All Seminars

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Title: MLK Lecture
Colloquium: Education
Speaker: Robert "Bob" Parris Moses of The Algebra Project
Contact: Andra Gillespie, angille@emory.edu
Date: 2015-01-20 at 4:00PM
Venue: Winship Ballroom DUC
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Abstract:
TBA
Title: An Erdos-Ko-Rado Theorem for cross t-intersecting families
Seminar: Combinatorics
Speaker: Sang June Lee of Duksung Women's University
Contact: Vojtech Rodl, Rodl@mathcs.emory.edu
Date: 2015-01-12 at 4:00PM
Venue: E406
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Abstract:
A central result in extremal set theory is `the Erdos-Ko-Rado Theorem' (1961) which investigates the maximum size of families X of k-subsets in [n] such that two members in X intersect with at least t elements.\\ \\ Two families X and Y of k-subsets in [n] are called `cross t-intersecting' if, for every members A in X and B in Y, we have that A and B intersect with at least t elements. The cross t-intersecting version of the Erdos-Ko-Rado Theorem was conjectured but still open.\\ \\ In this talk we verify the conjecture for all integers t>13 except finitely many n and k for each fixed t. Our proofs make use of a weight version of the problem and randomness. This is joint work with Peter Frankl, Norihide Tokushige, and Mark Siggers.
Title: Reliable direct and inverse methods in computational hemodynamics
Defense: Dissertation
Speaker: Luca Bertagna of Emory University
Contact: Luca Bertagna, lbertag@emory.edu
Date: 2014-12-15 at 11:00AM
Venue: E408
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Abstract:
In the last 25 years, the use of mathematics to study the behavior of the human cardiovascular system significantly increased, not just as a descriptive qualitative tool, but also for quantitative analysis of patients conditions and even treatment design. The robustness of this tool depends on the reliability of the results. Data Assimilation (DA) is a set of techniques that can help to improve the specificity of the models, by incorporating available data (e.g., measurements), making the results of the simulations patient specific. On the other hand, the numerical methods used in the simulations must be accurate enough to guarantee that the computed solution accurately describes the real behavior of the system.\\ \\ This work is divided into two parts. In the first, we focus on the problem of the estimation of the compliance of a vessel using DA techniques. In particular, we use measurements of the displacement of the vessel wall to estimate its Young's modulus, and we focus on the issue of the computational costs associated with the solution of the inverse problem. The second part of this work concerns the accurate simulation of flows at moderately large Reynolds numbers. In particular, we focus on a particular discretization of the Leray system, proposing a new interpretation of the method as an operator-splitting scheme for a perturbed version of the Navier-Stokes equations, and we use heuristic arguments to calibrate one of the main parameters of the model.\\ \\ For both these parts we will perform numerical experiments, on 3D geometries, to validate the approaches. In particular, for the first part, we will use synthetic measures to validate our approach, while for the second part, we will test the method on a benchmark proposed by the Food and Drug Administration, comparing out results with experimental data.
Title: Approximating Stability Radii
Seminar: Numerical Analysis and Scientific Computing
Speaker: Manuela Manetta of School of Mathematics Georgia Institute of Technology
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2014-12-05 at 12:00AM
Venue: W301
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Abstract:
The distance of a n × n stable matrix to the set of unstable matrices, the so-called distance to instability, is a well-known measure of linear dynamical system stability. Existing techniques compute this quantity accurately but the cost is of the order of multiple SVDs of order n, which makes the method suitable for medium-size problems. A new approach is presented, based on Newton’s iteration applied to the pseudospectral abscissa, whose implementation is obtained by discretization of differential equations for low-rank matrices, and is particularly suited for large sparse matrices.
Title: On the signature of a quadratic form
Seminar: Algebra
Speaker: Jeremy Jacobson of Emory
Contact: David Zureick-Brown, dzb@mathcs.emoy.edu
Date: 2014-12-02 at 4:00PM
Venue: W306
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Abstract:
The signature of a quadratic form plays an important role in the study of quadratic forms in a Witt group. For any algebraic variety X over the real numbers R, it allows one to relate quadratic forms over X to the singular cohomology of the real points X(R). This has applications to bounding the order of torsion in the Witt group of quadratic forms over X.
