Math Mondays

A weighted shift of multiplicity two with weight sequence {λn} is a bounded linear operator T on l² such that

T(x0, x1, x2, . . .) = (0, 0, λ0x0, λ1x1, λ2x2, . . .),

For all n ≥ 0 where λn ∈ C. The square root of T is a bounded operator Q such that Q² = T. It is known that the weighted shift of multiplicity one do not have any square root. This is not the case when we consider a weighted shift T of multiplicity two. In this talk, we present necessary and sufficient conditions on the weight sequence so that the set of square roots of T is non-empty. We show that when such conditions are satisfied, the set contains a certain special class of operators. We also present a complete description of all operators in the set of square roots of T.

Join us on Monday, Jan. 27, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Visiting Assistant Professor of Mathematics Tomas Miguel Rodriguez. We hope to see you there!

Sea ice is a crucial component of the Earth’s climate system, affecting the ocean circulation, the atmospheric temperature, and the marine ecosystems. However, sea ice is not a simple solid material; it is a complex mixture of ice crystals, brine pockets and air bubbles, that changes its structure and properties depending on the environmental conditions.

In this talk, Noa Kraitzman, senior lecturer in applied mathematics at Macquarie University, will explore how we can model and understand the behaviour of sea ice at different scales, from the microscopic interactions of ice and salt to the macroscopic effects of heat transfer and fluid flow. She will present two mathematical models: a thermodynamically consistent model for the liquid-solid phase change in sea ice that incorporates the effects of salt, using multi-scale analysis to derive a quasi-equilibrium Stefan-type problem. And a new rigorous derivation of bounds on the sea ice effective thermal conductivity obtained through Padé approximates and using Stieltjes integrals.

Join us on Monday, Feb. 3, at 3:10 p.m. in Hayes 109 to hear this exciting presentation. We hope to see you there!

Declare your love for math! Celebrate with snacks and treats during this special Math Monday event. We will also be doing fun, themed math activities for the occasion. Take this opportunity to declare your math major or math or stats minor during the celebration!

Join us on Monday, Feb. 10, at 3:10 p.m. in Hayes Hall 109 for this exciting celebration of mathematics. We hope to see you there!

What are the acute angles in a 3-4-5 triangle? Are they nice, say rational in degrees? We'll use the Gaussian integers — the square lattice in the complex numbers — to study those questions. Like the ordinary integers, the Gaussian integers possess unique factorization. The existence of the greatest common divisor is the crucial step in proving that fact. We present a simple geometric argument for that step using repeated subtraction. With unique factorization in hand, we characterize the Gaussian integers having a positive integer power that is real. That characterization sheds light on the nature of the acute angles in Pythagorean triple triangles.

Join us on Monday, Feb. 24, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Jack Calcut, professor of mathematics at Oberlin College and Conservatory. We hope to see you there!

Stallings introduced the concept of Stallings to aid in the study of free groups, which creates a "folded graph" associated with a subgroup of a free group. Dani-Levcovitz adapted this concept to the setting of Right-Angled Coxeter Groups. In this talk, we will introduce Coxeter Groups and folded graphs, and demonstrate how to use these graphs to compute intersections of subgroups of Coxeter groups.

Join us on Thursday, March 20, at 11:10 a.m. in Tomsich 101 to hear this exciting presentation from Jake Murphy, visiting assistant professor of mathematics at The College of Wooster. We hope to see you there!

Biostatistics remains a relatively unknown field yet is a great career opportunity for undergraduate students studying mathematics, statistics, biology, psychology — really anyone interested in how mathematical modeling can be applied to human health. Biostatistics is also experiencing competition with the growing field of data science, although there is great overlap between the two disciplines. The first half of this talk will provide information on the biostatistics department at the University of Michigan, and includes a quick overview of the similarities and differences between biostatistics and data science, and the educational background needed for anyone seeking to study biostatistics in graduate school. In the the other half of this talk, Thomas Braun will share some of his recent research on Bayesian statistical methods for randomized controlled clinical trials that seek to include data from patients who refuse to be randomized are allowed to instead receive their preferred treatment.

Join us on Monday, March 24, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Thomas Braun, professor of biostatistics at the University of Michigan. We hope to see you there!

Research can be a daunting task even for those with experience. At an R1 university with many laboratory scientists as colleagues, novelty in even undergraduate research is sometimes insisted upon. But is it necessarily the best path for an aspiring analyst in the mathematical sciences? This talk discusses my research experience as an academic statistician and focuses on managing undergraduate capstones in Statistics. Examples involving the inverse birthday problem and baseball data analytics are provided. General advice on undergraduate research for students and faculty will be discussed.

Join us on Monday, March 31, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Ken Ryan, professor of statistics at West Virginia University. We hope to see you there!

