## Spring 2021

### April

**4/22****Dr. David Altman, Willamette University***The Role of Molecular Motors in Regulating a Cell’s Material Properties*

Molecular motors are force generating biomolecules in a cell capable of doing work and creating directed motion. In my lab, we study myosins, a family of molecular motors with members implicated in processes including muscle contraction, trafficking of cellular cargo, and cell motility. We seek to understand how these motors regulate their complex cellular environment, and how the environment in turn regulates the motors. In this talk, I will highlight our work probing the ways in which myosin motors can modify material properties of a cell through their ability to cross-link cellular components. I will focus on our previous work studying muscle fibers as well as current studies probing the role of myosins in trafficking of waste in the retina.

**4/15****Dr. David Archer, Galois Inc.***“it is nothing to know something unless another knows you know it.”*

Privacy is an old and new conundrum. From de la Bruyere's "All confidence placed in another is dangerous if it is not perfect," to GDPR, it is a basic human right and an occasional necessity of Government to keep things private. On the other hand, it's a basic need of society to know certain things: "The FISA court issued this warrant correctly" speaks to both needs. Privacy's key defeater is that information is wealth, and avarice is the spur of much (including tech) industry. What role will we as the inventors of tech play? Pirate? Arms dealer? Some nascent technologies let us do better: Guardian. Inveigher against the zero sum privacy lie. Zero knowledge (ZK) is one such technology. For example, in the software world, we can use ZK to publicly disclose software vulnerabilities, pressuring profit-focused vendors to take action without giving yet another zero-day to the hungry malware industry. With ZK we can also publicly prove security of software without revealing trade secrets. We'll talk about privacy, the implications of its theft (legal and otherwise), and the seeming Avalon where zero knowledge proof systems meet formal assurance of software.

**4/8****Corrine Yap, Rutgers University***Everything is Connected: A Tour of Methods in Combinatorics*

In undergraduate math classes, we learn about the important theorems and strategies for tackling problems in a given field - probability, algebra, combinatorics, topology, number theory. In math graduate school, we choose one of these as a specialty and become experts on a subtopic (or subsubsubtopic) within that field. But how do the broad areas of math relate to each other? What can we learn from people outside our specialty? I'll discuss some examples of how my field, combinatorics, has utilized techniques from the other areas of math mentioned above, and what mathematicians can learn from STEM, art, and society at large.

**4/1****Dr. John Mackey, Carnegie Mellon University***Recent Advances in Computer Assisted Proofs*

Many old combinatorial problems have recently been solved using SAT solvers. We'll discuss how to encode problems into CNF (conjunctive normal form) logical formulas, and how SAT solvers can find satisfying assignments or prove that no such assignments exist.

### March

**3/18****Dr. Inga Johnson, Willamette University***An Introduction to Topological Data Analysis (TDA) and the Mapper Algorithm*

Topology is an area of mathematics that is interested in measuring and understanding shape. Topologists have tools to measure holes, loops, voids, connectedness, and tools that measure algebraic and differential structures within shapes. These tools work in any dimension and are designed to measure features that persist even if the shape is distorted continuously. Scientists and statisticians are also interested in shape; in particular how shape can be used to understand data and help visualize high dimensional data. In this talk I'll describe a topological technique introduced in a 2007 paper by Gurjeet Singh, Facundo Memoli and Gunnar Carlsson called the Mapper algorithm which has gone on to uncover many patterns and shapes within high dimensional data. For example, Mapper, in concert with statistical techniques, has been applied to recognize three subgroups within study of type 2 diabetes patients. TDA tools in general have been used to study data in many settings such as natural image data, identifying patient subsets in cancer studies, voting patterns in the U.S. House of Representatives, and team stratification in the NBA.

**3/10****Dr. Kathryn Nyman, Willamette University***How to Crush Your Opponents: A Brief Introduction to Combinatorial Games*

Combinatorial games are 2-player games where players take turns moving from one game position to another, following a set of specific rules. The last player who is able to move is (typically) the winner. No moves are secret or left to chance in a combinatorial game. While combinatorial games can get pretty complicated, we'll look at some that we can get a handle on strategy-wise. Bring a pile of pennies for the games, or better yet, a pile of delicious chocolate candies. No background is needed for this talk - just come, have fun and learn how to win some games.

