grants, directed a teaching center that served an entire university, and was interviewed about his career in the March 2020 *Journal of Statistics Education*. His 115 papers connect mathematics/statistics to varied realms, including: language, culture, diversity, ethics, social justice, contemplative pedagogy, religion, lotteries, and music. Over 55 of his published poems (one of which was selected by Albuquerque’s Poet Laureate for a 2021 NEA Big Read event) are centered in mathematics/statistics. For more information: https://larrylesser.com/poet-larry-ate/

**Friday, April 2nd, 3:00-4:00pm**

**Randy Cone, Salisbury University**

**Title: Mathematics, Consistency, and Beethoven**

**Abstract****:** Where does Mathematics belong? One perspective is: Mathematics is an attempt to investigate the nature and content of certain types of self-consistent systems. With this in mind, we explore self-consistency within the art of Beethoven by examining a series of related mathematical visualizations. Prior to the presentation, please find the horn calls in the first movement of Beethoven's Fifth Symphony.

**Bio:** Dr. Randall E. Cone is an Associate Professor of Mathematics and Computer Science at Salisbury University. He is the recipient of the 2019 University System of Maryland Board of Regents 'Excellence in Teaching' Award. His current research programs are varied, including: Blockchain Consensus Algorithms, Feature Extraction in Semi-Structured Data, and Mathematics within the Digital Humanities. Dr. Cone loves to share ideas with his students, colleagues, and friends - whether those ideas are mathematical, musical, artistic, scientific, or chicken.

Meet the speaker ahead of his presentation at the Math Club Social from 2:00-3:00 pm on Gather.Town!

**Friday, February 26th, 3:00-4:00pm**

##### Ezra "Bud" Brown, Virginia Polytechnic Institute and State University

##### Phoebe Floats!

Join the UNO Mathematics Department, the Nebraska Gamma Chapter, and Dr. Ezra "Bud" Brown to celebrate our new inducties to the National Mathematics Society Pi Mu Epsilon.

**Abstract: **This is a story that begins with a remark about Phoebe, a moon of Saturn, which leads to a question about floating bodies. Along the way, we'll encounter Archimedes' take on this question, solids of revolution, cubic equations, Newton's method, the behavior of Newton's method under iteration, and repelling periodic points. There is a surprise ending!

**Bio:** Ezra (Bud) Brown grew up in New Orleans, has degrees from Rice and LSU, taught at Virginia Tech for 48 years, and retired in 2017 as Alumni Distinguished Professor Emeritus of Mathematics. He has done research in number theory, combinatorics, and expository mathematics -- but one of his favorite papers is one he wrote with a sociologist. He is a frequent contributor to journals of expository mathematics, and has been known to impersonate Alex Trebek at the spring meetings of the MD-DC-VA section of the Mathematical Association of America. He and the late Richard Guy are the authors of the Carus Monograph “The Unity of Combinatorics” that was published by the American Mathematical Society in May 2020. Bud enjoys baking biscuits (they're better if you use softened butter), singing (anything from opera to rock’n’roll), playing jazz piano, and watching an occasional bird.

View a recording of Dr. Brown's colloquium (and our Pi Mu Epsilon inducion) here!

**Friday, February 12, 3:00-4:00pm. This talk is being organized with the Student Chapter of the Association for Computing Machinery.**

**Zachary Sam Zaiss, Quantitative UX Researcher at Google**

**Using k-means clustering to identify common patterns in product usage**

**Abstract: **In tech companies, the User Experience (UX) discipline is concerned with understanding product users’ needs and motivations, so the product can be shaped to meet those needs. One way UXers keep users’ needs front and center is via **personas** -- profiles of prototypical users, based on interviews and observations. Now in the age of big data, a question emerges: Can we observe unique persona behaviors in our product usage data? And how closely will analysis on that data align with what we learn from qualitative interviews?

In this talk, Zach will introduce a machine learning method called k-means clustering, and discuss some of the core concepts behind the technique. He’ll also discuss how k-means clustering, and methods like it, are presently used by many tech companies to better understand usage patterns in their products.

