9/8  Hanson Smith, Richard Guy's Strong Law of Small Numbers and How Not to Make Friends 
AbstractThis talk will be a guided tour through Richard Guy's wonderful paper The Strong Law of Small Numbers. The main theorem is, "You can't tell by looking." Following Guy, we will prove this by intimidation. Audience participation, questions, and guesses are highly encouraged. We'll conclude the talk with an exciting application to web comics! 

9/22  Shahed Sharif, SIKE Attack: How to Break PostQuantum Crypto 
AbstractOver the past few years, the National Institute of Standards and Technology has been running a competition to standardize new cryptographic protocols which are safe from quantum computers. This past July, one of the top contenders, SIKE, was spectacularly broken. I will give an overview of the attack and explain the consequences. 

10/6 
Mikaela Meitz, Hamiltonian Neural Network Exploration for Electron Particle Tracking Slides 
AbstractIn the field of accelerator physics, there is a burgeoning interest in using machine learning methods for aiding in the design and optimization of charged particle accelerators. The Advance Light Sources (ALS) at the Lawrence Berkeley National Laboratory is a periodic circular accelerator called a synchrotron that emits ultraviolet and soft xray beams by accelerating electron bunches nearly as fast as the speed of light. These accelerators are prone to beam instability resulting in particle loss and consequently creating less xray brightness. The stability of an electron over thousands of revolutions is important to the performance of the accelerator. During these machinesâ€™ design or upgrade process, electron particle tracking is needed to ensure the particle dynamics are sufficient for the intended scientific use, but can be computationally expensive. If the dynamic aperture, the stability region of phase space in the synchrotron, is too small, then adjustments are made and the process is repeated until the desired result is achieved. Optimizing the dynamic aperture can require doing this tracking several times while iterating the accelerator design. Machine learning methods may alleviate some of the need for these expensive computations by making particle integration faster and easier to parallelize. This research explores electron particle tracking with the use of Hamiltonian Neural Networks. Machine learning based Hamiltonian Neural Networks (HNN) constrains the model learning to obey Hamiltonian mechanics so that the neural network can learn conservation laws from data. We compare the performance of HNN to other machine learning based models. 

10/20  Kimberly Ayers, Baby Sharkovskii doo doo doo 
AbstractIt's time to get sharky—Sharkovskii, that is! Have you ever looked at the usual ordering on \(\mathbb{N}\), and thought, "I bet I can do better"? Well, Oleksandr Mykolaiovych Sharkovskii did just that in 1964 when he proved what is now called Sharkovskii's Theorem. This is Dr. Ayers's favorite theorem in the entire world. Come hear her talk about discrete dynamics, bifurcations, chaos theory, weird orderings on the natural numbers, graph theory, and even applications to candy making. 

11/3  Sandie Hansen, Math on the Brain: Using Neuroscience to Better Understand How People Learn Math 
AbstractA humanâ€™s natural number sense first developed as a basic survival skill, but the abstract mathematics we teach in classrooms today is not. Using neuroscience and cognitive psychology research, we shall discuss why math is so hard for so many people and whether there is really such a thing as a "math person". The evolution of mathematics has exponentially outpaced that of the human brain, by studying the cognitive mechanisms involved in processing mathematical operations we will build a better understanding of how students learn math and we will consider how to adapt the math classroom using more brainfriendly methods. 

11/17  Wayne Aitken, Filters and Ultrafilters 
Abstract
In calculus and especially in analysis we learn about a
plethora of types of limits: onesided limits, twosided limits, limits
of sequences, limits of functions, limits with finite values, limits
with infinite values, not to mention limsups and liminfs and limits of
"nets". What do these definitions of limits have in common? 