All Seminars
| Title: Accounting for Helicity in 3D NSE Computations |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Leo Rebholz of Clemson University |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2009-10-21 at 12:45PM |
| Venue: W306 |
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| Abstract: It has recently become known that helicity, defined as the mean streamwise vorticity, is a fundamentally important quantity of the 3D Navier-Stokes equations. Helicity is a conserved quantity of inviscid flow, is cascaded jointly with energy through the inertial range, and is physically interpreted to be the degree to which a flow's vortex lines are tangled and intertwined. Until recently however, helicity has been ignored in NSE computations. In this talk I will show how helicity can be more accurately treated in finite element computations of the 3D NSE, which in turn leads to more accurate simulations. I will discuss two numerical schemes: one which enforces helicity preservation by the NSE nonlinearity (to mimic the continuous case) - joint work with Vince Ervin, and a second that solves for helicity directly inside of a velocity-vorticity method - joint work with Maxim Olshanskii. Numerical examples will be given that demonstrate the effectiveness of the methods. |
| Title: Constructing elliptic curves of high rank over function fields |
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| Seminar: Athens-Atlanta Number Theory |
| Speaker: Doug Ulmer of Georgia Tech |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2009-10-20 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: There are now several constructions of elliptic curves of high rank over function fields, most involving high-tech things like $L$-functions, cohomology, and the Tate or BSD conjectures. I'll review some of this and then give a very down-to-earth, low-tech construction of elliptic curves of high ranks over the rational function field $\mathbf{F}_p(t)$. |
| Title: Using mass formulas to enumerate definite quadratic forms of class number one |
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| Seminar: Athens-Atlanta Number Theory |
| Speaker: Jonathan Hanke of University of Georgia |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2009-10-20 at 5:15PM |
| Venue: MSC W201 |
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| Abstract: This talk will describe some recent results using exact mass formulas to determine all definite quadratic forms of small class number in at least 3 variables, particularly those of class number one. The mass of a quadratic form connects the class number (i.e. number of classes in the genus) of a quadratic form with the volume of its adelic stabilizer, and is explicitly computable in terms of special values of zeta functions. Comparing this with known results about the sizes of automorphism groups, one can make precise statements about the growth of the class number, and in principle determine those quadratic forms of small class number. We will describe some known results about masses and class numbers (over number fields), then present some new computational work over the rational numbers, and perhaps over some totally real number fields. |
| Title: The coefficients of q-series and asymptotics for partition ranks and cranks |
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| Seminar: Algebra |
| Speaker: Karl Mahlburg of Princeton |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2009-10-19 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Dyson's rank and crank statistics have long been important in the combinatorial study of integer partitions. Both statistics were introduced in efforts to better understand the famous Ramanujan congruences for the partition function $p(n)$, and there is no apparent relation between their simple combinatorial definitions. The main results of this talk (essentially) prove a remarkable conjecture of Garvan that the moments of the crank are always larger than the moments of the rank. More generally, these inequalities are an important example of relations for the asymptotics of hypergeometric $q$-series that are governed by modularity properties. In this case, the crank is associated to a modular form, while the rank is associated to a mock theta function/harmonic Maass form. If time permits, I will also briefly discuss some ideas of Zagier for deriving asymptotic expansions in these settings. |
| Title: Maximal Chains and Antichains in Finite Partially Ordered Sets |
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| Seminar: Combinatorics |
| Speaker: Dwight Duffus of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2009-10-16 at 4:00PM |
| Venue: W306 |
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| Abstract: Fix integers n and k with n at least k, and n, k > 2. With Bill Sands, we proved that if P is a finite partially ordered set and every maximal chain C of P has between n and n + (n - k)/k - 2) elements, then P must contain k pairwise disjoint maximal antichains. We also constructed a family of examples to show that these inequalities are tight. We raised and made observations about the dual problem, which Dave Howard and Tom Trotter [Georgia Tech] have recently solved. |
| Title: Counting Problems in Number Theory |
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| Colloquium: Number Theory |
| Speaker: Manjul Bhargava of Princeton |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2009-10-15 at 5:30PM |
| Venue: MSC E208 |
