Doctoral Exam: Yvonne Niyonzima, NC State, Application of Mathematical Modeling in Toxicology and Human Immunodeficiency Virus
ZoomAdvisor Hien Tran (tran@ncsu.edu, contact for Zoom access)
Events
Loading view.
Mikhail Karphukin, Caltech, Eigenvalues of the Laplacian and min-max for the energy functional
SAS 4201The Laplacian is a canonical second order elliptic operator defined on any Riemannian manifold. The study of optimal upper bounds for its eigenvalues is a classical problem of spectral geometry going back to J. Hersch, P. Li and S.-T. Yau. It turns out that the optimal isoperimetric inequalities for Laplacian eigenvalues are closely related to…
Doctoral Exam: Benjamin Hollering, NC State, Computational and Combinatorial Techniques for Phylogenetic Algebraic Geometry
ZoomAdvisor Seth Sullivant (smsulli2@ncsu.edu, contact for Zoom access)
Juan Carlos, Centro de Modelización Matemática, Ecuador, Bilevel learning for inverse problems
ZoomIn recent years, novel optimization ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different quantities/functions of interest. A fruitful approach in this sense is bilevel optimization, where the inverse problems are considered as lower-level constraints, while on the upper-level a loss function based…
Doctoral Exam: Michael Merrit, NC State, Multifidelity Global Sensitivity Analysis for Complex Problems
ZoomAdvisor Pierre Gremaud, contact for Zoom access
Gloria Mari Beffa, University of Wisconsin, Discrete Geometry of Polygons and Soliton Equations
SAS 4201In this talk we will discuss the connection between invariant evolutions of polygons and completely integrable discrete systems via polygonal geometric invariants. We will give examples and show how some open problems for bi-Hamiltonian structures of discrete systems were made easier and solved using this correspondence. If time allows we will discuss some open problems.…
Doctoral Exam: Robert DeYeso, NC State, Obstructing Exceptional Surgeries using Immersed Curves
ZoomAdvisor Tye Lidman, contact for zoom link
Kamala Dadashova, NC State, Parameter subset selection for a mathematical model of antibody therapies for neurological diseases
SAS 1220A significant challenge in the development of drugs to treat central nervous system (CNS) disorders is to attain sufficient delivery of antibodies across blood-brain barriers (BBB). Since not all antibodies can pass through BBB, it is crucial to understand antibody exposure in the CNS quantitatively to construct drug characteristics and identify proper dosing regimens. We…
Doctoral Exam: Cashous Bortner, NC State, Identifiability Analysis of Two Families of ODE Models
ZoomAdvisor Seth Sullivant, contact for Zoom access
Alexey Miroshnikov, Discover Financial Services, Wasserstein-based fairness interpretability framework for machine learning models
SAS 4201The objective of this talk is to introduce a fairness interpretability framework for measuring and explaining the bias in classification and regression models at the level of a regressor distribution. In our work, we measure the model bias across sub-population distributions in the model output using the Wasserstein metric. To properly quantify the contributions of…
Daniel Stern, University of Chicago, Steklov Eigenvalues on Surfaces
SAS 4201As described in the previous week's talk by Mikhail Karpukhin, there is a rich interplay between isoperimetric problems for Laplace eigenvalues on surfaces and the study of harmonic maps and minimal surfaces in spheres. Over the last 10-15 years, a program initiated by Fraser and Schoen has revealed a similar relationship between isoperimetric problems for the…
Stéphane Gaubert, École Polytechnique, France, What tropical geometry tells us about linear programming and zero-sum games
ZoomTropical convex sets arise as ``log-limits'' of parametric families of classical convex sets. The tropicalizations of polyhedra and spectrahedra are of special interest, since they can be described in terms of deterministic and stochastic games with mean payoff. In that way, one gets a correspondence between classes of zero-sum games, with an unsettled complexity, and classes…
John Darges, NC State, Extreme learning machines for variance-based global sensitivity analysis
SAS 1220Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing alternative is to analyze instead the sensitivity of a surrogate model with the goal of lowering computational costs while…
Semyon Tsynkov, NC State, Imaging With Synthetic Aperture Radar
ZoomSynthetic aperture radars (SAR) use microwaves to obtain images of the Earth's surface from airplanes or satellites. SAR images can be taken during nighttime and prove insensitive to the clouds or dust in the atmosphere. Therefore, SAR complements the aerial or spaceborne photography, even though there are fundamental differences between the two technologies. For example,…
Albert Chern, UCSD, Geometric approaches to infinite domain problems
ZoomNumerical simulations on infinite domains are challenging. In this talk, we will take geometric approaches to analyze the problems and provide new solutions. One problem we tackle is the perfectly matched layer (PML) problem for computational waves on infinite domains. PML is a theoretical wave-absorbing medium attached to the truncated domain that generates no reflection…
Bianchini Stefano, SISSA, ITALY, Properties of mixing BV vector fields
ZoomWe consider the density properties of divergence-free vector fields b in L^1(,BV(^2)) which are ergodic/weakly mixing/strongly mixing: this means that their Regular Lagrangian Flow X_t is an ergodic/weakly mixing/strongly mixing measure preserving map when evaluated at t=1. Our main result is that there exists a G-set U made of divergence free vector fields such that – The map T associating b with…
Sonia Kovalesky Day
SAS Hall LobbyAWM is happy to announce that we will be bringing back our Sonia Kovalevsky (SK) Day event this year, which will take place on Saturday, April 9th from 9:15a-2:00p in SAS Hall on NCSU's campus. Sonia Kovalevsky was the first major female mathematician and, in honor of her, schools across the nation host an SK…
Gregor Kemper, Technical University of Munich, Distance geometry, algebra and drones
ZoomIs it always possible to reconstruct a point configuration in the plane from the unlabeled set of mutual distances between the points? This and other questions translate to invariant theory and ultimately into problems about polynomial ideals. As it turns out, the following question is related: Can a drone detect the walls of a room…
Harley Hanes, NC State, Sensitivity and Identifiability Analysis of Boundary Penalties in a Galerkin Reduced Order Model.
SAS 1220Galerkin reduced-order models (ROMs) approximate computational fluid simulations by reducing snapshot data to a basis of proper orthogonal decomposition (POD) modes and solving for modal coefficients with ordinary differential equations. Galerkin ROMs reduce computational cost and can approximate flows with alternate Reynolds numbers, while parametric reduced order models allow adjustment of other system parameters. However,…