**Bio: **Zachary Sam Zaiss is an Omaha native and alum of UNO (class of 2004), where he studied Computer Science, Math, and Psychology. His subsequent studies and career have been all about finding a blend between those three fields. After graduating UNO, Zach attended Carnegie Mellon University where he earned his Master’s degree in Human-Computer Interaction. Zach then worked at Microsoft as User Experience (UX) Researcher for 13 years. As online Data Science programs started gaining popularity, Zach enrolled in UC Berkeley’s Master of Information and Data Science (MIDS) program, leading him to pivot his career to a mix of UX and Data Science. Today, Zach leads a team of Quantitative UX Researchers at Google, working on the Google Cloud Platform.

**Friday, January 29th, 3:00-4:00pm**

**Melissa Emory, University of Toronto**

**Title: The Langlands Program: A grand unified theory**

**Abstract: **The Langlands program connects fields that do not appear to be related; such as algebra, geometry, analysis, and physics. Due to its wide scope and deep results, the Langlands program is considered a grand unified theory. In this talk we will give a general overview and discuss some of our recent results, time permitting.

**Bio:** Seeking a career change, Melissa Emory returned to college in her thirties and began a night course (Calculus 1) at UNO in 2007 and soon found herself working on Honors Calculus problems when a quiet moment could be found, even in the middle of the night. She decided to pursue a mathematics degree after encouragement from UNO faculty and attending the Nebraska Conference for Undergraduate Women in Mathematics at UNL. Melissa completed undergraduate research, partially supported by NASA EPSCoR minigrants, which led to support from members of the broader mathematics community. Once her youngest child left for college, she began her PhD program in mathematics at the University of Missouri where in 2018 she earned her PhD and won the Blumenthal Prize for her dissertation. She is currently a National Science Foundation postdoctoral fellow at the University of Toronto under the direction of Professor James Arthur. Melissa earned her BS in 2011 and MA in 2013 from UNO.

**Abstract: **Neural networks have been successfully applied to complex predictive modeling tasks in areas such as computer vision and natural language processing. On the one hand, they have been shown to be a very powerful mathematical modeling tool: a neural network can model a piecewise-linear function with an exponential number of pieces with respect to its number of artificial neurons. On the other hand, we may still need an unreasonably large neural network in order to obtain a predictive model with good accuracy in many cases. How can we reconcile those two facts?

In this talk, we apply traditional tools from operations research to analyze neural networks that use the most common type of artificial neuron: the Rectified Linear Unit (ReLU). First, we investigate both theoretically and empirically the number of linear regions that networks with such neurons can attain, which reflect the number of pieces of the piecewise linear functions modeled by those networks. With respect to that metric, we unexpectedly find that sometimes a shallow network is more expressive than a deep network having the same number of neurons. Second, we show that we can use optimization models to remove units and layers of a neural network while not changing the output that is produced, which thus implies a lossless compression of the network. We find that such form of compression can be facilitated by training neural networks with certain types of regularization that induce a stable behavior on its neurons.

This talk is based on papers coauthored with Christian Tjandraatmadja (Google Research), Srikumar Ramalingam (Google Research and The University of Utah), and Abhinav Kumar (Michigan State University).

**Bio: **Thiago Serra is an assistant professor of analytics and operations management at Bucknell University's Freeman College of Management. Previously, he was a visiting research scientist at Mitsubishi Electric Research Labs from 2018 to 2019, and an operations research analyst at Petrobras from 2009 to 2013. His current work focuses on theory and applications of machine learning and mathematical optimization. He has a Ph.D. in operations research from Carnegie Mellon University's Tepper School of Business, and received the Gerald L. Thompson Doctoral Dissertation Award in Management Science in 2018. During his PhD., he was also awarded the INFORMS Judith Liebman Award and a best poster award at the INFORMS Annual Meeting in 2016. His work on neural networks has been published at ICML, AAAI, and CPAIOR, and received a best poster award at the Princeton Day of Optimization in 2018, as well as a third place in the poster competition of the LatinX in AI workshop at ICML 2020.

#### Friday, November 13, 3:00-4:00pm

##### Daniel Miller, Data Scientist at Microsoft

##### Mangrove - what watery trees and automated statistical analysis have to do with each other

**Abstract: **Running controlled experiments on a diverse array of online and offline products is hard. Analyzing the results in a trustworthy and democratic way is even harder! I'll spend some time motivating the whys and hows of controlled experimentations (A/B testing) in the tech sector, then talk through a framework I built, called Mangrove, for automatically analyzing the results of A/B tests.