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| Abstract: There are some objects in number theory that are particularly fundamental -- examples include "number fields", "class groups", and "elliptic curves" -- yet very little is known about how many such objects there are having given invariants, or how these objects are distributed with respect to these invariants. In this talk, I will try to describe why number theorists are so interested in these questions, and will discuss a few recent results that give some answers. |
| Title: On Subgrid Pressure Modeling in Incompressible CFD |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Maxim Olshanskii of Moscow State University |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2009-10-13 at 4:00PM |
| Venue: W306 |
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| Abstract: In the talk we discuss a variational multiscale approach for the pressure subgrid modeling in the Galerkin method for incompressible Navier-Stokes equations. We relate the approach with a stabilization procedure of least-square type known as grad-div stabilization and consider the search of optimal stabilization parameters as a trade-off between mass and energy balance in the discrete system. Application to numerical simulation of laminar and turbulent flows is studied |
| Title: Informatics-based Quality Improvement in Healthcare: an Analytic Information Warehouse |
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| Seminar: Computer Science |
| Speaker: Andrew Post of Emory University |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2009-10-09 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: An increasing volume of patient data in clinical data warehouses makes possible the identification and analysis of populations with therapeutic responses, outcomes and clinical care processes that are reflected by multivariate trends and patterns over time. This presentation will describe a grid-based software system that is under development at Emory, the Analytic Information Warehouse (AIW), that aims to facilitate discovery and query of those patterns. The AIW will provide controlled terminology support in queries. It will also provide analytic services for extracting concepts from unstructured text, de-identification, discovering features of a patient population and predicting responses and outcomes. Schema adaptors will support connecting to Emory Healthcare's existing clinical data warehouse and other research and clinical databases with appropriate levels of security. These capabilities ultimately will provide broad support to Emory Healthcare and researchers in risk factor identification, prediction, and evaluation of interventions to improve patient care quality and outcomes.\\ \\ Bio:\\ \\ Andrew Post, MD, PhD is a Clinical Informatics Architect at Emory University's Center for Comprehensive Informatics, and Assistant Professor in the Department of Biomedical Engineering. Dr. Post completed an MD at the University of Pennsylvania, and a fellowship and PhD in Biomedical Informatics at the University of Pittsburgh. He is faculty lead of an Analytic Information Warehouse supporting informatics-based quality improvement and research at Emory. He has conducted research in temporal pattern detection, clinical decision support, clinical user interfaces and the promotion of cross-disciplinary collaborations in clinical and translational research environments. His roles have included hospital and research information systems planning. |
| Title: Chocolate key cryptography: a delicious way to send secret messages |
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| Demonstration: for undergraduates |
| Speaker: Ezra Brown of Virginia Tech |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2009-10-08 at 7:00PM |
| Venue: MSC W201 |
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| Abstract: The art and science of secure communication is called cryptography. To send someone a secret message, you need two things: (1) a message scrambler ("the cryptosystem"), and (2) a piece of information that tells the sender and the receiver just how the scrambling is done ("the key"). Keeping the key in the right hands and out of the wrong hands is a major problem for cryptographers, and public key cryptography is a solution to this problem that is at work on every computer and in every network in the world. This talk is about Chocolate Key Cryptography, which is a way to describe a certain public key cryptosystem that is easy to learn, fun, interactive, and delicious. Biographical Sketch: Ezra (Bud) Brown grew up in New Orleans, has degrees from Rice and LSU, and has been at Virginia Tech since 1969, where he is currently Alumni Distinguished Professor of Mathematics. Although most of his research has been in number theory and combinatorics, he once wrote a paper with a sociologist. During the summers, he works on problems of cryptography with an unnamed government agency. He has been honored with some teaching and writing awards. He enjoys singing in operas, playing jazz piano, and gardening, and he occasionally bakes biscuits for his students. |
| Title: A characterization of the polar reflectors |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Anastasia Svishcheva of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2009-10-06 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: I will speak about the characterization of the polar reflectors (duality transformations of the set of reflectors), i.e. the sufficient conditions for the transformation to be polarity. |