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Silvia Gazzola, University of Bath, Iterative regularization methods for large-scale linear inverse problems

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 Inverse problems are ubiquitous in many areas of Science and Engineering and, once discretized, they lead to ill-conditioned linear systems, often of huge dimensions: regularization consists in replacing the original system by a nearby problem with better numerical properties, in order to find a meaningful approximation of its solution. After briefly surveying some standard regularization…

Joonas Ilmavirta, Tampere University, Finland, The light ray transform

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When is a function in the spacetime uniquely determined by its integrals over all light rays? I will introduce the problem, discuss why we might care about it, and how one might go about proving such uniqueness results. Depending on time and audience interest, I can also discuss proofs and tensor tomography.   Organizer: T.…

Victor Magron, LAAS-CNRS, France, The quest of efficiency and certification in polynomial optimization

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In 2001, Lasserre introduced a nowadays famous hierarchy of relaxations, called the moment-sums of squares hierarchy, allowing one to obtain a converging sequence of lower bounds for the minimum of a polynomial over a compact semialgebraic set. Each lower bound is computed by solving a semidefinite program (SDP). There are two common drawbacks related to…

Samantha Kirk, NC State, How to Construct Representations of Twisted Toroidal Lie Algebras via Lattice Vertex Algebras

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If you take a simple finite-dimensional Lie algebra g and tensor it with the Laurent polynomials in one variable, then you will get an infinite-dimensional Lie algebra known as a loop algebra. Affine Lie algebras are the central extensions of such loop algebras and their representations have been of interest to several mathematicians. What happens if we tensor g with…

Lars Ruthotto, Emory University, Numerical Analysis Perspectives on Deep Neural Networks

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The resurging interest in deep learning is commonly attributed to advances in hardware and growing data sizes and less so to new algorithmic improvements. However, cutting-edge numerical methods are needed to tackle ever larger and more complex learning problems. In this talk, I will illustrate numerical analysis tools for improving the effectiveness of deep learning…

Roberto Cominetti, Universidad Adolfo Ibáñez, Chile, Convergence rates for Krasnoselskii-Mann fixed-point iterations

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A popular method to approximate a fixed point of a non-expansive map is C is the Krasnoselskii-Mann iteration. This covers a wide range of iterative methods in convex minimization, equilibria, and beyond. In the Euclidean setting, a flexible method to obtain convergence rates for this iteration is the PEP methodology introduced by Drori and Teboulle…

Vakhtang Putkaradze, Variational Methods for Active Porous Media

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Many biological organisms are comprised of deformable porous media, with additional complexity of an embedded muscle. Using geometric variational methods, we derive the equations of motion for the dynamics of such active porous media. The use of variational methods allows to incorporate both the muscle action and incompressibility of the fluid and the elastic matrix…

Julia Plavnik, Indiana University, On odd-dimensional modular tensor categories

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Modular tensor categories arise naturally in many areas of mathematics, such as conformal field theory, quantum groups and Hopf algebras, low dimensional topology, representations of braid groups, and they have important applications in condensed matter physics, modeling topological phases of matter. In this talk, I will start by introducing the relevant concepts (modular, braided and…

Paul Cazeaux, The University of Kansas, Twisted, incommensurate layered materials: modeling, computations and topology

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Two-dimensional crystals have been intensely investigated both experimentally and theoretically since graphene was exfoliated from graphite. Physicists have recently developed the ability to stack one layer on another with a twist angle controlled to the scale of .1 degree with the goal of creating two dimensional materials with desired electronic, optical, and mechanical properties. Unusual…

Tyrus Berry, George Mason University, A Manifold Learning Approach to Boundary Value Problems

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Mesh-free methods for boundary value problems (BVPs) can be convenient on manifolds where generating a mesh may be difficult or when the manifold is not known explicitly but is determined by data.  Moreover, BVPs are important in machine learning since they provide a rigorous method of regularization for many regression problems.  In this talk we…