Title: Changing the face of high school mathematics
Abstract: NCTM’s Catalyzing Change in High School Mathematics offers three reasons for learning math: expand professional opportunities; understand and critique the world; and experience the joy, wonder, and beauty of mathematics. For too many students, this vision is not a reality. Let’s explore what this vision could be like, particularly given opportunities for learning provided by “math action” technology, tools that perform mathematical tasks and/or respond to the user’s actions in mathematically defined ways.
Title: The implicitization problem and Rees rings
Abstract: A classical problem in elimination theory is called the implicitization problem. This problem consists of determining the equations of a variety that is given parametrically and has been extensively studied by applied mathematicians in geometric modeling and computer aided design. In this talk we will talk about the role Rees rings play in the implicitization problem. We will also explain how knowing the types of singularities of a variety can inform the search for its implicit equations.
Title: Splitting in the 4-sphere
Abstract: A classic theorem in 3D tells us that a split link of two components (i.e. two knots in the 3-sphere that don't link each other at all) can be split apart in a unique way. On the contrary, in recent joint work I showed that some split links of surfaces (i.e. two surfaces in S^4 that don’t “link” each other at all) can be split apart in multiple ways. (Or in other words, there exist two non-isotopic splitting spheres in the complement of such a link.) In this talk, I’ll discuss the classic 3D situation, what goes wrong with extending this theorem analogously to dimension 4, and some interesting theorems about knots in 4D that contradict classical intuition from 3D. This is joint work with Mark Hughes (BYU) and Seungwon Kim (Sungkyunkwan).
Title: Studying Successful Doctoral Students in Mathematics from Underrepresented Groups
Abstract: In this talk, we will share early findings from an NSF study of 75 doctoral students and recent PhDs in mathematics from underrepresented groups. The project has conducted in-depth, semi-structured interviews with four cohorts: newly accepted students, early graduate students (pre-qualifying exams), advanced graduate students (dissertation level), and recent PhDs (0-5 years since graduation). The research questions in the study are: (1) What are lived experiences of successful underrepresented students who are pursuing mathematics PhDs? and (2) What formal and informal structures are perceived by doctoral students as effective supports? Themes drawn from the interviews can inform department policies and practices to create environments that support students from underrepresented groups as they earn PhDs in mathematics.
Title: Success with less: erasure recovery and error correction using fewer bits
Abstract: Decoding algorithms for error-correcting codes typically take as input all symbols of a received word and attempt to determine the original codeword. In fractional decoding, only an alpha-proportion of symbols are used where alpha<1. Linear exact repair recovers erasures in codes over field extensions while limiting the amount of subsymbols shared over the network. In this talk, we will discuss such strategies for getting by with less, focusing on evaluation codes and codes from curves.
Title: Making undergraduate research work for faculty and students: An examples driven talk
Abstract: Getting involved in research has become a most for all undergraduate students. In this talk we will address questions such as: Why is this so important to do research? What exactly counts as research in mathematics? How do we make it work best for our students? How do we make it work for our faculty members? This will be an interactive talk and questions and audience participation will not only be welcome but encouraged!
Title: Games for PDEs
Abstract: The following approach of finding solutions to a partial differential equation Lu=0, proved to be quite versatile:
(i) develop an asymptotic expansion of a suitable family of averaging operators on u; the operators are parametrized by the radius \epsilon of averaging;
(ii) study the related mean value equation by removing higher order terms in the expansion;
(iii) interpret the mean value equation as the dynamic programming principle of a two-player game incorporating deterministic and stochastic components;
(iv) pass to the limit in the radius of averaging \epsilon, in order to recover solutions to Lu=0 from the values of the game process.
In my talk, I will explain this approach in the following contexts: p-Laplacian; non-local geometric p-Laplacian; Robin boundary conditions; and weighted Laplace-Beltrami operator on a manifold. In each case, finding the appropriate averaging principle and the related game, is the key starting point.
Title: The Elusion of Equity in Mathematics Education
Abstract: Mathematics educators have been talking about “equity” for decades, yet equity remains elusive. Indeed, our field continues to reproduce hierarchies. These hierarchies position some students as “gifted” or “advanced” and others as “low,” “struggling,” or “remedial,” with particularly grave consequences for children who are already marginalized because of their race, language, gender, class, and (dis)ability status. How and why does this happen—and what can it look like for teachers to deliberately and consistently disrupt hierarchy? In this talk, Dr. Nicole Louie will take up these questions. Drawing on her work with teachers in San Francisco and Chicago, she will describe some of the ways that teachers commonly find themselves drawn in by the gravitational force that hierarchical ways of thinking exert on many layers of society, but especially in education. She will also discuss ways of resisting this force, not only in the classroom but also in building professional communities that provide teachers with the necessary supports to approach escape velocity and challenge the gravity of hierarchies in mathematics education.
Title: The Elusion of Equity in Mathematics Education
Abstract: Mathematics educators have been talking about “equity” for decades, yet equity remains elusive. Indeed, our field continues to reproduce hierarchies. These hierarchies position some students as “gifted” or “advanced” and others as “low,” “struggling,” or “remedial,” with particularly grave consequences for children who are already marginalized because of their race, language, gender, class, and (dis)ability status. How and why does this happen—and what can it look like for teachers to deliberately and consistently disrupt hierarchy? In this talk, Dr. Nicole Louie will take up these questions. Drawing on her work with teachers in San Francisco and Chicago, she will describe some of the ways that teachers commonly find themselves drawn in by the gravitational force that hierarchical ways of thinking exert on many layers of society, but especially in education. She will also discuss ways of resisting this force, not only in the classroom but also in building professional communities that provide teachers with the necessary supports to approach escape velocity and challenge the gravity of hierarchies in mathematics education.