All Seminars
| Title: Forbidden subgraphs and spherical two distance sets |
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| Seminar: Discrete Math |
| Speaker: Zilin Jiang of Arizona State University |
| Contact: Liana Yepremyan, liana.yepremyan@EMORY.EDU |
| Date: 2022-04-01 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Given a real number \(\lambda\), what can we say about the family G(\(\lambda\)) of graphs with eigenvalues bounded from below by -\(\lambda\)The Cauchy interlacing theorem implies that that the family G(\(\lambda\)) is closed under taking (induced) subgraphs. Similar to Wagner’s theorem, which describes the family of planar graphs by finite forbidden minors, it is natural to ask for which \(\lambda\) the family G(\(\lambda\)) has a finite forbidden subgraph characterization. In this talk, I will illustrate the key ideas in answering this question, and I will demonstrate a peculiar connection to spherical two distance sets — a set of unit vectors in a Euclidean space the pairwise inner products of which assume only two values. Joint work with Alexandr Polyanskii, Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao. |
| Title: The Georgia Algebraic Geometry Symposium |
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| Seminar: Algebra |
| Speaker: {} of |
| Contact: David Zureick-Brown, david.zureick-brown@emory.edu |
| Date: 2022-04-01 at 5:00PM |
| Venue: MSC E208 |
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| Abstract: The Georgia Algebraic Geometry Symposium is a conference series, jointly organized by the University of Georgia, Emory University and Georgia Tech. \\ The conference will begin Friday late afternoon and end Sunday early afternoon. \\ See {https://www.math.emory.edu/$\sim$ dzb/conferences/GAGS2022/} for more information. \\ Speakers: \\ Evangelia Gazaki (University of Virginia) \\ Roman Fedorov (University of Pittsburgh)\\ Angela Gibney (University of Pennsylvania)\\ Philippe Gille (Institut Camille Jordan)\\ Diego Izquierdo (École Polytechnique)\\ Martin Olsson (University of California, Berkeley)\\ Karl Schwede (University of Utah)\\ Brooke Ullery (Emory University)\\ |
| Title: Multiphase fluid dynamics at leadership-class scale: Models, numerics, and algorithms |
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| Seminar: Computational Math |
| Speaker: Spencer Bryngelson of Georgia Institute of Technology |
| Contact: Yuanzhe Xi, yuanzhe.xi@emory.edu |
| Date: 2022-03-31 at 10:00AM |
| Venue: MSC W201 |
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| Abstract: Computational fluid dynamics (CFD) simulations utilize the lions share of HPC resources the world over. Still, the CFD community has a fragmented and generally closed-source software stack. This paradigm must change if the community hopes to keep pace with the rapid evolution of HPC resources,. In this talk I will present our efforts in this direction. State-of-the-art computational models for simulating multiphase flows will be presented with application to problems in biomedicine, defense, and energy. Algorithms for near-optimal performance on the latest HPC resources will be interrogated. I will also discuss our effort towards painless embedding of the ever more common data-driven models in scalable simulation codes. All software discussed in this talk is freely and openly available on our Github pages with permissive licensing: https://github.com/comp-physics and https://github.com/mflowcode |
| Title: Categorifying quadratic zeta functions |
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| Seminar: Algebra |
| Speaker: Andrew Kobin of Emory University |
| Contact: David Zureick-Brown, dzureic@emory.edu |
| Date: 2022-03-29 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Zeta functions show up everywhere in math these days. While some work in the past has brought homotopical methods into the theory of zeta functions, there is in fact a lesser-known zeta function that is native to homotopy theory. Namely, every suitably finite decomposition space (aka 2-Segal space) admits an abstract zeta function as an element of its incidence algebra. In this talk, I will show how many 'classical' zeta functions from number theory and algebraic geometry can be realized in this homotopical framework, and briefly advertise an upcoming preprint (joint with Jon Aycock) that categorifies the Dedekind zeta function of a quadratic number field. |
| Title: Improving Multigrid Methods with Deep Neural Networks |
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| Defense: Dissertation |
| Speaker: Ru Huang of Emory University |
| Contact: Ru Huang, ru.huang@emory.edu |
| Date: 2022-03-28 at 10:30AM |
| Venue: MSC N215 |
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| Abstract: Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from Partial Differential Equations (PDEs) and graph Laplacians from machine learning applications. There are two key components of multigrid, smoothing which aims at reducing high-frequency errors on each grid level, and coarse grid correction which interpolates the solution at the coarse grid. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. Meanwhile, as the multigrid hierarchy is formed, coarse-grid operators have significantly more nonzeros per row than the original fine-grid operator, which generates high parallel communication costs on coarse-levels. In this talk, I will first talk about my research on developing an efficient adaptive framework for learning optimal smoothers from operator stencils in the form of convolutional neural networks (CNNs). I will also talk about our deep learning framework for sparsifying coarse grid operators. I will demonstrate how these techniques can be used for challenging anisotropic rotated Laplacian problems, variable coefficient diffusion problems, and linear elasticity problems. |
