### Upcoming Spring Semester Events

**Wednesday, April 27, 4 pm, in Avery 19 (lower level)**

**with Isabel Safarik (UNL Mathematics) **

**Title:** Exploring the Navier Stokes Equations and their consequences

**Abstract:** As an undergraduate, I wondered how people went from being a calculus student to doing research in mathematics. I've learned that sometimes, all it takes is a problem to inspire you. In this talk, we will explore the (problematic) set of equations that inspired me--the Navier Stokes Equations. Additionally, I will discuss some of my current interests and projects involving non-local (peridynamic) operators and computations in Matlab.

### Previous Spring Semester Events

**Wednesday, April 20, 4 pm, in Avery 19 (lower level)**

**with Professor Grover (UNL Engineering) **

**Title:** Chaos is a friend of mine: Dynamical systems theory enables design of deep space missions and fluid robots

**Abstract:** The geometrical framework of dynamical systems theory was originally developed by Poincare to study the complicated (chaotic) dynamics of the three bodies moving under mutual gravitational forces. In this talk, we will first discuss the application of this theory to explain the (sometimes puzzling) motion of celestial bodies, as well as to design non-intuitive fuel-efficient space missions to moon and beyond. A typical particle meanders through the phase space of an N-body problem by travelling on invariant manifolds that connect different equilibria and periodic orbits. These invariant manifolds, created by the competing gravitational forces, act as `interplanetary superhighways'. Next, we will discuss the far reaching generalizations of this framework in the context of fluid mechanics, where we extend this theory to infinite dimensions and explain the complex dynamics of a new class of robotic fluid systems known as `active nematics’.

**Wednesday, April 13, 4 pm via Zoom (ID: 947 8772 9456; Password: MATH-CLUB), and broadcasting in Avery 115**

**Pi Mu Epsilon Lecture by Professor Ken Ono (Thomas Jefferson Professor and chair of Math Department, University of Virginia) **

**Title:** What is the Riemann hypothesis, and why does it matter?

**Abstract:** The Riemann hypothesis provides insights into the distribution of prime numbers, stating that the nontrivial zeros of the Riemann zeta function have a “real part” of one-half. A proof of the hypothesis would be world news and fetch a $1 million Millennium Prize. In this lecture, the speaker will discuss the mathematical meaning of the Riemann hypothesis and why it matters. Along the way, he will tell tales of mysteries about prime numbers and highlight some recent advances.

**Thursday, April 7, 4 pm**

**Fall 2022 Course Preview **(via Zoom link https://unl.zoom.us/j/96126104539)

**Did you miss the course preview on Thursday, April 7th? Click here to watch a recording of the Zoom meeting.**

- MATH 412: Modern Geometry
- MATH 417: Group Theory
- MATH 424: Introduction to Partial Differential Equations
- MATH 425: Mathematical Analysis
- MATH 435: Math in the City
- MATH 452: Graph Theory
- MATH 460: History of Mathematics
- MATH 489: Stochastic Processes - Professor Du wasn't able to attend.

**Wednesday, March 23, 4 pm in Avery 19 (lower level)**

**with Professor Bobaru (UNL Engineering). **

**Title:** “Surprising connections between tornadoes and … fracture?!?
and How peridynamic (nonlocal) models can help improve safety”

**Abstract:** Materials can fail from static or dynamic (impact) loading. The collapse of the Champlain Towers South, a 12-story beachfront condominium in the Miami suburb of Surfside, Florida, in 2021 happened from corrosion-induced fracture under static loading. Windows of spacecraft or in buildings in the tornado alley, can fail because of impact with debris. If we could simulate these types of phenomena and predict what would happen under various loading scenarios, we could improve the design of materials and structures to increase the safety and avoid catastrophic failures. The problems mentioned above tend to be difficult to predict using computational modeling and simulation: fracture in glass appears, at first, to be unpredictable, with various types of cracks intermingled; corrosion attack on the reinforcing bars in concrete leads to expansion of the bar (from lower-density corrosion products) which induces tensile loads and cracks growing in concrete in unexpected places. For the past 50-60 years, the approach for predicting this behavior was via mathematical models based on Partial Differential Equations (PDEs) and computational models (e.g. the Finite Element Method) that approximate solutions of such PDE-based problems. These descriptions, however, have severe limitations and lead to solutions with mathematical singularities that do not exist in reality. These models also require ad-hoc rules for how damage should form in a material and how it should evolve (turn left, right, go straight, spread diffusely?), which rarely match the experimental observations. In this talk, I will explain how our novel peridynamic (nonlocal) mathematical models have been able to predict, for the first time ever, physical behavior which, up to that point, was considered “unpredictable”. I will also discuss some recent computational methods that allow us to speed-up the computation of these nonlocal models.

**Wednesday, February 2, 4 pm online via Zoom (ID: 947 8772 9456; Password: MATH-CLUB)**

**with Sonya Irons (Director of Undergraduate Research) and Professor Petronela Radu (Undergraduate Chair and Advisor)**

**Title:** Undergraduate Research Opportunities in Math

**Abstract:** Come learn about undergraduate research in math! Undergraduate research is a great way to

- Build your resume
- Develop concrete skills
- Prepare for grad school
- Foster relationships with faculty and enrich your education
- Get paid!

### About Math Club

The Math Club is an umbrella organization for mathematics-related activities open to **all UNL students**. The Math Club sponsors events throughout the academic year in association with the Nebraska Alpha Chapter of Pi Mu Epsilon and the
Association for Women in Mathematics (AWM) undergraduate student chapter at Nebraska. Undergraduate students are **strongly encouraged** to contact the Math Club's faculty advisors to discuss events and meetings that they would like to see throughout the academic year and to help organize additional event and meetings.

**Subscribe** to the Math Club mailing list. Use **math-club** for the list name.

### Pi Mu Epsilon (ΠΜΕ)

Pi Mu Epsilon is a national mathematics honor society that promotes scholarly activity in mathematics among students in academic institutions. UNL's Nebraska Alpha Chapter, founded in 1928, was the 15th chapter out of over 350 chapters around the country.

Learn more about joining Pi Mu Epsilon.

#### Faculty Advisors

Try the

**UNL Math Challenge**

New problems are posted on the website above every other week.

Try it for fun, intellectual exercise, and a chance to win a

Gift Card to Dunkin Donuts!