**Bio: **Dan Miller started out school hoping to be a math professor, and got his undergraduate degree at UNO. While working on a math PhD at Cornell, he switched gears, and is now a data scientist in the Azure Machine Learning team at Microsoft. He lives in the Seattle area with his wife and cat.

#### Friday, October 30, 3:00-4:00pm

##### Nan Dong, Thomas Flaherty, and Janna Hart

##### Data Science in Practice: Alumni Discussion Panel

Join us for a discussion with three UNO Math: Data Science Alumni about their experiences applying Data Science in their respective fields!

**Bios:**

Nan Dong is a Model Validation Analyst II of Enterprise Data Management at First National Bank of Omaha. She received her bachelor’s degree in Healthcare Administration (minor in Mathematics) from UNO, and master’s degree in Mathematics with Data Science Concentration from UNO too. Nan started at First National Bank as an Intern in Decision Sciences Department, then joined the Model Validation team as an analyst. Her current job responsibility is to monitor and validate Internal & External statistics models. In the spare time, her favorite thing is to try new restaurants in Omaha area.

Thomas Flaherty is a former visual and UI/UX designer focusing on intuitive interactive visualizations, model building, and all things EHR (electronic health records) data. Thomas has earned a BS and MS in Mathematics with a concentration in Data Science from the University of Nebraska Omaha. When away from the keyboard, you might find Thomas in front of a plethora of synthesizers, on a bicycle, and/or drinking copious amounts of coffee.

Janna Hart is currently the Director of Data Science at Mutual of Omaha and the vice president of American Statistical Association Nebraska Chapter. She studied Mathematics and received my bachelor’s degree from UNO in 2005 – She began working at Mutual of Omaha in the same year as an Actuarial Analyst. Janna held several positions in several different areas at Mutual over the years. She started in product development where her responsibilities included creating reports and metrics for different levels of management. After a few years, she transitioned to focusing on Medicare Supplement product, which is a core product of the company. She then moved to Valuation where she was a product owner for a large, mulit-year, data warehousing project. Upon completion of that project, she moved to Internal Audit to have full access to all aspects of business including, Insurance, Banking, Real Estate, Security, Mortgage, etc. It was there she began to see a shift in the skillset required and decided to return to take classes at UNO in the area of Data Science. Since taking Data Science classes at UNO, she has become Director of Data Science. With the help and support of others, she created a Data Science Internship program, initiated a Data Science Community of Practice, hired multiple Data Science Interns, and created a team of 4 Data Scientists and 5 Business Intelligence Developers who support Internal Audit, Enterprise Risk Management, Compliance, Special Investigations and Legal.

#### Wednesday, October 28, 6:00-7:00pm [Hosted by the UN Robotics Club]

##### Dr. Travis Deyle, founder and CEO of Cobalt Robotics

##### A talk by Dr. Travis on his life, career, and experiences in the field of robotics

Dr. Travis Deyle is a UNOmaha Alumni. He obtained dual degrees from the Peter Kiewitt Institute -- CS & Math double-major from UNOmaha and EE & CompE double-major from UNL in 2004 & 2005.

Following his graduation from University of Nebraska, Travis worked on nuclear "stuff" at Sandia National Laboratories. He then obtained his Masters & PhD from Georgia Tech, where he built some of the first mobile robots to operate in real homes -- fetching & delivering medication for older adults and helping people with motor impairments to shave their face. Subsequently, he built cyborg dragonflies as a postdoc at Duke University -- building custom chips to read out the brain signals from dragonflies in flight. Travis then went on to coordinate R&D efforts for medical implants at GoogleX Life Sciences -- an endeavor that became the first independent Alphabet spinoff, now now called Verily Life Sciences. Dr. Deyle was named a MIT Technology Review "Top Innovators Under 35" in 2015.

Currently, Travis is the founder and CEO of Cobalt Robotics, which creates service robots that provide benefits across a host of shared services: physical security, facilities management, and employee health & safety. Under Dr. Deyle’s leadership, the Cobalt Robotics has deployed robots all over the world with clients ranging in size from small startups to large Global-1000 multinationals, making Cobalt the leader in security robots. The company is based out of Silicon Valley and has raised more than $55 Million from world-class investors such as Sequoia Capital, Bloomberg Beta, and Toyota Research.