| Title: Generating Graphs with Deep Learning and Graph Theory |
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| Defense: Dissertation |
| Speaker: Yuliang Ji of Emory University |
| Contact: Yuliang Ji, yuliang.ji@emory.edu |
| Date: 2022-03-25 at 9:00AM |
| Venue: MSC E406 |
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| Abstract: Deep generative models attract lots of attention in recent years. With deep neural networks and specific designs, deep generative models can generate high-quality realistic data. In this dissertation, I focus on combining the deep generative models with the traditional graph theory algorithms to reduce the dependence on the volume of the training data and improve the quality of the generated graphs. I first propose a deep learning method to improve the Havel-Hakimi graph realization algorithm to generate doppelganger graphs from a single graph. Second, I present a few new architectures of normalizing flow models with improved performance and theoretical guarantees. Finally, I develop a permutation invariant method via leveraging graph theory and denoising diffusion models for generating molecular graphs. |
| Title: The Laplace and Heat Operators on Quantum Graphs |
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| Defense: Dissertation |
| Speaker: Kenny Jones of Emory University |
| Contact: Wesley Jones, wesley.kenderdine.jones@emory.edu |
| Date: 2022-03-24 at 3:00PM |
| Venue: Emerson E363 |
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| Abstract: This presentation will introduce general strategies, techniques, and results for differential operators on quantum graphs. The focus of the talk will be on new results presented in my doctoral dissertation. The first result is a sharp diameter bound on the spectral gap for quantum graphs. Followed by a new technique for bounding the heat kernel on quantum graphs and several bounds for the heat kernel. Finally, I will present an original equation and derivation of the mean value theorem for the heat equation on quantum graphs and give a bound for the mean value theorem. |
| Title: Codes from Fiber Products of Curves |
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| Seminar: Algebra |
| Speaker: Mckenzie West of University of Wisconsin - Eau Claire |
| Contact: David Zureick-Brown, dzureic@emory.edu |
| Date: 2022-03-22 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Error correcting codes are used to store information efficiently while still allowing for recovery in the case of partial loss. Recently work has begun to construct codes using the algebraic geometric properties of curves over finite fields. In this talk, we'll introduce the general construction of codes from fiber products curves and provide a few explicit examples of locally recoverable codes created using these methods. This collaborative work started at the inaugural Rethinking Number Theory workshop in October 2020. |
| Title: Weak degeneracy of graphs |
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| Seminar: Discrete Math |
| Speaker: Anton Bernshteyn of Georgia Tech |
| Contact: Liana Yepremyan, liana.yepremyan@EMORY.EDU |
| Date: 2022-03-16 at 4:00PM |
| Venue: MSC E406 |
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| Abstract: Motivated by the study of greedy algorithms for graph coloring, we introduce a new graph parameter, which we call weak degeneracy. This notion formalizes a particularly simple way of "saving" colors while coloring a graph greedily. It turns out that many upper bounds on chromatic numbers follow from corresponding bounds on weak degeneracy. In this talk I will survey some of these bounds as well as state a number of open problems. This is joint work with Eugene Lee (Carnegie Mellon University). |
| Title: Scale Inverse Problems: Low-Rank Approximations and Optimization |
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| Defense: Dissertation |
| Speaker: Chang Meng of Emory University |
| Contact: Chang Meng, chang.meng@emory.edu |
| Date: 2022-03-03 at 12:00PM |
| Venue: MSC W501 |
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| Abstract: Inverse problems can be found in a variety of scientific applications, and the development of efficient and reliable methods remain an essential and challenging task. In this thesis, we introduce novel low-rank solvers for linear systems that arise from large scale inverse problems, which are usually ill-posed and require the use of regularization to obtain meaningful solutions. The new methods are developed around the concept of regularization: i) the low-rank, Kronecker product based forward model approximation method involves the approximation of a truncated singular value decomposition; and ii) the low-rank Krylov subspace methods are based on nuclear norm regularization. We explore the performance of these novel low-rank methods in various imaging applications such as image deblurring, inpainting and computer tomography. Besides applications where the forward model is known and fixed, we also consider an extended application, where the forward model is not exactly known and requires calibration. In this context, we are able to not only apply our new low-rank methods, but also propose a new hybrid machine learning and block coordinate descent algorithm that effectively improves solution accuracy. |