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Upcoming Seminars

Memorial Union on sunny day

Join us for an upcoming seminar featuring mathematics faculty and invited speakers on one of our seven research topics. You may also see upcoming seminars by topic:


Developing a computational approach for moving-habitat models in two dimensions

STAG 111
Applied Mathematics and Computation Seminar

Speaker: Jane McDonald

ABSTRACT:Moving-habitat models describe a species’ dynamics over a climate-driven shifting habitat. They lend insight into the mechanisms promoting a species’ persistence in the face of climate change. In our approach, reaction-diffusion equations track the species’ density in time over the whole space. The suitable habitat, defined by a positive intrinsic growth rate, is bounded by a closed curve, called the interface, which shifts in time. Across the interface, there is a jump in density resulting from the consideration of habitat-dependent dispersal rates and habitat bias. Such a system motivates the development of a numerical method which can capture a jump in density across a moving interface. We introduce a mixed weak formulation for this system, where a dual variable acts as a Lagrange multiplier. For this problem, we construct a finite element method. We prove well-posedness for continuous and discrete cases. For the no-shift case, we derive a priori error estimates for the… Read more.


A $Web(SL_n^{-})$ Embedding through $\tilde{A}_{n-1}$ buildings

Bexell 328
Algebra and Number Theory Seminar

Speaker: Emily McGovern

In this talk, we describe an embedding of $Web(SL_n^{-})$, a diagrammatic monodical category, into a class of graph planar algebras. These graph planar algebras arise from affine type A buildings, a combinatorial structure developed by Tits in the 1970s. The relationship between finite projective geometries and affine buildings is key in establish the existence of an embedding functor in positive characteristic graph planar algebras. Read more.


Two talks on nonlinear heat equation by Madison Phelps and Praveeni Mathangadeera

STAG 111
Applied Mathematics and Computation Seminar

Speaker: Praveeni Mathangadeera and Madison Phelps

Madison Phelps:Nonlinear Solvers for Permafrost Problems Abstract: We study the nonlinear heat equation with phase change between liquid and ice with the enthalpy-temperature relationship, w-theta, in three variants. For Stefan problem (ST), this relationship is usually a multivalued graph where the phase transition resembles a shifted Heaviside function. For permafrost problems (P), w-theta is continuous, but its inverse requires a nonlinear solver. For soil with trapped air and large pores, we consider a model denoted (P*) where w-theta includes a multivalued graph but also has piecewise continuous properties. When the model is discretized in space by FV (finite volumes) and in time (implicitly), we require nonlinear solvers at two levels: a global one for the PDE, and a local one at each grid cell of the PDE. We give an overview of the choices available solvers including the recently popular Newton-Anderson variants which we test on simple model problems. Then we show their… Read more.


Sex Differences in Glutathione Metabolism and Their Consequences

Zoom
Dynamical Systems Seminar, Mathematical Biology Seminar, Probability and Data Science Seminar

Speaker: Allison Cruikshank

Glutathione (GSH) is the main antioxidant in the body and conjugates and eliminates a variety of toxicants, reactive oxygen species, and heavy metals. Clinical and experimental evidence has accumulated that females in humans and other mammals have higher glutathione levels than males. Understanding how hepatic GSH levels depend on estradiol is important since oxidative stress contributes to certain diseases, and oxidative stress is reduced by GSH. We use mathematical modeling to explore the causes and consequences of sex differences in GSH levels, including the stability of GSH during the menstrual cycle and variations in one-carbon metabolism in pre- and post-menopausal women undergoing hormone supplementation. Read more.


Sex Differences in Glutathione Metabolism and Their Consequences

Zoom
Dynamical Systems Seminar, Mathematical Biology Seminar, Probability and Data Science Seminar

Speaker: Allison Cruikshank

Glutathione (GSH) is the main antioxidant in the body and conjugates and eliminates a variety of toxicants, reactive oxygen species, and heavy metals. Clinical and experimental evidence has accumulated that females in humans and other mammals have higher glutathione levels than males. Understanding how hepatic GSH levels depend on estradiol is important since oxidative stress contributes to certain diseases, and oxidative stress is reduced by GSH. We use mathematical modeling to explore the causes and consequences of sex differences in GSH levels, including the stability of GSH during the menstrual cycle and variations in one-carbon metabolism in pre- and post-menopausal women undergoing hormone supplementation. Read more.


Sex Differences in Glutathione Metabolism and Their Consequences

Zoom
Dynamical Systems Seminar, Mathematical Biology Seminar, Probability and Data Science Seminar

Speaker: Allison Cruikshank

Glutathione (GSH) is the main antioxidant in the body and conjugates and eliminates a variety of toxicants, reactive oxygen species, and heavy metals. Clinical and experimental evidence has accumulated that females in humans and other mammals have higher glutathione levels than males. Understanding how hepatic GSH levels depend on estradiol is important since oxidative stress contributes to certain diseases, and oxidative stress is reduced by GSH. We use mathematical modeling to explore the causes and consequences of sex differences in GSH levels, including the stability of GSH during the menstrual cycle and variations in one-carbon metabolism in pre- and post-menopausal women undergoing hormone supplementation. Read more.


Kernel methods for operator learning and discovering equations with scarce data

STAG 111
Applied Mathematics and Computation Seminar

Speaker: Bamdad Hosseini

ABSTRACT: Operator learning, the data-driven approximation of nonlinear maps between function spaces, and equation learning, the problem of discovering PDEs that govern physical systems, are two focus areas of scientific machine learning and applications of AI in science. In this talk I will discuss mathematically simple, efficient, and competitive methods for both of these tasks using the framework of reproducing Kernel Hilbert spaces. I will also discuss a unifying view point that unites operator and equation learning. Various theoretical results and numerical benchmarks will also be discussed. Read more.


The effect of Anderson acceleration on the convergence order of superlinear and sublinear nonlinear solvers

TBA
Applied Mathematics and Computation Seminar

Speaker: Leo Rebholz

We consider the effect of Anderson acceleration (AA) on the convergence order of nonlinear solvers in fixed point form $x_{k+1}=g(x_k)$, that are looking for a fixed point of g. While recent work has answered the fundamental question of how AA affects the convergence rate of linearly converging fixed point iterations (at a single step), no analytical results exist (until now) for how AA affects the convergence order of solvers that do not converge linearly. We first consider AA applied to general methods with convergence order r, and show that AA changes the convergence order to (at least) (r+1)/2 for depth m=1; a more complicated expression for the order is found for the case of larger m. This result is valid for superlinearly converging methods and also locally for sublinearly converging methods where r<1 locally but r$\rightarrow$1 as the iteration converges, revealing that AA asymptotically slows convergence for superlinearly converging methods but (locally) accelerates it for… Read more.


A Tensor-Train Stochastic Finite Volume Method for Uncertainty Quantification

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Svetlana Tokareva

ABSTRACT: Many problems in physics and engineering are modeled by systems of partial differential equations such as the shallow water equations of hydrology, the Euler equations for inviscid, compressible flow, and the magnetohydrodynamic equations of plasma physics. The initial data, boundary conditions, and coefficients of these models may be uncertain due to measurement, prediction, or modeling errors.The stochastic finite volume (SFV) method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. The SFV method has shown great promise as a weakly-intrusive PDE solver for uncertainty quantification. However, in many relevant applications, the dimension of the stochastic space can make traditional implementations of the SFV method infeasible or impossible due to the so-called curse of dimensionality. We introduce the Tensor-Train SFV (TT-SFV) method within the tensor-train framework to manage the curse of dimensionality. This integration,… Read more.