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Numerical Analysis Seminar: Pejman Sanaei, Georgia State University, On mathematical modeling and simulation of flight stability of objects, tissue engineering and droplets

SAS 4201

In this talk, I will present 3 problems on fluid structure interaction: 1) Flight stability of wedges: Recent experiments have shown that cones of intermediate apex angles display orientational stability with apex leading in flight. Here we show in experiments and simulations that analogous results hold in the two-dimensional context of solid wedges or triangular prisms in planar…

Geometry and Topology Seminar: Dilara Siraeva, Fulbright Scholar, NC State, Symmetry reduction of a gas dynamic system of PDEs with a special state function

SAS 4201

In this talk, I will present new results on the symmetry reduction of gas dynamic systems of PDEs following the general framework presented by  Lev Ovsyannikov in his article  "The “podmodeli” program. Gas dynamics" https://www.sciencedirect.com/science/article/pii/0021892894901376 The gas dynamics systems of equations, with an arbitrary state equation, has an 11-dimensional Lie algebra of symmetries which generates a group…

Algebra and Combinatorics Seminar: Andrew Harder, Lehigh University, The geometry of 2-loop Feynman integrals

SAS 2235

Speaker’s webpage: https://math.cas.lehigh.edu/andrew-harder In particle physics, many quantities of interest are expressed in terms of Feynman integrals. These integrals are attached to combinatorial objects called Feynman graphs, and can be expressed as integrals over (infinite) domains inside the real plane. In examples, one often finds that Feynman integrals are equal to special values of functions that…

Differential Equations and Nonlinear Analysis Seminar: Mihaela Ifrim, University of Wisconsin Madison, Global solutions for 1D cubic defocusing dispersive equations: Part I

SAS 4201

This article is devoted to a general class of one dimensional NLS problems with a cubic nonlinearity. The question of obtaining scattering, global in time solutions for such problems has attracted a lot of attention in recent years, and many global well-posedness results have been proved for a number of models under the assumption that…

Applied Math Graduate Student Seminar: Walker Powell, NC State, Model Reduction and Validation Tools for Large-Scale Models

SAS 1220

Of primary importance in computational science and applications is quantification and improvement of predictive capabilities of large-scale parameterized models, which often require the use of multi-query techniques that are intractable for computationally expensive models. This research focuses on three primary thrusts: sensitivity analysis, reduced-order modeling, and uncertainty quantification and algorithm and implementation choices that scale favorably…

Numerical Analysis Seminar: Koffi Enakoutsa and Xinghao Dong , UCLA, The Morrey Conjecture: Insights from Numerical Simulations on Quasi-Convexity and Rank-One Convexity.

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The Morrey Conjecture concerns quasi-convexity and rank-one convexity of functions. While the former implies the latter, it's unclear if the converse is true. Sverak proved the conjecture in 3D, but it remains unresolved in the planar case. Analyzing these properties analytically is difficult, especially for vector-valued functions, hence we perform numerical simulations using example functions…

Geometry Topology Seminar: Jacek Brodzki, University of Southampton, England, Topological Learning and disorder in structured nano materials

SAS 4201

Disorder is a fact of life, and controlling it on the nanoscale is complex, expensive, and of limited use. On the other hand, disordered materials do offer a range of possible applications if we know how to identify their useful features. To this end, we propose an approach through Topological Learning  to quantify disorder and…

Algebra and Combinatorics Seminar: Sean Sanford, The Ohio State University, Real Fusion Categories

SAS 2235

Fusion categories are algebraic gadgets that have seen many applications in topology and mathematical physics.  In particular, they can be used to encode topological quantum field theories in the sense of Atiyah.  Classical examples of fusion categories include C-Rep(G), the category of finite dimensional complex representations of a finite group G.  Because of their connections…

Differential Equations and Nonlinear Analysis Seminar: Mikhail Perepelitsa, University of Houston, Kinetic modeling of Myxobacteria motion with nematic alignment

SAS 4201

Motivated by motion of myxobacteria, we review several kinetic approaches for modeling motion of self-propelled, interacting rods. We will focus on collisional models of Boltzmann type and discuss the derivation of the governing equations, the range of their validity, and present some analytical and numerical results. We will show that collisional models have a natural…

Pure Math Graduate Student Seminar: Tim Ablondi, Koszul Duality in a Hypertoric Setting

SAS 2102

Hypertoric varieties are quaternionic analogs of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and hyperkahler geometry.  In the last decade, hypertoric varieties have appeared prominently in investigations of symplectic duality, a mathematical incarnation of 3d mirror…

Symbolic Computation Seminar: Máté Telek , University of Copenhagen, Reaction networks and a generalization of Descartes’ rule of signs to hypersurfaces

SAS 4201

The classical Descartes’ rule of signs provides an easily computable upper bound for the number of positive real roots of a univariate polynomial with real coefficients. Descartes' rule of signs is of special importance in applications where positive solutions to polynomial systems are the object of study. This is the case in reaction network theory…

Numerical Analysis Seminar: Elizabeth Newman, Emory University, How to Train Better: Exploiting the Separability of Deep Neural Networks

SAS 4201

Deep neural networks (DNNs) have gained undeniable success as high-dimensional function approximators in countless applications. However, there is a significant hidden cost behind triumphs - the cost of training. Typically, DNN training is posed as a stochastic optimization problem with respect to the learnable DNN weights. With millions of weights, a non-convex and non-smooth objective…

Differential Equations and Nonlinear Analysis Seminar: Fabio Ancona, University of Padova, Italy, Hard congestion limit of the p-system in the BV setting

SAS 4201

We are concerned with the rigorous justification of the  so-called hard congestion limit from a compressible system with singular pressure towards a mixed  compressible-incompressible system modeling partially congested dynamics, in the framework of BV solutions. We will consider small BV perturbations of reference solutions constituted by (possibly interacting) large interfaces, and we will  analyze the dynamics of…

Numerical Analysis Seminar: Elizabeth Newman, Emory University, Diving Deep Learning I

SAS 4201

Deep learning is one of the most universal techniques in the modern big data era, achieving remarkable success across imaging, healthcare, natural language processing, and more.  As applications begin to rely more heavily on deep learning, it is crucial that we understand how these algorithms make predictions and how we can make them better (e.g.,…