Friday, November 1, 2024
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. Kelsey Quaisley, Oregon State University
Faculty Host: Dr. Steven Boyce
Title: Guiding Principles for Equity-Oriented Professional Development for Mathematics Graduate Teaching Assistants
Abstract: Instruction that is active and attends to diversity, equity, and inclusion (DEI) has become increasingly important in mathematics education. As teaching assistants, graduate students impact the mathematical experiences of thousands of undergraduate mathematics students. Therefore, their professional development and growth as educators is critical, especially when considering that many graduate teaching assistants pursue careers in teaching mathematics. In this talk, I share guiding principles for developing a mathematics graduate teaching assistant professional development program that focuses on active learning and diversity, equity, and inclusion. Importantly, my collaborators and I ground this work in DEI, rather than having DEI as a one-time or add-on component. Further, I discuss the implementation of a professional development program we designed using these principles. This includes how we adapted this program at three institutions and how the instructors of this professional development have supported mathematics graduate teaching assistants’ growth as teachers in enacting active, diverse, equitable, and inclusive classroom practices. I share our thoughts on effective professional development for mathematics graduate teaching assistants in advancing their understanding of active learning and equitable teaching by highlighting elements of the program that are shared across our institutions.
Biography: Dr. Kelsey Quaisley is a Postdoctoral Scholar in the Department of Mathematics at Oregon State University. She received her M.A. from the Department of Mathematics at the University of Nebraska-Lincoln in 2018 and her Ph.D. from the Department of Teaching, Learning, and Teacher Education at the University of Nebraska-Lincoln in 2023. Her research focuses on preparing and supporting newer instructors of mathematics to develop equitable and inclusive teaching practices. Further, she utilizes critical and arts-based methodologies in her research, including storytelling, poetic transcription, and metaphors. She aims to illuminate and elevate K-16 mathematics instructors and leaders’ engagement and ideas surrounding equity and inclusion with these methods.
Friday, November 8, 2024
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. Ricardo Baptista, California Institute of Technology
Faculty Host: Dr. Safa Mote
Title: Towards large-scale data assimilation with structured generative models
Abstract: Accurate state estimation, also known as data assimilation, is essential for geophysical forecasts, ranging from numerical weather prediction to long-term climate studies. While ensemble Kalman methods are widely adopted for this task in high dimensions, these methods are inconsistent at capturing the true uncertainty in non-Gaussian settings. In this presentation, I will introduce a scalable framework for consistent data assimilation. First, I will demonstrate how inference methods based on conditional generative models generalize ensemble Kalman methods and correctly characterize the probability distributions in nonlinear filtering problems. Second, I will present a dimension reduction approach for limited data settings by identifying and encoding low-dimensional structure in generative models with guarantees on the approximation error. The benefits of this framework will be showcased in applications from fluid mechanics with chaotic dynamics, where classic methods are unstable in small sample regimes.
Biography: Dr. Baptista is an incoming Assistant Professor at the University of Toronto in the Department of Statistical Sciences and is currently a visitor at Caltech. Ricardo received his PhD from MIT, where he was a member of the Uncertainty Quantification group. The core focus of his work is on developing the methodological foundations of probabilistic modeling and inference. He is broadly interested in using machine learning methods to better understand and improve the accuracy of generative models for applications in science and engineering.
Friday, November 22, 2024
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. Noel Walkington, Carnegie Mellon
Faculty Host: Dr. Jeffrey Ovall
Title: Modeling Multiphase Porous Flows
Abstract: In order to model many geological flows of contemporary interest it is necessary to include the thermodynamics of the underlying processes. Examples include CO_2 sequestration and the release of greenhouse gasses dissolved in melting permafrost. Tractable models of such problems can only involve gross (macroscopic) properties, since a precise description of the physical system is neither available nor computationally tractable.