Title: Assessing Motor Function in Parkinson
Defense: Masters Thesis
Speaker: Noah Adler of Emory University
Contact: Noah Adler, ndadler@emory.edu
Date: 2014-11-11 at 1:00PM
Venue: Woodruff Library, Rm. 213
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Abstract:
Abstract: Parkinson’s disease (PD) is a neurodegenerative disease resulting in motor- and movement-related impairments. A clinical diagnosis of Parkinson’s disease requires clinically detectable motor symptoms, which do not occur until six to eight years after the nigral neurons in the brain begin to degenerate. By detecting PD at an earlier stage, patients can begin therapy sooner, and consequently receive better treatment and care. Therefore, in order to detect motor defects prior to clinical detection, we developed a web-based, user-friendly computer task called Predictive Movement and Trajectory Tracking (PMATT). This task was administered to 23 PD patients and 14 normal controls while recording computer cursor movements. Using machine learning techniques, we calculated fifteen significant motor-related behavioral metrics which strongly distinguish the two groups of patients. By implementing a J48 classifier with these behavioral metrics, over 97% of subjects were correctly classified with an AUC of 0.992. From these results, we conclude that PMATT may be a helpful tool in screening for PD. Since it is easily scalable and automated for individual use, PMATT can be effortlessly administered to the general population. Furthermore, its use in research may help provide insights into the development of motor impairment in pre-clinical PD and help track symptom progression with a higher precision than is currently possible.​
Title: Analysis and Simulation of Bingham fluid problems with Papanastasiou-like regularizations: Primal and Dual formulations
Defense: Dissertation
Speaker: Anastasia Svishcheva of Emory University
Contact: Anastasia Svishcheva, asvish@emory.edu
Date: 2014-11-11 at 4:00PM
Venue: W301
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Abstract:
Today I will talk about Analysis and Simulation of Bingham fluid problems with Papanastasiou-like regularizations. I discuss the mixed formulation of Bingham-Papanastasiou problem, its well-posedness and show the numerical results. In general, common solvers for the regularized problem experience a performance degradation when the regularization parameter m gets greater. The mixed formulation enhanced numerical properties of the algorithm by introduction of an auxiliary tensor variable.\\ \\ I also introduce a new regularization for the Bingham equations, so called Corrected regularization. Corrected regularization demonstrates better accuracy than other ones. I show its well-posedness, and in addition, compare its numerical results with the results obtained with the applications of other regularizations.
Title: Mathematical problems in visual sciences
Seminar: Analysis and Differential Geometry
Speaker: Professor Jacob Rubinstein of Israel Institute of Technology - Technion
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2014-11-10 at 4:00PM
Venue: W303
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Abstract:
This talk should be of general interest to mathematicians and researchers in visual science and ophthalmology. It will be accessible to graduate students.
Title: Distinct edge weights on graphs
Seminar: Combinatorics
Speaker: Michael Tait of The University of California, San Diego
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2014-11-04 at 1:00PM
Venue: E408
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Abstract:
A Sidon set is a subset of an abelian group which has the property that all of its pairwise sums are distinct. Sidon sets are well-studied objects in combinatorial number theory and have applications in extremal graph theory and finite geometry. Working in the group of integers with multiplication, Erdos showed that one cannot find a Sidon set that is asymptotically denser than the primes. In this talk, we show that one can obtain the same result with a much weaker restriction than requiring a Sidon set. This complements work of Bollobas and Pikhurko from 2004. We also discuss an open problem that they posed, with some ideas for how to attack it. This is joint work with Jacques Verstraete.
Title: Joint Athens-Atlanta number theory seminar (at Georgia Tech)
Seminar: Algebra
Speaker: Arul Shankar and Wei Zhang of
Contact: TBA
Date: 2014-11-04 at 4:00PM
Venue: TBA
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Abstract:
TBA