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## 2021-2022 Academic Year Colloquium Schedule

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### September 16, 2021

 Title: Visual Representations of Natural Numbers using Geometric Patterns Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: Natural numbers can be visually represented by a geometric arrangement of simple visual motifs. This representation is not unique because any partition of an integer $n$ can generate at least one geometric pattern. Thus the number of partitions of $n$ is a lower bound on the number of geometric patterns. For example, there are 17977 partitions for the number 36; it is both a square number $(6^2)$ and a triangular number $(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8).$ Aesthetic considerations often favor patterns with some degree of symmetry, such as patterns that fix a single point or wallpaper patterns. A series of geometric designs for the numbers 1–100 were created to visually highlight some properties of each number. The designs use a variety of motifs and arrangements to provide a diverse yet cohesive collection. One application of these patterns is as a teaching tool for helping students recognize and generalize patterns and sequences. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### September 23, 2021

 Title: Opportunities in Pathogen War Gaming Speaker: Lauren Ancel Meyers Professor Department of Integrative Biology The University of Texas at Austin Austin, Texas Abstract: Video of a talk given for the Hertz Foundation on May 6, 2021. Dr. Lauren Ancel Meyers discussed the new Center for Advanced Pathogen Threat and Response Simulation (CAPTRS) and its pioneering vision to apply sophisticated war gaming technology to build robust health and socioeconomic lines of defense against future pathogen threats. CAPTRS has three core elements that differ from the science today: (1) an AI-based synthetic threat lab that generates a universe of pathogen threats; (2) a multi-disciplinary collaboration hub where researchers convene to develop solutions; and (3) the situation room where Pathogen War Gaming™ technology will be used to simulate real-time responses and their consequences. Location: ONLINE Time: VIRTUAL Citation Click for BibTeX citation Flyer Click for a printable flyer

### September 30, 2021

 Title: The Extraordinary Theorems of John Nash Speaker: Cédric Villani Member of Parliament, France Abstract: Fields medal winner Cédric Villani takes us through the very special world of mathematical creation of John Nash, who founded several new chapters of game theory and geometric analysis in just a few revolutionary contributions that seemed to come from nowhere. On 23 May 2015, John Forbes Nash tragically died in a taxi accident, just after receiving the most prestigious award that a mathematician can dream of, the Abel Prize. This tragic episode was the last event in a life which was so full of amazing events that Nash became an icon of human genius, recipient of the Nobel Prize and hero of a Hollywood movie looking at his life marked by mental illness. But most of all, Nash was a prophet who founded several new chapters of game theory and geometric analysis in just a few revolutionary contributions that seemed to come from nowhere. Fields medal winner, Cédric Villani takes us through this very special world of mathematical creation. A talk given at The Royal Institution on 29 April 2016. Video link Location: ONLINE Time: VIRTUAL Citation Click for BibTeX citation Flyer Click for a printable flyer

### October 7, 2021

 Title: The New Industrial Revolution Speaker: Abstract: This video illuminates disruptions to the world of work—AI, robotics, globalization and labor practices. The COVID-19 pandemic was a new driver of change; at the pandemic's height, unemployment flipped from its lowest rate in 50 years to its highest level in a century. This video is part of the three-part series Future of Work that explores monumental changes in the workplace and the long-term impact on workers, employers, educators and communities. Employment is part of the American Dream. Will the future provide opportunities for jobs that sustain families and the nation? See the additional Panel Discussion. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### October 14, 2021

 Title: Topological Modeling of Complex Data Speaker: Gunnar Carlsson Professor Department of Mathematics Stanford University Palo Alto, California, USA Abstract: One of the fundamental problems faced by science and industry is that of making sense of large and complex data sets. To approach this problem, we need new organizing principles and modeling methodologies. One such approach is through topology, the mathematical study of shape. The shape of the data, suitably defined, is an important component of exploratory data analysis. In this talk, we will discuss the topological approach, with numerous examples, and consider some questions about how it will develop as mathematics. A talk given at Joint Mathematics Meetings on 10 January 2018. Video link Location: ONLINE Time: VIRTUAL Citation Click for BibTeX citation Flyer Click for a printable flyer

### October 28, 2021

 Title: On Euclid's Game: The Fractal Structure of Losing Positions in the Calkin-Wilf Tree Speaker: Michael A. Jones Managing and Associate Editor Mathematical Reviews American Mathematical Society Ann Arbor, MI Abstract: Introduced by Cole and Davie in 1969, Euclid is a combinatorial game based on the operations of the Euclidean algorithm. Using geometry, I'll prove Cole and Davie's result that describes which player should win under optimal play and how this depends on the Golden Ratio. The play of the game can be described as moving along the branches of the Calkin-Wilf tree. I will review how the Calkin-Wilf tree provides an enumeration of the positive rational numbers. I will explain how Euclid is played and its relationship to the Calkin-Wilf tree. Finally, I will prove that the arrangement of the losing positions in the tree form a fractal. This work is joint with Michael Ivanitskiy and Brittany Shelton. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### November 4, 2021