**Abstract:** Topological Data Analysis (TDA) provides a robust set of tools that have theoretical and practical capacities to understand the "shape of data" in any number of dimensions and on multiple scales, placing the concept of shape, as applied to data analysis, on a solid mathematical foundation. In the past few years, TDA tools have found numerous applications in many fields including neuroscience, bioscience, machine learning, data visualization, in the study of triangulated manifolds, and time-varying data, among others. We show new developments that allow us to utilize persistent homology in object recognition. In particular, We use persistent homology along with functions that arise naturally when studying graphs and meshes, such as the eigenfunctions of the Laplacian and PageRank, to study similarity amongst geometric and combinatorial objects.

**Bio: **Mustafa Hajij is an Assistant Professor of Data Science at the Department of Mathematics and Computer Science at Santa Clara University. He received his Ph.D. from Louisiana state university in 2015. He was a postdoctoral researcher at the University of South Florida between 2015 and 2017. He then spent a year as a postdoc scholar at the Department of Computer Science and Engineering at Ohio state university and another year as a research scientist at KLA Corporation. His current research interests lie in the interaction between deep learning and geometry. He wrote over 40 articles on various topics in Mathematics, Computer Science, and Engineering.

#### Friday, September 18, 3:00-4:00pm

##### Gary Towsley, Professor Emeritus from SUNY Geneseo

##### The Solution of the Cubic Equation in Sixteenth Century Italy. What Actually Happened?

**Abstract:** During the first half of the Sixteenth Century, mathematicians in Italy solved a problem that had been worked on for thousands of years - namely solving a cubic equation or finding a root of a cubic polynomial. They also managed to solve the quartic equation also. There is an interesting story as to how these discoveries occurred and the conflicts between the discoverers. That is not the story in this talk. Instead we will look at the actual mathematical solution and see how it came about through the combination of two very different kinds of mathematics.

**Biography:** Gary Towsley earned his Ph.D. in Mathematics from the University of Rochester in 1975, studying compact Riemann surfaces. He began teaching at SUNY Geneseo in 1974 and retired as Distinguished Teaching Professor of Mathematics in June 2020. His mathematical interests are in the areas of Algebraic Geometry, compact Riemann surfaces, Number Theory, and the History of Mathematics. In 2000 he received the Deborah and Franklin Tepper Haimo Award for Excellence in College and University Teaching from the Mathematical Association of America. Recipients of this award were asked to give a talk at the Joint Math Meetings held in January. Dr. Towsley spoke on "What does Dante have to do with Mathematics?"

View the slides from Dr. Towsley's presentation!

## Fall 2019

**Friday, November 15, 3:00 PM, DSC 115**

##### Jacob Cleveland

##### A Pseudo-Metric on Artifical Neural Networks

Abstract: Artificial Neural Networks have shown great potential to solve many difficult problems, including image classification, language translation, and medical diagnosis. The main reason for this is that they are quite good for finding patterns in large datasets. However, the internal structure of neural networks is not well understood. We attacked this problem via Topological Data Analysis (TDA), specifically using Persistent Homology, the go-to tool of TDA, and the Discrete Wasserstein Metric to study a potential method of comparison of Neural Networks. This talk will cover the basics of Dense and Convolutional Neural Networks, Persistent Homology, and the Discrete Wasserstein Metric.

This last summer, Jacob was an intern in the Space Communications and Navigations branch of NASA'S Glenn Research Center in Cleveland, Ohio. While there, they worked to serve the cognitive communications projects by studying Artificial Neural Networks. Specifically, through the use of Topological Data Analysis, they investigated methods by which to compare and classify neural networks using the topological structure they exhibit. This involved computing persistent homology for neural networks and comparing the peristence diagrams using the Wasserstein Metric, Fisher Information Metric, and Relative Entropy. The research is ongoing and Jacob is continuing the work through a NASA Nebraska Space Grant Fellowship this fall and spring.

