All Seminars
| Title: Analysis and Simulation of Bingham fluid problems with Papanastasiou-like regularizations: Primal and Dual formulations |
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| Defense: Dissertation |
| Speaker: Anastasia Svishcheva of Emory University |
| Contact: Anastasia Svishcheva, asvish@emory.edu |
| Date: 2014-11-11 at 4:00PM |
| Venue: MSC 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 |
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| 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: MSC 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 |
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| 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: MSC 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) |
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| 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: |
| Title: Semidefinite programming in extremal graph theory |
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| Seminar: Combinatorics |
| Speaker: Florian Pfender of The University of Colorado, Denver |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2014-11-03 at 4:00PM |
| Venue: W302 |
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| Abstract: Razborov developed in 2007 the theory of flag algebras. Within this theory, densities of small substructures in large combinatorial structures can be described and computed. His so called "plain flag algebra method" uses semidefinite programming to optimally combine a large number of true inequalities to get bounds on densities in many contexts.\\ \\ One context the method can be used in is the inducibility of graphs. We are looking to maximize the number of induced copies of a given small graph in a very large graph. Whenever the extremal graph to a problem has a simple blow-up structure, the plain method often works very well. But when the structure is more complicated, the bounds tend to get weaker. We recently expanded the plain method to be able to deal with an iterated blow-up structure, which often appears as extremal construction for inducibility questions. |
| Title: Regularization by Krylov-Tikhonov methods |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Silvia Gazzola of University of Padova |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2014-10-31 at 12:00PM |
| Venue: MSC W301 |
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| Abstract: Krylov subspace methods have always played a central role in the iterative regularization of large-scale linear discrete ill-posed problems, which arise in a variety of scientific and engineering applications; we are particularly interested in image deblurring and denoising issues. In addition to a purely iterative approach to regularization, some "hybrid" Krylov-Tikhonov methods have also been derived, which merge an iterative and a variational (Tikhonov-like) approach to regularization. The purpose of this talk is to survey some classical Krylov and Krylov-Tikhonov methods, and to present some original ones, comparing their performance on some meaningful test problems. Particular emphasis will be posed on the strategies to be employed to set the regularization parameters and matrices in the Krylov-Tikhonov framework. |
| Title: High Performance Spatial Query Processing for Large Scale Spatial Data Warehousing |
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| Defense: Dissertation |
| Speaker: Ablimit Aji of Emory University |
| Contact: James Lu, jlu@mathcs.emory.edu |
| Date: 2014-10-31 at 3:00PM |
| Venue: MSC W303 |
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| Abstract: Support of high performance queries on large volumes of spatial data have become important in many application domains, including geowspatial problems in numerous fields, location based services, geo-social networks, and emerging scientific applications that are increasingly data- and compute-intensive. There are two major challenges for managing and querying massive spatial data: the explosion of spatial data, and the high computational complexity of spatial queries due to the multi-dimensional nature of spatial analytics. High performance computing capabilities are fundamental to efficiently handling of massive spatial datasets. MapReduce based computing model provides a highly scalable, reliable, elastic and cost effective framework for processing massive data on a cluster or cloud environment. While the MapReduce model fits nicely with large scale problems through data partitioning, spatial queries and analytics are intrinsically complex to fit into the MapReduce model easily. Meanwhile, hybrid systems combining CPUs and GPUs are becoming commonly available in commodity clusters, but the computing capacity of such systems is often underutilized. Providing new spatial querying and analytical methods to run on such architecture requires us to answer several fundamental research questions that are of practical importance. The goal of my dissertation is to create a framework with new systematic methods to support high performance spatial queries for spatial big data on MapReduce and CPU-GPU hybrid platforms, driven by real-world use cases. Towards that end, we have researched multi-level parallelism methods of spatial queries running on these platforms. Specifically, we have conducted following studies: 1) create new spatial data processing methods and pipelines with spatial partition level parallelism through a simple programming model MapReduce and propose multi-level indexing methods to accelerate spatial data processing, 2) develop two critical components to enable data parallelism: effective and scalable spatial partitioning in MapReduce (pre-processing), and query normalization methods for partition effect, 3) integrate GPU-based spatial operations into MapReduce pipelines 4) investigate optimization methods for data skew mitigation, and CPU/GPU resource coordination in MapReduce, and 5) support declarative spatial queries for workload composition, and create a query translator to automatically translate the queries into MapReduce programs. Consequently, we have developed Hadoop-GISb a MapReduce based high performance spatial querying system for spatial data warehousing. The system supports multiple types of spatial queries on MapReduce through spatial partitioning, implicit parallel spatial query execution on MapReduce, and effective methods for amending query results through handling bound- ary objects. Hadoop-GIS utilizes global partition indexing and customizable on demand local spatial indexing to achieve efficient query processing. Hadoop-GIS is integrated into Hive to support declarative spatial queries with an integrated architecture. The systems and developed approaches are released as an open source software package for use. |
| Title: The genus of a division algebra |
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| Seminar: Algebra |
| Speaker: Igor Rapinchuk of Harvard |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2014-10-28 at 4:00PM |
| Venue: W306 |
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| Abstract: In this talk, I will address the following problem. Suppose D and D' are central division algebras over a field K. What can be said about D and D' if they have the same maximal subfields? I will discuss various motivations for this question and recent results. I will also mention some generalizations to arbitrary absolutely almost simple algebraic groups. This is joint work with V. Chernousov and A. Rapinchuk. |
| Title: Embeddings of maximal tori in classical groups and explicit Brauer–Manin obstruction |
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| Seminar: Algebra |
| Speaker: Eva Bayer of EPFL |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2014-10-28 at 5:00PM |
| Venue: W306 |
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| Abstract: This is a joint work with Parimala and Ting–Yu Lee. Embeddings of maximal tori into classical groups over global fields of characteristic $\neq$ 2 are the subject matter of several recent papers (for instance by Prasad and Rapinchuk, Fiori, Lee), with special attention to the Hasse principle. The aim of this talk is to describe a complete criterion for the Hasse principle to hold, and to give necessary and sufficient conditions for a classical group to contain a maximal torus of a given type. The embedding problem will be described in terms of embeddings of \'etale algebras with involution into central simple algebras with involution. |
| Title: On the Number of B_h Sets of a Given Size |
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| Seminar: Combinatorics |
| Speaker: Domingos Dellamonica of Sao Paulo |
| Contact: Vojtech Rodl, rodl@mathcs.emory.edu |
| Date: 2014-10-27 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: For an integer h bigger or equal to 2, a $B_h$ set is a set of integers with the property that every collection containing h of its elements yield a unique sum (and repetitions are allowed). For $h = 2$, such sets are also called Sidon sets. In this talk we will describe our recent results on estimating $F(n, s, h)$, which we define as the number of $B_h$ sets of cardinality s containing integers from $[n] = {1, 2, ..., n}$. It is not hard to see that for $s > n^(1/h)$, we have $F(n, s, h) = 0$. Indeed, in this case there are more h-sums than possible outcomes for the sums. On the other hand, there are constructions of B-h sets having cardinality $c.n^(1/h)$, (with c depending on h only) hence we shall estimate the behavior of $F(n, s, h)$ for s up to $O( n^(1/h))$. Our counting shows the existence of a surprising threshold function $T(n)$: for values of $s << T(n)$, the B-h sets are abundant while for $s >> T(n)$ the B-h sets become very rare. More precisely, we show that $T(n) ~ n^{(1 + o(1))/(2h - 1)}$ and establish fairly precise estimates of $F(n, s, h)$ for the entire range of s. |