Friday, February 22 -- Holt 175, 4:00pm
Stefan Gille (University of Alberta)
Quadratic forms in algebra
Abstract: Quadratic forms have their origin in number theory and are an interesting mathematical object with a long algebraic history. However, these forms are not only studied for their own sake but also play a role in other areas of algebra, as for instance algebraic groups or vector bundles. The aim of the talk is to give some examples of applications of quadratic forms in algebra.
Friday, March 8 -- Holt 175, 3:30pm
Daniel Vallieres (California State University - Chico)
Analogies between number theory and graph theory
Abstract: We will present a few analogies between number theory and graph theory. If time permits, we will also present some results obtained jointly with Kyle Hammer, Thomas Mattman, and Jonathan Sands.
Friday, March 15 -- Holt 175, 3:30pm
Estrella Johnson (Virginia Tech)
Taking an instructional innovation to scale: Characterizing, supporting, and evaluating inquiry-oriented instruction
Abstract: Inquiry-oriented instruction has shown promise in regards to many features of student success, including conceptual understanding, affective gains, and persistence in STEM degrees. However, instructional change is difficult (especially at scale) and the research literature has documented a number of challenges instructors face when shifting their instructional practice. During this talk I will provide a characterization of inquiry-oriented instruction; discuss an instructional support model that was developed to support inquiry-oriented instruction in undergraduate mathematics courses; and present preliminary evaluation findings, drawing on a national sample of content assessment data, collected from 513 students at 46 different institutions. Analysis of this assessment data revealed no difference in the performance of men and women in the comparison sample; however, under the inquiry-oriented treatment, a gender performance difference was present with men outperforming women. In an effort to understand this finding, I present related research literature on gendered experiences in collaborative settings and our preliminary analysis into the experiences of our students in these inquiry-oriented courses.
Friday, March 29 -- Holt 175, 4:00pm
Martha Byrne (Sonoma State University)
Mean Girls: Everything That's Wrong With Math In the Popular Media
Abstract: What is math? Who does math? What does it mean to do math? The answers to these questions from people outside the mathematical community are often startling and troubling to those of us who love the field. But pop culture supports these troubling views through the typical portrayals of people doing mathematics in movies and tv shows. We'll talk about some of the ways that these portrayals contribute to the uniquely negative way math is positioned in society and how it all adds to issues of inequity in mathematics.
Friday, April 5 -- Holt 175, 3:30pm
Natalie Hobson (Sonoma State University)
Sophie Germain: Bridging art and algebra
Abstract: It was Germain who once said, "Algebra is but written geometry and geometry is but figured algebra." Germain is most notable for her work writing equations to model the effects of vibrations on the smallest of particles. Her work is visible in our tallest buildings and longest bridges. This 18th century mathematician was forced to work under a male pseudonym but persisted through societal challenges and mathematical mistakes to make the most spectacular of discoveries. In this talk, we will explore the life and work of this unshakable mathematician.
Friday, April 19 -- Holt 175, 3:30pm
Carolyn Abbott (University of California, Berkeley)
Random walks on groups acting on hyperbolic spaces
Abstract: Imagine you are standing at the point 0 on a number line, and you take a step forward or a step backwards, each with probability 1/2. If you take a large number of steps, is it likely that you will end up back where you started? What if you are standing at a vertex of a 4-valent tree, and you take a step in each of the 4 possible directions with probability 1/4? This process is special case of what is called a random walk on a space. If the space you choose is the Cayley graph of a group (as these examples are), then a random walk allows you to choose a "random" or "generic" element of the group by taking a large number of steps and considering the label of the vertex where you end up. One can ask what properties a generic element of the group is likely to have: for example, is it likely that the element you land on has infinite order? In this talk, I will discuss the algebraic and geometric properties of generic elements of groups which act "nicely" on hyperbolic metric spaces, with a focus on how such elements interact with certain subgroups of the group. These results will apply to generic elements of hyperbolic groups, relatively hyperbolic groups, mapping class groups, many fundamental groups of 3-manifolds, the outer automorphism group of a free group of rank at least two, and CAT(0) groups with a rank one element, among many others. This is joint work with Michael Hull.
Friday, April 26 -- Holt 175, 4:00pm
Delmar Larsen (University of California at Davis)
Realizing the 5R Dream: The LibreTexts’s Quest to Build a Centralized OER Platform
Abstract: It is becoming ever clearer that new and innovative educational efforts are required to facilitate the greater creativity, flexibility, and increased learning capability needed for post-secondary education in the future. Unfortunately, rapidly rising undergraduate fees and textbook costs are serious factors that impede access to higher education for many students; many of which do not have the funds to benefit from these new advances that are often commercialized. Growing textbook costs are a serious barrier for under-served, at-risk students and open-educational resources (OER) textbooks are a growing approach to address these issues. The Libretexts project (http://LibreTexts.org) is designed as a collaborative OER platform to simultaneously enable the dissemination and evaluation of existing resources and as a dynamic “courseware” to facilitate new education developments and approaches, with an emphasis on data-driven assessment of student learning and performance. Since its inception ten years ago, the Libretexts has been exponentially growing and currently reaches over 60 million students per year and is the most visited chemistry website and online OER textbook resource in the world.
Friday, May 3 -- Holt 268, 2:30pm
Dov Zazkis (Arizona State University)
Borrowing Methods from Psychology to Study Reading of Mathematical Proof
Abstract: As students transition to upper-level mathematics courses their ability to read mathematics (in particular proofs) becomes progressively more important to their success. However, the majority of proof education research has focused on writing rather than reading of proofs. I report on a research program which borrows methods and frameworks from reading research. This research program has deepened what is known about differences in novice vs. expert reading of mathematical proof. The research team is currently working on leveraging this knowledge to develop short modules aimed at providing significant improvement in student’s reading of proof.
Friday, May 10 -- Holt 175, 3:00pm
Luca Candelori (Wayne State University)
Integrality properties of the Weil representation of a finite quadratic module
Abstract: The Weil representation of a finite quadratic module is an essential tool in studying the transformation laws of theta functions. This complex, finite- dimensional representation factors through a finite quotient of the metaplectic cover of the modular group and it has a canonical basis of delta functions. With respect to this basis, the matrix entries of the Weil representation lie in a cyclotomic field extension. In this talk we prove that after a suitable change of basis the matrix entries can be taken to lie in the ring of integers of the cyclotomic extension. For cyclic quadratic modules of even prime-power order, we exhibit a canonical choice for such an integral basis. The original motivation behind this question was the development of Integral Topological Quantum Field Theory by Gilmer and Massbaum. We discuss the connections with this integral theory, as well as with integral TQFTs afforded by more general modular tensor categories. This is joint work with Richard Ng and Yilong Wang at LSU, and with Yilong Wang and Shaul Zemel at Hebrew University.