## Fall 2020

### November 2020

**11/5****Max Lipton, Cornell University***Electrostatic Knot Theory*

A knot is a continuous image of a circle in $\mathbb{R}^3$. Suppose a knot has uniformly distributed electric charge. This generates an electric field in the surrounding space, and a critical point is a point in space where the net electric forces cancel. It is of physical and mathematical significance to try to understand the critical points of the potential and their behavior. How many are there, what are their dynamical behavior, and how does this relate to other topological properties of the knot?

### October 2020

**10/29****Dr. Hannah Alpert, University of British Columbia***Non-Attacking Rooks on Polyominoes*

You know how to place rooks on a standard chessboard so that no two rooks are in the same row or column. Just place them along the diagonal! But what if you cut the board to form an irregularly-shaped set of squares, called a polyomino? Will this new puzzle be the next Sudoku? We'll talk about how to turn a puzzle idea into research questions and theorems. Joint work with Érika Roldán.

**10/22****Dr. Kelly McConville, Reed College***The Many Hats a Statistician Wears in Forestry Research*

Since 2008, I have been collaborating with the US Forest Inventory and Analysis Program on a wide range of research projects related to monitoring status and trends in forested ecosystems across the US. In true Team Science fashion, these projects have involved ecologists, foresters, analysts, statisticians, undergraduates, and one statistics graduate student turned liberal arts statistics professor. In this talk, I will share some of that work with you and my reflections on the role of a liberal arts statistics professor in collaborative research projects. This talk will be accessible to all students interested in data and will provide some concrete examples of what it means “to do statistics research”.

### October

**10/15Dr. Nathan Carlson, California Lutheran University**

*A Surprising Connection between Two Proofs of the Infinitude of Primes*

In Book IX of his foundational work

*The Elements*, written in 300BC, the Greek mathematician Euclid included his celebrated proof that there are an infinite number of primes. While this is the most well-known proof, and has been studied by students of mathematics throughout the centuries, many other proofs of the infinitude of primes have been found. These include a classic proof by Euler and recent proofs by Pinasco and Whang. In 1955 Furstenberg gave an unusual topological proof involving arithmetic progressions. After dispensing with the topological language, the essential number theory in this proof was recently uncovered by Mercer. On the surface neither version seems to bear much resemblance to Euclid’s original proof. In this talk the speaker gives a variation of the Furstenberg/Mercer proof that in fact looks much like that classical proof. (This variation appeared as a short note in the American Mathematical Monthly in 2014). This demonstrates that while Furstenberg’s proof seems unusual, at its core it is in fact quite similar to the first and most well-known. Basic topological and number-theoretic background will be given.

**10/8Professor Christina Edholm, Scripps College**

*Mathematical Models of Infectious Disease: An Introduction and Application to COVID-19*

Be it the Ebola or Buruli ulcers, we are constantly informed about infectious diseases and the ramifications. We can combat infectious diseases using mathematics to gain insight into diseases dynamics and outbreaks. Sometimes models will capture a country level of interactions, and other models focus on the cellular level of disease interaction. Based on the disease and question, mathematical models can range from deterministic systems of ordinary differential equations to computational agent-based models. We will explore a model of COVID-19 spread consisting of several interconnected modified SEIR differential equations to investigate the dynamics between different populations at the 5Cs and the influence of mitigation techniques such as students adhering to health protocols and contact tracing.

**10/1Dr. James Tanton, Princeton University **

*Explode Your Mind with Exploding Dots*

It's a global phenomenon in mathematics! Over 6 million people -- students, educators, maths enthusiasts – from over 170 countries and territories across the planet are united by the stunning wonder of a common piece of mathematics they already thought they knew so well. It’s the story of Exploding Dots. Let me share this mind-blowing story with you too!

### September

**9/17Seth Bell ('23), Willamette University **

*Routing by matching*

*on*

*convex pieces of grid graphs*

We present an upper bound for the routing number of graphs that are the intersection of a convex polygon with the square lattice grid. The routing number is a graph invariant introduced in 1993 by Alon, Chung, and Graham and has been studied for path, tree, and star graphs, but not for classes of graphs chosen according to a geometric criterion. The geometric motivation for this goal is a continuous version of the problem: studying the set of arrangements of nnn disjoint identical disks within a polygon. The routing number is a discrete analogue of the diameter of such a configuration space. We show that, consistent with the bound for rectangular grid pieces, the routing number of grid pieces contained within convex polygons grows linearly in the diameter of the graph.