"Interface problems naturally arise when modeling physical phenomena occurring across multiple physical media. Mathematically, they are described by differential equations with discontinuous coefficients that model material properties. These discontinuities pose challenges to classical numerical methods (e.g., finite difference and finite element methods), which we address by developing a high-order finite element space that leverages the local geometry of the interface.

"In this talk, I will start from the basics of the finite element methods for elliptic problems and the challenges therein, then I will cover the recent developments on unfitted finite element methods for interface problems with a focus on the geometry-conforming immersed finite element method."

Join us on Monday, April 7, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Haroun Meghaichi, assistant professor of mathematics at The Ohio State University. We hope to see you there!

Julia VanLandingham, SMSS Ph.D. candidate at Clemson University, will discuss recent changes in cryptography and modern encryption systems.

While means of encryption date back thousands of years, mathematical algorithms used by modern systems are shockingly recent. We will explore some of these modern systems, recent changes in cryptography, and an avenue of ongoing research. We will mainly feature lattice-based cryptography, but no prior knowledge of cryptography or lattices is required.

Julia VanLandingham was born and raised in Westerville, Ohio, where she then attended Otterbein University to earn a BS in mathematics and a BA in computer science. She is now in her fourth year in the Ph.D. program at Clemson University researching Number Theory with applications to cryptography. When not doing math, she loves to volunteer at local robotics competitions, go to Clemson baseball games and send cute animal videos to her mom.

Join us on Monday, April 14, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Julia VanLandingham, SMSS Ph.D. candidate at Clemson University. We hope to see you there!

The Department of Mathematics and Statistics will be recognizing this year's outstanding students in mathematics. We will be presenting several departmental awards, recognizing our senior class, and welcoming this year's group of inductees to Pi Mu Epsilon, the U.S. Honorary National Mathematics Society.

This year's invited address will be presented by Amy Lerner, associate professor of biomedical engineering and mechanical engineering at the University of Rochester, and Erin Leatherman, associate professor of statistics at Kenyon College.

Join us on Monday, April 21, at 3:10 p.m. in the Community Foundation Theater to celebrate our wonderful math and stats majors.

Our first Math Monday of the new year is set for September 2. Please join us for a Math Nature Walk, which will start at 3:10 p.m. Plan to meet at the outside doors to Hayes Hall. We will leave shortly after 3:10.

A drink station will be available before the walk, but you are encouraged to bring your own water bottles. This is your chance to catch up with old friends and meet new ones as we say hello to all our fellow math and stats faculty and students. We hope to see you there!

Meet and greet with your fellow math/stat students and the math and statistics faculty at this year's First-Year Welcome Tea. Say hello to our math community and hear about all the exciting news in math and statistics. Learn about exciting opportunities and our Math Monday series.

Join us on the Peirce Patio (weather permitting) at 3:10 p.m. on Monday, Sept. 9. We will be offering a variety of snacks with lemonade and iced tea. Celebrate another year of mathematics and statistics here at Kenyon. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. 

This week's panelists include several students who worked both on and off campus for their research.

Jimmy Baker '26 worked with Professor Holdener this summer through the Kenyon Summer Science Scholars program on the abundance index and triperfect numbers, a topic within number theory.

Kyle Kelley '25 engaged in a remote research experience through Virginia Commonwealth University researching how polynomials of graphs represent themselves in respective Lie algebras.

Christophe Leblanc '25 worked with Professor Snipes this summer through the Kenyon Summer Science Scholars program on the Lavrentiev Phenomenon, which is a problem in the calculus of variation.

Lief Schaumann '25 was a part of the REU Program at Moravian University where he worked with several other participants on a topic in number theory known as integer covering systems.

Join us on Monday, Sept. 16, at 3:10 p.m. in Hayes Hall 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. 

This week's panelists include some of our sophomores and juniors and their studies over the summer.

Wisdom Akanwe ‘27 worked as a data analytics intern and business consultant at Impact Academy in Tulsa. Wisdom’s group was tasked with proposing a viable business plan for Circle Cinema (the first arthouse Cinema in Tulsa) to expand its audience to Hispanic and Black communities.

Moe Belgith ‘26 and Godwin Idowu ‘27 worked with Professor Aydin through the Kenyon Summer Science Scholars Program.

Peter Dunson ‘27 worked through the BDSI at the University of Michigan, using Bayesian clustering to find meaningful subgroups of ICU-admitted heart failure patients.

Join us on Monday, Sept. 23, at 3:10 p.m. in Tomsich 101 (note the new location this week) to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Noah Aydin, professor of mathematics, and Marissa Gee, assistant professor of mathematics, will present a double feature of mathematics research for Math Monday, sharing more information on their work and its impact in the greater mathematical community.

Aydin will give a brief introduction to coding theory and talk about the ongoing undergraduate research program at Kenyon and how you might get involved.

