All Seminars
| Title: Patch Normalizing Regularizer: Reconstruction using only one ground truth image |
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| Seminar: Computational and Data Enabled Science |
| Speaker: Paul Hagemann of TU Berlin |
| Contact: Lars Ruthotto, lruthotto@emory.edu |
| Date: 2022-10-06 at 10:00AM |
| Venue: MSC W301 |
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| Abstract: Reconstructing images from measurements (e.g. sinograms in CT) is a very active research topic. However in many domains, such as medical or material sciences, ground truth data is very hard or costly to obtain. In this talk, we will leverage the idea of patch-based learning for reconstructing images. The regularizer will learn the patch distribution from very few ground truth images by randomly subsampling 6x6 patches and learning their distribution. More specifically, we will use a normalizing flow to learn the patch distribution of the ground truth image, which we call patchNR. In reconstruction, we will minimize a sum of the negative log likelihood of the patches and the data fidelity term. Our method will be compared to other regularization techniques which use little data for CT, material and texture images. Furthermore, an outlook on how our method can be leveraged to perform zero shot superresolution will be given. |
| Title: Smooth limits of plane curves and Markov numbers |
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| Seminar: Algebra |
| Speaker: David Stapleton of The University of Michigan |
| Contact: David Zureick-Brown, david.zureick-brown@emory.edu |
| Date: 2022-10-04 at 4:00PM |
| Venue: MSC N304 |
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| Abstract: When can we guarantee that smooth proper limits of plane curves are still plane curves? Said a different way --- When is the locus of degree d plane curves closed in the (open) moduli space of smooth genus g curves? It is relatively easy to see that if d>1, then d must be prime. Interestingly, this is not sufficient -- Griffin constructed explicit families of quintic plane curves with a smooth limit that is not a quintic plane curve. In this talk we propose the following conjecture: Smooth proper limits of plane curves of degree d are always planar if d is prime and d is not a Markov number. We discuss the motivation and evidence for this conjecture which come from Hacking and Prokhorov's work on Q-Gorenstein limits of the projective plane. |
| Title: About the Lp theory for the non-cutoff Boltzmann equation |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Ricardo Alonso of Texas A$\&$M at Qatar |
| Contact: Maja Taskovic, maja.taskovic@emory.edu |
| Date: 2022-09-29 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: In this talk we discuss different technical elements to obtain a priori estimates for Lp norms of weak solutions to non-cutoff kinetic equations using as example the homogeneous/inhomogeneous Boltzmann equation. Rather than a detailed-proof talk, we point out difficulties and give some intuition related to the main steps of the strategy. In particular, we discuss the localization process of Boltzmann type operators which cover an ample range of operators such as the fractional Laplacian. |
| Title: Counting Elliptic Curves Over Number Fields |
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| Seminar: Algebra |
| Speaker: Tristan Phillips of The University of Arizona |
| Contact: David Zureick-Brown, david.zureick-brown@emory.edu |
| Date: 2022-09-27 at 4:00PM |
| Venue: MSC N304 |
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| Abstract: Let $E$ be an elliptic curve over a number field $K$. The Mordell--Weil Theorem states that the set of rational points $E(K)$ of $E$ forms a finitely generated abelian group. In particular, we may write $E(K) = E(K)_{tors}\oplus \mathbb{Z}^r$, where $E(K)_{tors}$ is a finite torsion group, called the torsion subgroup of $E$, and $r$ is a non-negative integer, called the rank of $E$. In this talk I will discuss some results regarding how frequently elliptic curves with a prescribed torsion subgroup occur, and how one can bound the average analytic rank of elliptic curves over number fields. One of the main ideas behind these results is to use methods from Diophantine geometry to count points of bounded height on modular curves. |
| Title: The Art of Repeatedly Project your Problems |
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| Seminar: Computational and Data Enabled Science |
| Speaker: Matthias Chung of Emory University |
| Contact: TBA |
| Date: 2022-09-22 at 10:00AM |
| Venue: MSC W301 |
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| Abstract: Inference by means of mathematical modeling from a collection of observations remains a crucial tool for scientific discovery and is ubiquitous in application areas such as signal compression, imaging restoration, and supervised machine learning. With ever-increasing model complexities and growing data size, new specially designed methods are urgently needed to recover meaningful quantities of interest. We consider the broad spectrum of linear inverse problems where the aim is to reconstruct quantities with a sparse representation on some vector space; often solved using the (generalized) least absolute shrinkage and selection operator (lasso). The associated optimization problems have received significant attention, in particular in the early 2000s, because of their connection to compressed sensing and the reconstruction of solutions with favorable sparsity properties using augmented Lagrangians, alternating directions and splitting methods. We provide a new perspective on the underlying l1 regularized inverse problem by exploring the generalized lasso problem through variable projection methods. We arrive at our proposed variable projected augmented Lagrangian (vpal) method. We provide numerical examples demonstrating the computational efficiency for various imaging problems. |
| Title: Jordan Decompositions of Tensors |
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| Seminar: Algebra |
| Speaker: Luke Oeding of Auburn University |
| Contact: David Zureick-Brown, david.zureick-brown@emory.edu |
| Date: 2022-09-21 at 2:30PM |
| Venue: MSC E208 |