**Friday, November 8, 3:00 PM, DSC 115**

##### Sarah McCarty

##### Sampling to Characterize Cantor Sets

Abstract: Generalized Cantor sets are special sets of numbers between 0 and 1 with a fractal-like structure. They each have a Cumulative Distribution Function (CDF), F(x), where F(x) is the fraction of the set less than x. These functions also have a fractal-like structure. The talk looks into the question of “How many points do we need to know on the graph to be able to graph the whole thing?” The talk will also briefly cover getting involved with Research Experiences for Undergraduates (REUs) in general.

The research was conducted during a summer 2019 REU at Iowa State University. Dr. Eric Weber, assisted by graduate students, advised. The project was funded by the National Science Foundation (NSF).

**Friday, October 11, 3:00 PM, DSC 115**

##### Alan Hylton, Research Computer Engineer, NASA Glenn Research Center

Alan has worked for the NASA Glenn Research Center in Cleveland since 2006 as an intern, contractor, and a federal employee. Alan’s work began in the Biosciences and Technology Branch, and in 2009 he began work in communications where he focused on laser communications and networking research. He looks forward to meeting students and talking about internships, opportunities, and attempting to answer questions.

##### NASA's Gaze Towards Mathematics

Abstract: In this talk, we will discuss some applications of algebra, topology, and algebraic topology to engineering problems at NASA. We will take a tour of some of the work that has been done, take a look upon the tremendous amount of work yet to be done, and talk about what can be done in the intersection of computer science, mathematics, and engineering.

**Friday, October 4, 3:00 PM, DSC 115**

##### Brad Horner, UNO Graudate Student

##### Adventures in S^{3}

Abstract: A one-dimensional sphere is just a circle in the plane, a two-dimensional sphere is the familiar one sitting inside three dimensions. What does the three-dimensional sphere within four-dimensional space look like? This is an expository talk with two people in mind: general audiences interested in what math in four dimensions looks like, and those interested in learning about algebraic topology. Some textbook topological constructions are explained - gluing, joins, smash, bundles - with fun pictures. How to visualize or reason about goings-on in 4D is discussed with cross-sections & stereographic projection, as well as how quaternions model 3D & 4D rotations. Connections are made to more advanced topics, like the exotic 7-sphere and stable homotopy groups. Artwork of the Hopf bundle (renderings of the Bloch sphere parametrizing qubits) is showcased.

**Friday, September 6, 3:00 PM, DSC 115**

##### Dr. Gregory Gelfond, Research Fellow College of IS&T at UNO

##### Developing Mathematical Identities through Authentic Problem Solving

In the present day, the role of the university and the meanings of words such as science and engineering have become blurry. This has profound ramifications in many areas but of particular interest is in how we understand these various fields of study and the interplay between them. In this talk I present my views on the western scientific tradition, the distinction between science and engineering, and the nature uniqueness of computing science as a scientific discipline.

**Friday August 30, 3:00pm, DSC 115**

##### Dr. Cory A. Bennett, Associate Professor of Education at Idaho State University

##### Developing Mathematical Identities through Authentic Problem Solving

Effectively implementing problem solving poses many challenges especially when the focus of learning mathematics centers on procedures or discrete concepts and when students do not see themselves as capable student mathematicians. As a result, problem solving can be a difficult skill to teach across K-16 classrooms. There is often a lack of time during the school day and students do not typically understand the actual nature and process, which requires critical thinking, persistence, organization, and flexible thinking. This presentation shares the initial findings from an on-going project examining the extent to which one problem solving structure helped students from diverse backgrounds and cultures better understand what it means to be a mathematician and do mathematics through authentic experiences.

**All are welcome to join!**

## Spring 2019

**Friday April 12, 3:00pm, DSC 115**

##### Meggan Hass, University of Nebraska - Lincoln

##### Multiplication - More Than Meets the Eye

Abstract: It’s easy to think that at this point in your life, you know all there is to know about elementary mathematics. After all, how many different ways are there to multiply? In this talk, we will first explore the type of knowledge that exists at the intersection of purely mathematical content and pedagogical knowledge. In particular, we will investigate the idea that there is more to know about multiplication and division than pure math experts know. In the second part of the talk, we will look at examples of this type of knowledge by discussing scratch work from students taking a standardized assessment. This work comes from an internship with Educational Testing Service (ETS) in 2019. The goal is that we all leave the talk appreciating the nuance in what mathematics students know and can do.

