All Seminars
| Title: A reexamination of the Birch and Swinnerton-Dyer cubic surfaces |
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| Seminar: Algebra and Number Theory |
| Speaker: Mckenzie West of Emory University |
| Contact: Michael H. Mertens, michael.mertens@emory.edu |
| Date: 2015-11-10 at 4:00PM |
| Venue: W304 |
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| Abstract: The Hasse principle asks whether solutions to an equation in a local field extend to those in a global field. This does not always happen, the Brauer-Manin obstruction being a common explanation. A conjecture of Colliot-Thelene and Sansuc implies that a Brauer-Manin obstruction exists for every cubic surface which fails to satisfy the Hasse principle. In 1975, Birch and Swinnerton-Dyer gave some early examples of cubic surfaces which have a Brauer-Manin obstruction: (cubic norm) = (linear) (quadratic norm). They make a rough number theoretic argument for the Brauer-Manin obstruction in the case that the Hasse principle fails, focusing on the particular fields and constants. We make use of advancements in arithmetic geometry, taking a geometric look at these objects and utilizing the correspondence between the Brauer group and the Picard group of a surface in order to update and generalize their arguments. |
| Title: Truncating low-rank preconditioner updates for sequences of linear systems |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Eric de Sturler of Virginia Tech |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2015-11-09 at 4:00PM |
| Venue: MSC E408 |
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| Abstract: In many applications, we need to solve sequences of large linear systems. If good preconditioners are required for fast convergence, we may need to compute many preconditioners. This can be very expensive. One could compute a single preconditoner for all systems or recompute the preconditioner infrequently, but this may lead to very large number of iterations. An alternative is to update the preconditioner in some efficient manner while maintaining the quality of the preconditioner. One such approach is to update the preconditioner by low-rank updates, typically applied in a multiplicative way, which can be done very cheaply. However, this has the problem that applying the preconditioner (during the iterative solve) gets increasingly expensive. We discuss two methods to truncate such low-rank updates while maintaining good preconditioner quality. We give applications from solid state physics and nonlinear partial differential equations. |
| Title: Algebraic Iterative Reconstruction Methods - A Users' Guide |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Per Christian Hansen of Technical University of Denmark and Silvia Gazzola, Hariot Watt University |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2015-11-06 at 1:00PM |
| Venue: W302 |
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| Abstract: Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising, for example, in tomographic image reconstruction. This includes both the Algebraic Reconstruction Techniques (ART) and the Simultaneous Iterative Reconstruction Techniques (SIRT), both of which rely on semi-convergence. Hybrid Krylov subspace methods have also become popular in recent years, which are used to stabilize the semi-convergence behavior. We survey these methods and explain their convergence properties, and we discuss some practical issues such as stopping rules and the choice of the relaxation parameter. We finish with some examples that illustrates our MATLAB implementation of these methods. |
| Title: Fusion system and classifying spaces |
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| Seminar: Algebra and Number Theory |
| Speaker: Justin Lynd of University of Montana |
| Contact: John Duncan, john.duncan@emory.edu |
| Date: 2015-11-06 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: Given a finite group, one can form its classifying space, and then its reduced integral cohomology. This cohomology is a finite abelian group in each degree and so is a product of its p-primary components, as p ranges over the prime divisors of the group order. There are corresponding "p-local" constructions at the group and space level that reflect the p-primary part of group cohomology. At the level of the group, one is led to a category called the p-fusion system. At the space level, one has p-completion in the sense of Bousfield and Kan. That these two constructions preserve essentially the same data is known as the Martino-Priddy conjecture, which was first proved in 2004 (p odd) and 2006 (p=2) by B. Oliver. I'll give an introduction to fusion systems and the broad outline of a proof of a generalization of this conjecture, due to A. Chermak, B. Oliver, and G. Glauberman and myself. |
| Title: Geometric Range Search over Encrypted Spatial Data |
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| Seminar: Computer Science |
| Speaker: Ming Li of University of Arizona |
| Contact: Vaidy Sunderam, vss@emory.edu |
| Date: 2015-11-06 at 3:00PM |
| Venue: MSC W303 |
