All Seminars

Title: Future of education in data science: what mode shall we take?
Colloquium: Numerical Analysis and Scientific Computing
Speaker: Dave Yuen of Columbia University and China University of Geosciences, Wuhan
Contact: Yuanzhe Xi, yuanzhe.xi@emory.edu
Date: 2018-10-31 at 4:00PM
Venue: MSC N304
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Abstract:
In the past several years, education of Big Data has expanded beyond the realm of computer science. This movement is occurring all over the USA and now in China because of educational reformation taken place there. In this lecture I will discuss from my own experience in both countries how this phenomenon is happening. We are witnessing a reformation and a struggle between computer science, applied mathematics and the user community. Geosciences is a discipline noted for its wealth of data, as are also other disciplines, such as medicine and finances. We will discuss the need for education and contrast this with training of students to use industrial programs for gaining immediate employment.
Title: Motivic equivalence for classical algebraic groups and critical varieties
Seminar: Algebra
Speaker: Anne Qu\'eguiner-Mathieu of Paris
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2018-10-30 at 4:00PM
Venue: MSC W301
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Abstract:
Two quadratic forms are called motivic equivalent if the corresponding quadrics have isomorphic Chow motives. A theorem due to Vishik provides a purely algebraic characterization of motivic equivalence, in terms of so-called higher Witt indices of quadratic forms. Charles De Clercq proved an analogous result for classical algebraic groups. As a consequence, if two quadratic forms are motivic equivalent, then not only the quadrics, but projective homogeneous varieties of any type under the action of the respective orthogonal groups have isomorphic motives. The talk will explain a generalization of this last observation to all classical algebraic groups, due to a joint work with De Clercq and Zhykhovich.
Title: Space Object Shapes from Unresolved Imaging in Space Situational Awareness
Seminar: Analysis and Differential Geometry
Speaker: Carolin Frueh of School of Aeronautics and Astronautics, Purdue University
Contact: Vladimir Oliker, oliker@emory.edu
Date: 2018-10-30 at 4:00PM
Venue: MSC W303
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Abstract:
Space Situational Awareness is concerned with the knowledge of objects in the near-earth realm. The vast majority of those objects are human-made; only about three percent of the currently tracked objects are active satellites, the others are objects without a function (anymore), dead satellites, mission-related objects, upper stages, and fragments. For objects in high altitude orbits, only non-resolved measurements are available, e.g. in the electro-optical realm, which means that shape and attitude information is not readily available. Shape information allows to characterize and identify the objects and their potential origin; furthermore, the shape influences the orbit of the objects via orbital perturbations. As a result shape information is also of interest for accurate prediction for collisions and reentry. In contrast to natural objects, human-made objects expose a variety of surface materials and sharp edges. In general, human-made shapes are not optimal in the sense of reducing surface area relative to the mass/volume of the object, hence leading to larger area-to-mass ratios than natural objects. Light curve measurements, i.e. brightness measurements over time are sufficiently easy measurements to obtain, however, especially for less reflective resp. small objects, significant noise is inherent to those measurements. In this talk, the general problem of Space Situational Awareness is discussed. Specific attention is given to engineering solutions to the problem of shape retrieval from light curve measurements. An inversion scheme is shown determining first the Extended Gaussian Image and then finding iterative approximations for the solution of Minkowski problem. Following a multi-hypothesis approach, likely shapes hypotheses are ranked fusing multiple measurement instances. The effect of the measurement noise and measurement geometry are discussed and results are shown for simplified shapes.
Title: Nonlocal Models in Computational Science and Engineering
Seminar: Numerical Analysis and Scientific Computing
Speaker: Marta D'Elia of Sandia National Lab
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2018-10-26 at 10:00AM
Venue: Atwood 215
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Abstract:
Nonlocal continuum theories such as peridynamics and nonlocal elasticity can capture strong nonlocal effects due to long-range forces at the mesoscale or microscale. For problems where these effects cannot be neglected, nonlocal models are more accurate than classical Partial Differential Equations (PDEs) that only consider interactions due to contact. However, the improved accuracy of nonlocal models comes at the price of a computational cost that is significantly higher than that of PDEs. In this talk, I will present nonlocal models and the Nonlocal Vector Calculus, a theory that allows us to treat nonlocal diffusion problems in almost the same way as PDEs. Furthermore, I will present current open challenges related to the numerical solution of nonlocal problems and show how we are currently addressing them. Specifically I will describe an optimization-based local-nonlocal coupling strategy and briefly introduce a technique to improve the performance of Finite Element (FE) approximations. The goal of local-nonlocal coupling methods is to combine the computational efficiency of PDEs with the accuracy of nonlocal models. These couplings are imperative when the size of the computational domain or the extent of the nonlocal interactions are such that the nonlocal solution becomes prohibitively expensive to compute, yet the nonlocal model is required to accurately resolve small scale features. Our approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. I will present consistency and convergence studies and, using three-dimensional geometries, I will also show that our approach can be successfully applied to challenging, realistic, problems. Finally, I will briefly introduce a new concept of nonlocal neighborhood that helps improving the performance of FE methods and show how our approach allows for fast assembling in two-dimensional computations.