Gee will speak on work involving optimal control questions. Mathematical models are powerful tools for predicting the world — given some input, they can tell us about likely outcomes. In some scenarios, there are parameters in the model that we can control, like the rate of fishing when modeling a commercial fishery, or the direction of motion when modeling an autonomous vehicle. Optimal control is the study of how we can choose the parameters that will give us the "best" outcome, like maximizing profit or minimizing cost, based on a particular model. Gee's research uses techniques from math modeling, differential equations, and numerical methods to answer optimal control questions like how a rover can safely navigate the terrain on Mars, or how an animal can find food while avoiding being eaten by a predator.

Join us on Monday, Sept. 30, at 3:10 p.m. in Tomsich 101 (note the new location this week) to hear these exciting presentations and perhaps learn how you too can get involved in mathematics and statistics research hear at Kenyon. We hope to see you there!

Get ready for some fun activities using modeling as we welcome founder and director of the Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE), Brian Winkel. We will engage in active modeling of birth and immigration for a population of M&M's (yummy) and collect data from a video on time and height of a falling column of water, with some elementary science development of a reasonable model. Further, we will demonstrate models involving other phenomena (e.g., change in size of a shopping mall due to high speed highway access) and some with efforts to explain collected data from various courses in mathematics. We have found over years of teaching undergraduate mathematics that real world modeling engages students AND faculty, thus we look forward to sharing with attendees.

After completing his Ph.D. in Ring Theory in in 1971, Brian Winkel's first teaching position was at a small liberal arts college, Albion. Drawn by the many applications of mathematics he turned his mathematical life to teaching mathematics through applications and modeling. Along the way he founded and edited several journals, among them Cryptologia and PRIMUS, the former about all aspects of cryptology and the latter about teaching undergraduate mathematics. Both journals are offered by the Mathematical Association of America freely through the their member portal. Winkel has taught at a number of different  schools: liberal arts colleges, research 1 universities, engineering institutes and the military academy. In 2011 he founded and directs SIMIODE, Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations, where one can find hundreds of modeling scenarios for teaching and learning differential equations in a modeling-first approach.

Join us on Monday, Oct. 7, in Hayes Hall 109 for this fun and exciting presentation. We hope to see you there!

Alumni from across the country and students here on campus are invited to join this virtual talk, which is one of six faculty talks organized to celebrate Kenyon’s bicentennial. Professor of Mathematics Judy Holdener will deliver the October lecture on the history of her department, and she will be joined by three alumni who will share the nature of their work spanning theoretical mathematics, applied mathematics and statistics — the three tracks within Kenyon’s mathematics major. 

The presenting alumni are:

Christine Breiner ’99, associate professor of mathematics, Brown University

Alton Barbehenn ’17, data scientist, University of California at San Francisco

Katerina Tang ‘21, research assistant, Cornell University

Attendees can register for the event at: kenyon.edu/events/mathematics-at-kenyon/2024-10-15.

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. 

This week's panelists include two more students in our Mathematics & Statistics program.

Cael Elmore '25 did research at the Florida Summer Institute in Biostatistics and Data Science where he followed up on high rates of type 2 diabetes that emerged in the Marshall Islands after the United State's nuclear testing program (1950s) disrupted native agriculture on the islands. The research, conducted with researchers at the University of Arkansas, Florida International University, and Florida Atlantic University, suggested a culturally sensitive diabetes self-management education program as an alternative to the current standard of care, with promising results for the future.

Andrew Mayer '26 worked with Professor Leatherman and Alexander Powell '18 as Kenyon Summer Science Scholars to closely examine the effect of age on specific basketball skills. They took a primarily Bayesian approach while also integrating machine learning and nonparametric methods. Powell, who has worked in the NBA since graduating from Kenyon, provided proprietary data which was used to conduct the analyses.

Join us on Monday, Oct. 21, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Sundials measure the passage of time by keeping track of the movement of the shadow of a stick (called the gnomon). These analog timepieces have been around for millennia, the earliest known being sundials in Ancient Egypt dating back to about 1500 BC. In this talk we will introduce a digital sundial, whose shadows spell out the time in numerals. After demonstrating the device, we will explore the theory of digital sundials in the context of projection mappings. We encounter cool art, fractals and geometric series along the way.

Join us on Monday, Oct. 28, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Associate Professor of Mathematics Marie Snipes. We hope to see you there!

Looking for a break from all the homework and exams? This week’s Math Monday is a relaxing breather from course work and a thank you for attending our Math Monday sessions this fall. Free snacks and drinks provided by AVI Dining Services will be available at the door. Join us on Monday, November 18, at 3:10 p.m. in Hayes 109 for all the fun. We hope to see you there!

This semester, our seniors majoring in mathematics and statistics pursued independent research projects on a topic of interest. The research topics spanned a wide range. These students will present their work at a poster session this week to share their work with the wider Kenyon community. Come support your fellow math and stat students!

The poster session will be held in Peirce Hall in the Alumni Dining Room from 11:10 a.m. to 1 p.m. on Tuesday, December 3. We hope to see you there!