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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.,…

COS Events: Faculty-Staff Meeting

Riddick 301

Please save the date for the College of Sciences’ annual Faculty and Staff meeting at 4 p.m. on Wednesday, April 20, in 301 Riddick Hall. Interim Dean John Blondin will join us as we discuss topics that are important to you. There will be time for you to ask questions too.A reception in the Riddick Hearth…

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

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.,…

Pure Math Graduate Student Seminar: Ian Klein, NC State, The Chromatic Symmetric Function and the Stanley-Stembridge Conjecture

SAS 2102

Symmetric functions are very interesting combinatorial objects. After decomposing certain symmetric functions in terms of different bases, we can often combinatorially interpret the resulting coefficients. This is made particularly easy if those coefficients are positive (or controllably negative). The chromatic symmetric function is one such symmetric function, and its decomposition has been of interest for…

Colloquium: Alison Marsden, Stanford University, Multi-Physics Modeling of Flow and Cardiac Function in Pediatric Cardiology

SAS 2203

Congenital heart disease affects 1 in 100 infants and is the leading cause of infant mortality in the US. Among the most severe forms of congenital heart disease is single ventricle physiology, in which the heart develops with only one functional pumping chamber. These patients typically undergo three open chest surgeries, culminating in the Fontan…

Geometry and Topology Seminar: Joonas Ilmavirta, University of Jyväskylä, Finland, Geophysics and algebraic geometry

SAS 4201

Many areas of interest within the Earth are anisotropic, meaning that the speed of sound is different in different directions. It turns out that pressure waves are far better behaved than shear waves, but fortunately the different polarizations are coupled together through algebraic geometry. I will explain the surprising power of algebraic geometry in the…

Algebra and Combinatorics Seminar: Roeland Wiersema, University of Waterloo, Here comes the SU(N): multivariate quantum gates and gradients

SAS 2235

Variational quantum algorithms use non-convex optimization methods to find the optimal parameters for a parametrized quantum circuit in order to solve a computational problem. The choice of the circuit ansatz, which consists of parameterized gates, is crucial to the success of these algorithms. Here, we propose a gate which fully parameterizes the special unitary group…