Title: Diffusion generated methods for target-valued maps
Seminar: Numerical Analysis and Scientific Computing
Speaker: Braxton Osting of University of Utah
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2018-10-26 at 2:00PM
Venue: MSC N304
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Abstract:
A variety of tasks in inverse problems and data analysis can be formulated as the variational problem of minimizing the Dirichlet energy of a function that takes values in a certain target set and possibly satisfies additional constraints. These additional constraints may be used to enforce fidelity to data or other structural constraints arising in the particular problem considered. I'll present diffusion generated methods for solving this problem for a wide class of target sets and prove some stability and convergence results. I’ll give examples of how these methods can be used for the geometry processing task of generating quadrilateral meshes, finding Dirichlet partitions, constructing smooth orthogonal matrix valued functions, and solving inverse problems for target-valued maps. This is joint work with Dong Wang and Ryan Viertel.
Title: Joint Athens-Atlanta Number Theory Seminar
Seminar: Algebra
Speaker: Larry Rolen and Bianca Viray of Vanderbilt and University of Washington
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2018-10-23 at 4:00PM
Venue: TBA
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Abstract:
(At University of Georgia; more info later.)
Title: Optimal Transport on Finite Graphs with Applications
Seminar: Numerical Analysis and Scientific Computing
Speaker: Haomin Zhou of Georgia Institute of Technology
Contact: Manuela Manetta, manuela.manetta@emory.edu
Date: 2018-10-19 at 2:00PM
Venue: MSC N302
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Abstract:
In this talk, I will discuss the optimal transport theory on discrete spaces. Various recent developments related to free energy, Fokker-Planck equations, as well as Wasserstein distance on graphs will be presented, some of them are rather surprising. Applications in game theory and robotics will be demonstrated. This presentation is based on several joint papers with Shui-Nee Chow (Georgia Tech), Luca Dieci (Georgia Tech), Wen Huang (USTC), Wuchen Li (UCLA), Yao Li (U. Mass), Jun Lu (Shunfeng) and Haoyan Zhai (Georgia Tech).
Title: Rainbow fractional matchings
Seminar: Combinatorics
Speaker: Zilin Jiang of The Massachusetts Institute of Technology
Contact: Dwight Duffus, dwightduffus@emory.edu
Date: 2018-10-19 at 4:00PM
Venue: MSC W301
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Abstract:
Given edge sets E_1, ..., E_n, a rainbow set consists of at most 1 element from each E_i. Drisko's theorem says that any family of 2n-1 perfect matchings of size n in a bipartite graph has a rainbow perfect matching. In this talk, we will present a connection, found by Alon, to the well-known result of Erdos, Ginzburg and Ziv in additive number theory, and we will give a short proof of Drisko's theorem using Barany's colorful Caratheodory theorem from Discrete Geometry. If the bipartiteness assumption is removed, Drisko's result is no longer true. However, it may well be the case that 2n matchings suffice. Our new discrete-geometric proof leads to the discovery of a fractional version of the conjecture: Let n be an integer or a half integer. If the fractional matching number of each of the 2n graphs is at least n, then there is a rainbow edge set of fractional matching number at least n. This is joint work with Ron Aharoni and Ron Holzman.
Title: Existence and uniqueness of Green's function to a nonlinear Yamabe problem
Colloquium: Analysis and Differential Geometry
Speaker: Yanyan Li of Rutgers University
Contact: Vladimir Oliker, oliker@emory.edu
Date: 2018-10-18 at 4:00PM
Venue: MSC W303
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Abstract:
For a given finite subset S of a compact Riemannian manifold (M; g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M minus S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the new conformal metric belongs to the boundary of the given cone. This is a joint work with Luc Nguyen.
Title: On a Question of Gross and McMullen
Seminar: Algebra
Speaker: Eva Bayer Fluckinger of EPFL
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2018-10-16 at 4:00PM
Venue: MSC W301
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Abstract:
In a joint work with Lenny Taelman, we characterize the irreducible polynomials that occur as a characteristic polynomial of an isometry of an even, unimodular lattice with given signature, answering a question of Gross and McMullen. It turns out that the criteria are local ones, and that in the case of an irreducible polynomial, one has a local-global principle. This is no longer true for reducible polynomials. The aim of the talk is to describe these results, and give to a criterion for the local-global principle to hold.