 Title: Planning for Graduate Study in Mathematics and Computer Science Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: A degree in mathematics or computer science is excellent preparation for graduate school in areas such as mathematics, statistics, computer science, engineering, finance, and law. Come learn about graduate school and options you will have to further your education after graduation. Location: Palenske 227 Time: 3:30 Citation Click for BibTeX citation Flyer Click for a printable flyer

### November 11, 2021

 Title: Mathematical Devices at the Smithsonian: An Insider's View Speaker: Amy Shell-Gellasch Mathematics and Statistics Eastern Michigan University Ypsilanti, Mi Abstract: As an historian of mathematics living in the Washington D.C. area from 2012-2017, Dr. Shell-Gellasch was an independent researcher at the Smithsonian's National Museum of American History. In that capacity she researched mathematical items held in the Smithsonian's collections and created the online content for those items on the museum's website. She also contributed to the museum's blog "Oh Say Can You See". In this talk Dr. Shell-Gellasch will share the research she did at the Smithsonian and highlight several of her favorite items and the science and mathematics behind them. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### November 18, 2021

 Title: Graphs, Geometry and Gerrymandering Speaker: Moon Duchin Associate Professor of Mathematics Department of Mathematics Tufts University Medford/Somerville, Massachusetts, USA Abstract: What are all the ways to draw the lines, when you're dividing up a state to get representation? If you can't find them all, can you choose a good sample? I'll discuss some surprisingly simple questions about graphs and geometry that can help us make advances in policy and civil rights. A talk given on October 23, 2021 as part of the Gathering for Gardner (G4G) Celebration of the Mind event. Video link Location: ONLINE Time: VIRTUAL Citation Click for BibTeX citation Flyer Click for a printable flyer

### December 2, 2021

 Title: Robots Made for People — Social Robots that can Make a Useful Contribution to Society Speaker: Kerstin Dautenhahn Canada 150 Research Chair in Intelligent Robotics Electrical and Computer Engineering The University of Waterloo Waterloo, Ontario, Canada Abstract: Social robots are robots that are designed in a human-centered manner to interact with people efficiently, but using socially acceptable, 'natural', interaction styles, so that they can operate in human environments alongside and in cooperation with people. This is the key approach of the Social and Intelligent Robotics Research Lab (SIRRL) at University of Waterloo. Such robots are different from traditional manufacturing robots which had to be fenced in to avoid injury to human workers. Social robots need to be intelligent and adaptive to work in dynamic, unpredictable, human-inhabited environments, not treating humans as 'objects' but as social entities. Similarly, humans will respond to interactive robots socially. Social robots come in different sizes and shapes, from humanoid to animal-like to machine like appearances, each associated to different expectations of their skills and abilities. Rising costs in domains such as healthcare, therapy, the need for supporting healthy aging, providing inclusive education, as well as the predicted next industrial revolution involving robotic co-workers (co-bots) — creates a real potential for social robots to make a significant contribution to society. My talk will outline some of the main concepts, challenges, and provide examples of research in those areas, as well as field studies of deploying social robots. A talk given in 2021 as part of a seminar series from the University of a Waterloo's Department of Electrical and Computer Engineering. Video link Location: ONLINE Time: VIRTUAL Citation Click for BibTeX citation Flyer Click for a printable flyer

### February 3, 2022

 Title: Machine Learning and Computer Vision applied in Geological Data and PolSAR images Speaker: Mauricio Marengoni Professor Math and Computer Science Albion College Albion, MI Abstract: In this talk we will see some examples of Machine Learning techniques applied to geological data in the pre-salt area of the Brazilian coast in order to identify possible areas for oil and gas exploration. In the second part of the talk we will look at some PolSAR (Polarimetric Synthetic Aperture Radar images and we will see some problems on application of these images and talk on how computer vision can help in this area. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### February 17, 2022

 Title: Careers in Mathematics and Computer Science Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, MI, USA Abstract: A degree in mathematics or computer science is excellent preparation for employment in areas such as teaching, actuarial science, software development, engineering, and finance. Come learn about career opportunities awaiting you after graduation. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### February 24, 2022

