# Colloquium for Fall 2018

If you are interested in giving a talk, please email caherrera@csuchico.edu

Colloquia are typically held on Friday in Holt 175. Refreshments are served at 3:00pm and the talk begins at 3:30pm. Everyone is invited to attend.

#### Friday, Sept. 7 -- Holt 175, 4:00pm

**Isaiah Lankham (University of California Office of the President)Propensity Score Matching: A Cautionary Tale**

Abstract: Imagine you've been hired as a data analyst for a pre-college outreach program called 2&Thru, and you're asked to show how the program is effective. In other words, are high-school graduates who participate more likely to enroll in, persist at, and graduate from college than if they hadn't participated?

From a statistical standpoint, this sounds like an ideal setup for randomized controlled trials (RCTs): Randomly assign students to either a treatment group (those who participate in 2&Thru) or a control group (those who don't), and compare the two groups' outcomes. However, random assignment would be unethical since the outcomes of 2&Thru participation are potentially life-altering. We can't intentionally deny program benefits, so we'll need a better way of estimating the counterfactual, meaning the results 2&Thru participants would have had if they hadn't participated.

Fortunately, there's a clever workaround called propensity score matching (PSM), which allows us to mimic the effects of randomized group assignments. By identifying the factors (aka covariates) most important in determining a student's propensity to self-select for program participation, we can match 2&Thru participants to comparable non-participants using logistic regression and build a quasi-control group. Because the entire technique hinges on selection of the "right" set of covariates, the "wrong" set will quickly lead to invalid conclusions, as will be demonstrated.

#### Friday, Sept. 14 -- Holt 175, 3:30pm

**John Lind (California State University, Chico)The algebra of spheres**

Abstract: A thread can wind around a peg any number of times—and to a topologist this counting of the winding number is what the integers are! In this talk I will explore a generalization of this idea to higher dimensions. We can ask in a similar way how many times a sphere of a given dimension can wrap around another sphere. Contemporary methods that attempt to answer this question are complex and abstract, so I will use pictures to harness our geometric intuition. By the end, I will try to convince you that the patterns we detect in the spheres are shadows of a fundamental object of algebra.

#### Friday, Sept. 21 -- Holt 175, 3:30pm

**Jonathan Sands (University of Vermont)A potential game-changer for speedy factoring: Shor's algorithm in quantum computing**

Abstract: In 1994, Peter Shor showed that factoring could be done in polynomial time if significant quantum computing becomes a reality. This would imply that standard cryptosystems such as RSA are no longer secure. We present Shor's algorithm for a general mathematical audience, focusing on the number theory and requiring no previous knowledge of quantum mechanics.

#### Friday, Oct. 19 -- Holt 175, 3:30pm

**Thomas Mattman (California State University, Chico)There are too many knotted graphs!**

Abstract: (Joint with Goldberg and Naimi) The powerful Graph Minor Theorem of Robertson and Seymour ensures that, for any graph property, whatsoever, there is an associated finite list of graphs that are minor minimal with respect to that property. For example, with Thomas, they show that the seven graphs in the Petersen family are exactly the minor minimal intrinsic linked (MMIL) graphs.

A graph is intrinsically linked (knotted) if every embedding in R^3 has a pair of non-trivially linked cycles (a non-trivially knotted cycle). Through 2003, 41 MMIK (minor minimal intrinsically knotted) graphs were known. We have 220 new examples and our methods suggest there are likely "many, many more."

The talk will begin with a gentle introduction to graph theory. Undergraduate students are encouraged to attend.

#### Friday, Oct. 26 -- Holt 175, 3:30pm

**Christine Herrera (California State University, Chico)The struggle is real!**

Abstract: This talk will discuss a study that examined the development of preservice teachers (PSTs) understanding of productive struggle using video episodes which PSTs analyzed through the lens of professional teacher noticing. The goal of the study was to give PSTs opportunities to observe students struggling with the course content the PSTs were studying and to enact their specialized content knowledge and pedagogical knowledge for teaching simultaneously. Findings suggest that the PSTs develop the ability to attend to and interpret the mathematics underlying the student struggles through video analyses. They also begin to identify teaching strategies and practices that appear potentially useful for supporting productive struggle. One implication for this study is to carefully weave opportunities to develop teaching practices such as support of productive struggle into the content course for teaching. The PSTs may better bridge the stance between being a student and becoming a teacher in what productive struggle looks like in learning mathematics.

#### Friday, Nov. 9 -- Holt 175, 3:30pm

**Carolyn Yarnall (California State University, Dominguez Hills)Approval Voting in Product Societies**

Abstract: In approval voting, individuals vote for all platforms they find acceptable. A natural question in this setting is: when is agreement possible? What conditions guarantee that some fraction of the voters agree on a single platform? Previous results have been shown in this vein for platforms that form a linear (e.g. liberal to conservative) or a circular (e.g. voting on time of year to hold an event) spectrum. However, what if individuals are voting on two issues simultaneously? Such situations can be modeled as the product of two voting societies. In this talk we will use combinatorial geometric methods to investigate the agreement of "product societies" and consider a variety of examples.