**All are welcome to join! **

*Talk to be preceded by a panel on PhD programs in Mathematics, 2:15-2:45pm in DSC 208.*

**Friday March 29, 3:00pm, DSC 115**

##### Shane Buresh, Nebraska Commission for the Blind & Visually Impaired

##### Diane Ditmars, Retired Teacher of the Visually Impaired & UNL Adjunct Lecturer for Intermediate Braille (Math Braille Code & Tacticle Graphics)

##### Getting In Touch with How the Blind and Visually Impaired do Math

Like most things in the world, mathematical endeavors and other stem activities are traditionally oriented to the sense of sight. Graphics and spatial representation of concepts dominate the methods of computation and task completion. What if someone needing to complete such tasks for work or pleasure lacks functioning sight to be successful at performing these tasks in those traditional ways? Do we say, “That’s too bad” or “I guess the visually impaired and blind can’t do math”? Too often those in society do, however, it is a myth fueled by lack of information and not reality that seems to make these statements seem true.

Please make plans to join Shane Buresh, Transition Coordinator from NCBVI and former blind math teacher and Diane Ditmars, retired teacher of the visually impaired and adjunct lecturer for Intermediate Braille which includes math Braille Code and Tactile Graphics" for the UNL teacher training program, for a colloquium discussion and hands on demonstration, that will illustrate the true capacity of the blind and visually impaired to participate in fields often thought by many to be off-limits to this population. The presenters will share strategies, stories and examples of successful methods that will leave the attendee with a fresh perspective and an ever-changed paradigm shift which demonstrates that sight is just one and certainly not the only sense that everyone can use to insure success at math, stem or whatever they desire.

**All are welcome to join! **

**Monday March 11, 2:30pm, DSC 115**

##### Dr. Adam Levine, Duke University

##### The Topology of Manifolds

Topology is a field of geometry that deals with the classification of the shapes of spaces up to continuous deformation. For instance, a topologist considers a sphere and a blob to be equivalent, and likewise a doughnut and a coffee cup, whereas the sphere and the doughnut are inequivalent. Intuitively, the distinction is that the doughnut has a hole while the sphere does not; topology gives us the tools to make this distinction rigorous. In this talk, I will survey the history of this exciting field, ranging from the 19th century to the present day, and describe some of the strange things that occur when we pass from surfaces to spaces of higher dimension. I'll also discuss some applications of topology to questions including the knotting of DNA, the shape of the universe, and the analysis of big data.

**All are welcome to join! **

**Friday March 1, 3:00pm, DSC 115**

##### Dr. Melissa Emory, University of Toronto

##### Connections Between Zeta functions, L-functions, and Integrals

The Langlands program connects fields that do not appear to be related; such as algebra, geometry, analysis, and physics. Due to its wide scope and deep results, the Langlands program is considered a grand unified theory. In this talk we will discuss our recent result in the Langlands program which connects a certain integral with zeta functions and L-functions.

**All are welcome to join! **

**Friday February 15, 3:00pm, DSC 115**

##### Dr. Xiao Xiao, Utica College

##### How to differentiate a number?

In this talk, we will introduce an alternative way to differentiate a number and discuss some basic properties of this new differentiation. In particular, we will see how solving certain differential equations in this setting is related to some of the most famous unsolved conjectures in number theory.

**All are welcome to join! **

**Friday February 1, 3:00pm, DSC 115**

##### Dr. Nicholas Kass, University of Nebraska at Omaha

##### A Linear Introduction to Nonlinear Waves

Partial Differential Equations (PDEs) are useful for modeling and understanding a wide variety of physical phenomena and also offer many unique and rewarding challenges for both mathematicians and those in computer science. In this talk we will derive several classical PDEs including the transport, heat, and wave equations from their physical principles and visualize the solutions with a variety of tools. Along the way we will discover that even simple equations can produce oftentimes unexpected difficulties, and it is these challenges which will serve as an introduction to several notions integral to a modern treatment of PDEs including weak derivatives, weak solutions, and energy methods.

With this background we will motivate a nonlinear generalization of the wave equation afforded by the p-Laplacian and ascertain its unique behavior in the presence of a variety of source and damping terms.