This talk will first briefly review the role thermodynamics plays in classical continuum mechanics; in particular, how dissipation principles give rise to bounds above and beyond the natural conservation properties. The development of macroscopic models of geological flows involving multiple components undergoing changes of phase will then be considered. These models involve an amalgamation of classical and continuum thermodynamics to yield systems of conservation laws which inherit natural dissipation principles. The convexity (concavity) of the free energy (entropy) functions is essential for the development of stability estimates of solutions to these equations, and the development of stable numerical schemes.
Biography: Noel Walkington is a numerical analyst and professor of mathematics at Carnegie Mellon University. He holds degrees in mechanical engineering and mathematics and enjoys working at the interface of the two. His research interests center around the development and analysis of algorithms for the solution of partial differential equations (PDEs) that arise in engineering and science. He is particularly interested in bringing new tools to bear upon challenging problems that arise in the numerical approximation of PDEs, including the design and analysis of 2D and 3D mesh generation algorithms that resolve difficult geometric features.
Friday, February 7, 2025
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. Laurent Younes, John Hopkins University
Faculty Host: Dr. Bruno Jedynak
Title: Shape Alignment via Allen-Cahn Nonlinear-Convection
Abstract: We present a phase field method on shape registration to align shapes of possibly different topology. A soft end-point optimal control problem is introduced whose minimum measures the minimal control norm required to align an initial shape to a final shape, up to a small error term. Inspired by level-set methods and large deformation diffeomorphic metric mapping, the controls spaces are integrable scalar functions to serve as a normal velocity and smooth reproducing kernel Hilbert spaces to serve as velocity vector fields. The paths in control spaces then follow an evolution equation which is a generalized convective Allen-Cahn. The existence of mild solutions to the evolution equation is proved, the minimums of the time discretized optimal control problem are characterized, and numerical simulations of minimums to the fully discretized optimal control problem are provided.
Biography: Laurent Younes is a professor in the Department of Applied Mathematics and Statistics and Director of the Centre for Imaging Science at Johns Hopkins University, that he joined in 2003, after ten years as a researcher for the CNRS in France. He is a former student of the Ecole Normale Supérieure (Paris) and of the University of Paris Orsay from which he received his Ph.D. in 1988. His work includes contributions to applied probability, statistics, graphical models, shape analysis and computational medicine. He is a fellow of the IMS, of SIAM and of the AMS.
Friday, March 7, 2025
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. David Watkins, Professor Emeritus, Washington State University
Faculty Host: Dr. Jeffrey Ovall
Title: Bulge Chasing is Pole Swapping
Abstract: At the beginning of the era of electronic computing there was a big effort to produce software to make the newly constructed hardware useful. In the area of scientific computing, one need that was recognized early on was for efficient and reliable methods to compute the eigenvalues of a matrix. This need was met around 1960 by the so-called QR algorithm, especially the implicitly- shifted variant due to John Francis. For the generalized eigenvalue problem, Moler and Stewart introduced a variant of Francis’s algorithm called the QZ algorithm. These algorithms, with various bells and whistles added over the years, are still the dominant algorithms today. These are bulge- chasing algorithms. They create bulges at one end of a (Hessenberg) matrix or pencil and chase them to the other end. A few years ago a new class of algorithms, pole-swapping algorithms, was introduced by Camps, Meerbergen, Vandebril, and others. It turns out that pole swapping is a generalization of bulge chasing. It might happen that new pole-swapping codes will supplant the current QR and QZ codes in the major software packages. Whether this turns out to be true or not, the pole-swapping viewpoint is extremely valuable for a detailed understanding of what makes this class of algorithms, both bulge-chasing and pole-swapping, work.
Biography: Professor Watkins is a numerical analyst who has occupied himself with a variety of problems in science and engineering over a fifty-year career. His greatest interest is in matrix computations, especially eigenvalue problems. He is the author of four books and numerous other publications in this area.
