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Department of Mathematics

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:

Physics preserving enriched Galerkin methods

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Sanghyun Lee

In this talk, we consider new finite element methods for solving two different problems. One is coupled flow and transport systems in porous media and the other one is linear elasticity (mechanics) equation. The primary purpose of the study is to develop computationally efficient and robust numerical methods that could be free of both oscillations due to lack of local conservation and locking effects. The locally conservative enriched Galerkin (LF-EG), which will be utilized for solving flow problem is constructed by adding a constant function to each elements based on the classical continuous Galerkin methods. The locking-free enriched Galerkin (LC-EG) adds a vector to the displacement space. These EG methods employs the well-known discontinuous Galerkin (DG) techniques, but the approximation spaces have fewer degrees of freedom than those for the typical DG methods, thus offering an efficient alternative to DG methods. We present a priori error estimates of optimal order. We also… Read more.

Fokas Diagonalization

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Dave Smith

We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve initial boundary value problems (IBVP), we show that it is sufficient to solve IBVP whose spatial parts are described by such operators. We argue that the method described may be viewed as a reimplementation of the Fokas transform method for linear evolution equations on the finite interval. The results are extended to multipoint and interface operators, including operators defined on networks of finite intervals, in which the coefficients of the differential operator may vary between subintervals, and arbitrary interface and boundary conditions may be imposed; differential operators with piecewise constant coefficients are thus included. BIO: Dave Smith is an Applied Mathematician working at Yale-NUS College, Singapore since 2016. He completed his… Read more.

The Knave's Cosmological Theorem

Zoom
Number Theory Seminar

Speaker: Tamsyn Morrill

Abstract: The Look-Say sequence is a classic example of recursion. Its terms are verbalized descriptions of their predecessors --- initialized at 1 --- 11, 21, 1211, and so on. Conway demonstrated that the asymptotic growth rate of this sequence is the unique real root of a degree 71 monic polynomial. The general idea is to recast the problem in linear algebra through use of his Cosmological Theorem. Today I present a variation of this problem. A knave (of Smullyan's famed door-keeper puzzle) now controls the recursion. After working through some small examples, we will remake the Cosmological Theorem in the knave's image. Read more.

Global Sensitivity Analysis of Plasma Instabilities via Active Subspaces 

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Stephen Pankavich

The dynamics of laboratory and space plasmas are often driven by potentially uncertain values of physical parameters. For this reason, the utilization of computational methods to quantify such uncertainty represents an important tool to understand how certain physical phenomena depend upon fluctuations in the values of these parameters. In this direction, I'll discuss the construction and implementation of new computational methods, called active subspace methods, to quantify the induced uncertainty within the (linear) stability/instability rates generated by perturbations in a collisionless plasma near spatially homogeneous equilibria. BIO: Steve Pankavich is a Professor in the Department of Applied Mathematics and Statistics at the Colorado School of Mines, where he has served as a faculty member for 11 years. He earned a PhD in Mathematical Sciences from Carnegie Mellon University and was a Zorn Postdoctoral Fellow at Indiana University. Prior to joining Mines, he also held a… Read more.

Regularization Methods for Inverse Problems in Imaging

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Malena Espanol

Discrete linear and nonlinear inverse problems arise from many different imaging systems, exhibiting inherent ill-posedness wherein solution sensitivity to data perturbations prevails. This sensitivity is exacerbated by errors arising from imaging system components (e.g., cameras, sensors, etc.), necessitating the development of robust regularization methods to attain meaningful solutions. Our presentation commences with the exposition of distinct imaging systems, and their mathematical formalism, and subsequently introduces regularization techniques tailored for linear inverse problems. Then, we delve into the variable projection method, a powerful tool to address separable nonlinear least squares problems. BIO: Malena Español is an Assistant Professor in the School of Mathematical and Statistical Sciences at Arizona State University. She has a Bachelor's in Applied Mathematics from the University of Buenos Aires and a Master's and PhD in Mathematics from Tufts University; she was… Read more.

Development of the Arctic Coastal Erosion Model with a Demonstration at Drew Point, AK

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Jennifer Frederick

Erosion is accelerating along many stretches of the coastal Arctic, putting critical infrastructure at risk and threatening local communities. These permafrost-laden coastlines are increasing vulnerable to erosion due to declining sea ice and increasing duration of open water, more frequent storms during ice-free periods, and warming permafrost soils. However, predicting shoreline erosion rate remains extremely challenging because of the highly non-linear behavior of the coupled and changing environmental system. Although the Arctic comprises one-third of the global coastline and has some of the fastest eroding coasts, current tools for quantifying permafrost erosion are unable to explain the episodic, storm-driven erosion events. In this talk I will present the details of the development and calibration efforts for the Arctic Coastal Erosion (ACE) Model at Sandia National Laboratories. The ACE Model is a multi-physics numerical tool that couples oceanographic and atmospheric… Read more.