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| Abstract: The Jordan normal form for similar matrices is a powerful classification tool as it provides a test to determine which matrices are similar (in the same orbit), and whether one orbit contains another or not. We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra which acts on it and embed them into an auxiliary algebra. Viewed as endomorphisms of this algebra we associate adjoint operators to tensors. We show that the group actions on the tensor space and on the adjoint operators are consistent, which endows the tensor with a Jordan decomposition. We utilize aspects of the Jordan decomposition to study orbit separation and classification in examples that are relevant for quantum information. My talk will contain many examples and open questions. |
| Title: Short hands-on course on CUQIpy - a new Python platform for computational uncertainty quantification in inverse problems |
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| Seminar: Computational and Data Enabled Science |
| Speaker: Jakob Sauer Jørgensen of Technical University Denmark |
| Contact: Julianne Chung, julianne.mei-lynn.chung@emory.edu |
| Date: 2022-09-15 at 8:30AM |
| Venue: MSC N301 |
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| Abstract: CUQIpy (pronounced "cookie pie") is a new computational modelling environment in Python that uses UQ (Bayesian statistics and sampling) to access and quantify the uncertainties in solutions to inverse problems. The overall goal of the software package is to allow both expert and non-expert (without deep knowledge of statistics and UQ) users to perform UQ related analysis of their inverse problem while focusing on the modelling aspects. To achieve this goal the package utilizes state-of-the-art tools and methods in statistics and scientific computing specifically tuned to the ill-posed and often large-scale nature of inverse problems to make the UQ feasible. The training course will be very hands-on with Jupyter notebook exercises demonstrating basic and more advanced functionality of CUQIpy. No installation is necessary, as exercises will be run on our online platform accessed through a normal browser, so participants should just bring a laptop with wifi access to join the zoom meeting and the online platform (instructions will be given during the course). |
| Title: Short hands-on course on CUQIpy - a new Python platform for computational uncertainty quantification in inverse problems |
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| Seminar: Computational and Data Enabled Science |
| Speaker: Jakob Sauer Jørgensen of Technical University Denmark |
| Contact: Julianne Chung, julianne.mei-lynn.chung@emory.edu |
| Date: 2022-09-15 at 10:00AM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: CUQIpy (pronounced "cookie pie") is a new computational modelling environment in Python that uses UQ (Bayesian statistics and sampling) to access and quantify the uncertainties in solutions to inverse problems. The overall goal of the software package is to allow both expert and non-expert (without deep knowledge of statistics and UQ) users to perform UQ related analysis of their inverse problem while focusing on the modelling aspects. To achieve this goal the package utilizes state-of-the-art tools and methods in statistics and scientific computing specifically tuned to the ill-posed and often large-scale nature of inverse problems to make the UQ feasible. The training course will be very hands-on with Jupyter notebook exercises demonstrating basic and more advanced functionality of CUQIpy. No installation is necessary, as exercises will be run on our online platform accessed through a normal browser, so participants should just bring a laptop with wifi access to join the zoom meeting and the online platform (instructions will be given during the course). |
| Title: On deriving the Vlasov equation and its Hamiltonian structure |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Joseph Miller of University of Texas at Austin |
| Contact: Maja Taskovic, maja.taskovic@emory.edu |
| Date: 2022-09-15 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: The Vlasov equation is a nonlinear PDE used to model plasmas in physics. It can be rigorously derived from Newton's laws of motion for many particles via empirical measures, or by a hierarchy of equations called the BBGKY hierarchy in a mean-field limit. The Vlasov equation itself contains geometric information, called a Hamiltonian structure, which is shared by the finite particle dynamics. In this talk, I will explain how to rigorously derive one Hamiltonian structure from the other. This is joint work with Andrea R. Nahmod, Natasa Pavlovic, Matt Rosenzweig, and Gigliola Staffilani. |
| Title: Reduced order modelling as enabler for optimization and digital twins |
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| Seminar: Computational and Data Enabled Science |
| Speaker: Marco Tezzele of UT Austin |
| Contact: Alessandro Veneziani, avenez2@emory.edu |
| Date: 2022-09-08 at 10:00AM |
| Venue: MSC W301 |
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| Abstract: We present data-driven reduced order models with a focus on reduction in parameter space to fight the curse of dimensionality in design optimization. We show two extensions of the Active Subspaces (AS) technique: a kernel version exploiting an intermediate mapping to a higher dimensional space, and a local approach in which a clustering induced by a global active subspace is used for regression and classification tasks. Parameter space reduction methods can also be used within a multi-fidelity nonlinear autoregressive scheme to improve the approximation accuracy of high-dimensional functions, using only high-fidelity data. Finally, we integrate AS into the genetic algorithm to enhance the convergence during the optimization of high-dimensional quantities of interest. These methods, together with non-intrusive reduced order models based on proper orthogonal decomposition, are applied to the structural optimization of cruise ships and shape optimization of a combatant hull. The last part of the talk will be devoted to an ongoing work on digital twins and adaptive planning strategies in a Bayesian setting. |