Friday, April 11, 2025
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. Holly Swisher, Oregon State University
Faculty Host: Dr. Liubomir Chiriac
Title: Modular functions and the monstrous exponents
Abstract: In 1973 Ogg initiated the study of monstrous moonshine with the observation that the prime divisors of the monster group are exactly those for which the Fricke quotient X0(p)+p of the modular curve X0(p) has genus zero. Here, motivated by Deligne's theorem on the p-adic rigidity of the elliptic modular j-invariant, we present a modular function-based approach to explaining some of the exponents that appear in the prime decomposition of the order of the monster.
Biography: Professor Swisher received her Ph.D. in Mathematics from the University of Wisconsin - Madison in 2005, under the supervision of Professor Ken Ono. She was a Ross Assistant Professor in the Department of Mathematics at the Ohio State University from 2005-2006 before joining the Mathematics Department at Oregon State in 2006. Professor Swisher is a researcher in the areas of number theory and combinatorics. Her current work is focused on modular forms, partition theory, and hypergeometric series, including the interplay between them.
Friday, April 25, 2025
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. Zachary Grey, NIST Information Technology Laboratory
Faculty Host: Dr. Bruno Jedynak
Title: Separable Shape Tensors: Emerging Methods in Pattern Recognition
Abstract: Scientists often leverage image segmentation to extract shape ensembles containing thousands of curves representing patterns in measurements. Shape ensembles facilitate inferences about important changes when comparing and contrasting images---e.g., examining material microstructures. We introduce novel pattern recognition formalisms combined with inference methods over ensembles containing thousands of segmented curves. This is accomplished by accurately approximating eigenspaces of composite integral operators to motivate discrete, dual representations collocated at quadrature nodes. Approximations are projected onto underlying matrix manifolds and the resulting separable shape tensors constitute rigid-invariant decompositions of curves into generalized (linear) scale variations and complementary (nonlinear) undulations. With thousands of curves segmented from pairs of images, we demonstrate how data-driven features of separable shape tensors inform explainable binary classification utilizing a product maximum mean discrepancy; absent labeled data, building interpretable feature spaces in seconds without high performance computation, and detecting discrepancies below cursory visual inspections.
Biography: Zach is a staff applied mathematician in the Applied and Computational Mathematics Division within the Information Technology Laboratory at NIST - Boulder, CO. His research involves model-based dimension reduction and manifold learning for facilitating novel explanations and interpretations related to artificial intelligence and machine learning. Specifically, he often works with data-driven applications involving imaging/signal processing, geometry, and optimization.
Friday, May 30, 2025
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. David Ralston, SUNY Old Westbury
Faculty Host: Dr. J.J.P. Veerman
Title: Regular, Semi-Regular, and Proper Continued Fractions
Abstract: There are numerous equivalent derivations of the regular continued fraction of an irrational number. We begin with a review of the interpretation of the Gauss map as the (normalized length) rotation given by the first-return map of rotation by x (modulo one) on an interval of length 1-x. In joint work with N. Langeveld we develop similar schemes to produce both the semi-regular (numerators plus or minus one) and proper continued fraction (numerators arbitrary positive integers) representations of x. In both of these variants an irrational x has uncountably many such representations; our construction proposes a natural parameterization of each. We also give a characterization of which positive integers may appear as a denominator for proper continued fractions as an analogue to the classical characterization of regular continued fraction convergents as best approximations of the second kind.
Biography: David Ralston is an Associate Professor in the Mathematics department at SUNY Old Westbury, where he has taught since 2012. Before that he held postdoctoral positions at Ben Gurion University of the Negev and The Ohio State University, and he received his Ph.D. in 2008 at Rice University under Professor Michael Boshernitzan. His research focuses on applying techniques in ergodic theory to topics in number theory, especially renormalization techniques to the study of continued fractions. Other topics of research include geodesic flows on infinite translation surfaces, topics in symbolic dynamics, and studying growth rates of ergodic sums in certain skew product systems. He has also improved the materials available to his undergraduate students, producing lecture notes, recordings, and other resources for several courses.