**All are welcome to join! Flyer**

**Friday January 18th, 3:00pm, DSC 115**

##### Dr. Gregory Gelfond, University of Nebraska at Omaha Computer Science Department

##### On the Western Scientific Tradition and the Uniqueness of Computing Sciences

In the present day, the role of the university and the meanings of words such as science and engineering have become blurry. This has profound ramifications in many areas but of particular interest is in how we understand various fields of study. In this talk I present my views on the western scientific tradition, the distinction between science and engineering, and the nature and uniqueness of computing science as a scientific discipline.

**All are welcome to join! Flyer**

## Fall 2018

**November 16, 3:00pm, DSC 115**

##### Dr. Jim Lewis, University of Nebraska at Lincoln

##### Opportunities for Math Majors

Jim Lewis recently returned to Nebraska after serving as Acting Assistant Director for the Directorate for Education and Human Resources at the National Science Foundation. Join Jim for a conversation about opportunities for math majors.

Jim Lewis is the Aaron Douglas Professor of Mathematics at the University of Nebraska-Lincoln and Director of the UNL Center for Science, Mathematics, and Computer Education.

**All are welcome to join! Flyer**

**October 26, 3:00pm, DSC 115**

##### Dr. Rebekah Yates, Houghton College

##### A Cemtury at Home on the (Numerical) Range

One hundred years ago, the German mathematician Otto Toeplitz published a paper in which he defined the Wertvorrat, a subset of the complex plane that captures some of the essential information about bounded linear operators on Hilbert spaces. In the ensuing century, mathematicians of many specialties have studied this set that we today call the numerical range. Restricting our focus to the context of matrices, we will explore some of the properties of this fascinating set and some current research in this area. We'll introduce/review linear algebra topics as needed along the way so that everyone can feel at home on the numerical range. Flyer

**October 4, 2:30pm, DSC 111**

##### Dr. David Wright, Washington University - St. Louis

##### Connections Between Mathematics and Music

**Abstract: **It has been observed that mathematics is the most abstract of the sciences, music the most abstract of the arts. Mathematics attempts to understand conceptual and logical truth and appreciates the intrinsic beauty of such. Music evokes mood and emotion by the audio medium of tones and rhythms without appealing to circumstantial means of eliciting such innate human reactions. Therefore it is not surprising that the symbiosis of the two disciplines is an age old story. The Greek mathematician Pythagoras noted the integral relationships between frequencies of musical tones in a consonant interval; the 18th century musician J. S. Bach studied the mathematical problem of finding a practical way to tune keyboard instruments. In this talk, some musical and mathematical notions will be brought together.

**Biography: **David Wright is Professor Emeritus and former Chair in the Department of Mathematics at Washington University in St. Louis. He received his Ph.D. in Mathematics from Columbia University. A leading researcher in the fields of affine algebraic geometry and polynomial automorphisms, he has produced notable publications in these areas and has been an invited speaker at numerous international mathematics conferences. He served on the Council of the American Mathematical Society, and chaired its Committee on Education. As a musician, David is an arranger and composer of a cappella music, where his work often integrates the close harmony and barbershop styles with jazz, blues, gospel, country, doo-wop, and contemporary a cappella. He serves as Associate Director of the award winning male chorus Ambassadors of Harmony, from St. Charles, Missouri. David designed and teaches a university course in Mathematics and Music.

## Spring 2018

#### Friday April 13, 2:30pm, DSC 254

##### Dr. Wendy Smith, University of Nebraska-Lincoln

##### Enacting and supporting institutional change aimed at implementing active learning in undergraduate mathematics

**Abstract: **UNL has worked to reform precalculus through calculus 2 (P2C2) since 2011, and has seen significant increases in passing rates (e.g., College Algebra rose to and has been sustained at 80% after a historical passing rate of around 60%). The department undertook reforms holistically and systematically, in collaboration with a national network of faculty all working to change the culture around P2C2 courses. Dr. Smith will share what UNL has done, what the impact of the changes have been, the current work, and next steps.

**Biography: **Dr. Wendy Smith is the Associate Director of UNL's Center for Science, Mathematics and Computer Education. As a former middle level mathematics teacher and current mathematics education researcher, Dr. Smith's research has focused on studying change at the individual (attitudes, beliefs and knowledge), group (impact of professional development on teachers and their students), and institution levels (education policy and institutional change).