All Seminars
| Title: Umbral Moonshine |
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| Colloquium: Number Theory |
| Speaker: John Duncan of Case Western Reserve University |
| Contact: David Borthwick, davidb@mathcs.emory.edu |
| Date: 2015-02-03 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Umbral moonshine is a new and rapidly developing field at the intersection of number theory, group theory and mathematical physics. I will introduce the subject, describe its main challenges, and present some recent progress, including joint work with Michael Griffin and Ken Ono. |
| Title: Helioseismology from South Pole |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Stuart Jefferies of University of Hawaii |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2015-01-30 at 12:00PM |
| Venue: W306 |
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| Abstract: This talk will describe work on helioseismic observations from South Pole. The observations play a significant role in improving our understanding of the Sun's interior, not only with fundamental measurements such as the determination of the internal sound speed and rotational profiles, but also with the development of important techniques such as time-distance analysis. I will finish with a travel log of a typical expedition to South Pole. |
| Title: Descent and base change with view towards the Artin conjecture |
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| Colloquium: Number Theory |
| Speaker: Jayce Getz of Duke University |
| Contact: David Borthwick, davidb@mathcs.emory.edu |
| Date: 2015-01-27 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: The Langlands functoriality conjecture is a powerful unifying force in mathematics, illuminating connections between (at least) number theory, representation theory, mathematical physics, and algebraic geometry. It has only been established in limited, though important cases. In this talk we focus on a particular consequence of Langlands functoriality, namely the Artin conjecture, and use it as a touchstone to explain what is known and a new approach to move beyond it. |
| Title: Relative trace formulae with applications to arithmetic, geometry, and spectral theory |
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| Colloquium: Number Theory |
| Speaker: Heekyoung Hahn of Duke University |
| Contact: David Borthwick, davidb@mathcs.emory.edu |
| Date: 2015-01-26 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Relative trace formulae are arguably the most versatile and general tools available in the modern theory of automorphic forms. Starting with the oldest unsolved problem in mathematics and moving to Millennium prize problems we will explain concrete applications and motivation for relative trace formulae in low-dimensional cases. We will then explain our work on extending the relative trace formula to its natural level of generality with a view towards specific problems in arithmetic, geometry, and spectral theory. |
| Title: MLK Lecture “Constitutional People: The Algebra Project and The Mississippi Theater (1960 - 1965) of The Civil Rights Movement” |
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| 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: |
| Title: An Erdos-Ko-Rado Theorem for cross t-intersecting families |
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| 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: MSC 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 |
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| Defense: Dissertation |
| Speaker: Luca Bertagna of Emory University |
| Contact: Luca Bertagna, lbertag@emory.edu |
| Date: 2014-12-15 at 11:00AM |
| Venue: MSC 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 |
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| 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 12:00PM |
| Venue: MSC 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 |
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| 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’s Disease using a Web-based, Computerized and User-friendly Tool |
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| 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. |