 Title: Equilibria for the Wallet Game and the Paradoxical Role of Zero Speaker: Michael A. Jones Managing Editor/Associate Editor Mathematical Reviews American Mathematical Society Ann Arbor, MI Abstract: The wallet paradox was introduced by Martin Gardner in his Scientific American column. I will review the wallet game when players' fixed-mean distributions of money in their wallets are over nonnegative integer dollar amounts. Then, I will prove that there is no best strategy if the amount of money a player can carry in his or her wallet is unbounded. Curiously, the proof involves carrying no money (zero dollars) in one's wallet with high probability. However, if monetary amounts are bounded, then carrying no money is never part of a best strategy, as long as the mean is above one dollar. This talk is based on a paper of the same name, coauthored with Stanley R. Huddy and Michael Ivanitskiy. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### March 3, 2022

 Title: Can there be a physics of the brain? Speaker: Demian Cho Assistant Professor Physics Albion College Abstract: The brain is a distributive computational system with many neurons working together to create collective patterns. In this talk, I will describe two of my current effort to understand some aspects of the brain being done in Albion. Research done over the past couple of decades has indicated the brain may operate at the "edge of chaos," called a critical state. In biology, if the system of interest shows universal behavior, we typically try to explain it through the lens of evolution. So what are the evolutionary benefits of being in a critical state? The critical brain hypothesis posits that the brain functions near critical states to optimize its information processing capacity. In this talk, I will first introduce the hypothesis, then describe our work on synergistic information processing on a spiking neural network. The dynamics of the brain depend on the structure of the brain. Why then the brain has particular structures? What are evolutionary benefits? In the second part of the talk, I will describe the effort to address some of these questions by optimizing information processing under metabolic constraints. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### March 17, 2022

 Title: Cyber Analytic Development for Encrypted Network Traffic Classification Speaker: Dennis Ross, '08 Associate Group Leader Artificial Intelligence Technology and Systems MIT Lincoln Laboratory Lexington, MA Abstract: As encrypted network traffic becomes increasingly prevalent, cyber network operators are operating in the dark with regard to the kinds of traffic flowing through their networks. Machine learning (ML) techniques have recently emerged that can rapidly learn and provide contextual labels to encrypted traffic. However, as ML-based applications reach the hands of operators, they do not always understand the limitations of the underlying models and their predictions, as ML models often struggle or fail to communicate the confidence of their predictions. Without this nuanced understanding, operators may blindly trust a model's predictions, unaware that the model is only marginally confident or has never seen the input data during training. QUETAL is a software prototype that puts ML into the hands of cyber analysts to (1) enable them to train and deploy models where existing tools cannot make any predictions, and (2) provide contextualized uncertainties with each prediction that! allow analysts to filter visualizations according to their desired confidence level and understand where the model may be inaccurate. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### March 24, 2022

 Title: The Human Microbiome: Quantifying Volatility and Testing Community Level Associations. Speaker: Anna Plantinga Assistant Professor of Statistics Department of Mathematics and Statistics Williams College Williamstown, MA Abstract: The human microbiome, or the set of bacteria that live in and on a person, have been shown in the past decade to be associated with many facets of human health, including metabolism, immune function, and cognition. Longitudinal studies of the microbiome are becoming increasingly common as a way to investigate within- and between-subject variability in microbial profiles. The amount of instability, or volatility, in the microbial community has been associated with conditions such as irritable bowel disease, stress, and antibiotic treatment. However, there is no clear framework for quantifying the extent of volatility in the microbiome to enable association testing with outcomes of interest. We propose formal measures of qualitative (appearance or disappearance) and quantitative (abundance) volatility, explore patterns of volatility in real longitudinal microbiome datasets, propose a hypothesis testing framework, and assess performance across a range of study designs and simulation settings. We apply the approach to investigate microbiome volatility across irritable bowel syndrome subtypes. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### March 31, 2022

 Title: Escher, Coxeter, and a Poincare Disk Speaker: Eve Torrence Professor Emeritus Mathematics Randolph-Macon College Ashland, Virginia Abstract: In 1954 the artist M.C. Escher and the mathematician H. S. M. Coxeter met in Amsterdam and a decades long friendship and collaboration began. We will explore Escher's art and see how communication with Coxeter influenced his work. We will also see how Escher's art led Coxeter to explore geometric concepts. Along the way we will learn about hyperbolic geometry and discuss tessellation in Euclidean and non-Euclidean geometries. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer

### April 7, 2022

 Title: Working in Consulting Speaker: Murun Jargal, '20 Abstract: Consulting may seem like an elusive career path that can mean anything and take you anywhere. To shed light onto the matter, Murun will be sharing her experiences in Consulting, what projects she has worked on, and what technical skills the work demands. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation Flyer Click for a printable flyer