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| Abstract: Geometric range search is a fundamental primitive for spatial data analysis in SQL and NoSQL databases. It has extensive applications in Location-Based Services, computer-aided design and computational geometry. Due to the dramatic increase of data size, it is necessary for companies and organizations to outsource their spatial datasets to third-party cloud services (e.g. Amazon) in order to reduce storage and query processing costs, but meanwhile with the promise of no privacy leakage to the third party. Searchable encryption is a technique to perform meaningful queries on encrypted data without revealing privacy. However, geometric range search on spatial data has not been fully investigated nor supported by existing searchable encryption schemes. The main challenge, is that compute-and-then-compare operations required by many range search algorithms cannot be supported by any existing crypto primitives. In this talk, I will present our recent research progresses in privacy-preserving geometric range search over encrypted spatial data. The general approach is to adopt new representations of spatial data, and transform the range query algorithm to avoid compute-and-then-compare operations, so that existing efficient crypto primitives can be integrated. I will present two designs, the first one focuses on circular range search, and the second one can handle arbitrary geometric range query and is more efficient. The security of both schemes are formally proven under standard cryptographic assumptions. Finally, I will discuss some future research challenges and directions in this area. |
| Title: A generalization of the Euler-Glaisher bijection |
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| Seminar: Algebra and Number Theory |
| Speaker: Andrew Sills of Georgia Southern University |
| Contact: Robert Schneider, robert.schneider@emory.edu |
| Date: 2015-11-03 at 4:00PM |
| Venue: W304 |
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| Abstract: In 1748, Euler published his Introductio in Analysin Infinitorum. Chapter 16 of this work is the first systematic study of integer partitions in the mathematical literature. In it, he introduces infinite product generating functions and uses them to derive what is now known as Euler’s partition identity, an English translation of which reads as follows: “The number of different ways a given number can be expressed as the sum of different whole numbers is the same as the number of ways in which the same number can be expressed as the sum of odd numbers, whether the same of different.” In modern terminology, the preceding is rephrased as “the number of partitions of n into distinct parts equals the number of partitions of n into odd parts.” In 1883, J.W.L. Glaisher published the first bijective proof of Euler’s partition identity, along with a natural generalization: “the number of partitions of n where no part appears more than m - 1 times equals the number of partitions of n where no part is divisible by m.” By combining a construction of P.A. MacMahon called “partitions of infinity” and knowledge of George Andrews' “partition ideals of order 1” with Glaisher’s bijective proof of Euler’s identity, we are led to discover a large class of partition identities with straightforward bijective proofs. This is joint work with James Sellers and Gary Mullen of Penn State. All terms will be defined and illustrated with concrete examples, so the required mathematical background will be minimal, and the talk should be accessible to all graduate students. |
| Title: Rationally isomorphic hermitian forms and torsors of some non-reductive groups |
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| Seminar: Algebra and Number Theory |
| Speaker: Eva Bayer-Fluckiger of Ecole Polytechnique Federale de Lausanne |
| Contact: Raman Parimala, parimala@mathcs.emory.edu |
| Date: 2015-10-27 at 4:00PM |
| Venue: W304 |
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| Abstract: This is a joint work with Uriya First. Let R be a semi-local Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an R-algebra with involution that are rationally isometric are isometric over R. The result can be regarded as a first step towards a version of the Grothendieck-Serre conjecture for certain non-reductive group schemes over Spec R. |
| Title: The Era of Big Spatial Data |
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| Seminar: Computer Science |
| Speaker: Mohamed Mokbel of University of Minnesota |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2015-10-26 at 1:00PM |
| Venue: W302 |
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| Abstract: In recent years, there has been an explosion in the amounts of spatial and spatio-temporal data produced from several devices including smart phones, space telescopes, medical devices. Unfortunately, managing and analyzing such big spatial data is hampered by the lack of specialized systems, techniques, and algorithms. While big data is well supported with a variety of distributed systems and cloud infrastructure, none of these systems or infrastructure provide any special support for spatial or spatio-temporal data. This talk presents our efforts in indexing, querying, and visualizing big spatial and spatio-temporal data. We will describe our efforts within SpatialHadoop; our full-fledged MapReduce framework with native support for spatial data, including support for basic spatial operations, computational geometry, and spatial visualization. BIO: Mohamed F. Mokbel (Ph.D., Purdue University, MS, B.Sc., Alexandria University) is an Associate Professor in the Department of Computer Science and Engineering, University of Minnesota. His research interests include the interaction of GIS and location-based services with database systems and cloud computing. His research work has been recognized by five Best Paper Awards and by the NSF CAREER award. Mohamed was the program co-chair for the ACM SIGSPATIAL GIS conference from 2008 to 2010, IEEE MDM Conference 2011 and 2014, and the General Chair for SSTD 2011. He is an Asscoiate Editor for ACM TODS, ACM TSAS, VLDB journal, and GeoInformatica. Mohamed is a founding member of ACM SIGSPATIAL, and an elected Chair of ACM SIGSPATIAL 2014-2017. For more information, please visit: www.cs.umn.edu/~mokbel. |
| Title: The Georgia Algebraic Geometry Symposium |
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| Seminar: Algebra |
| Speaker: gags.torsor.org of |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2015-10-23 at 9:00AM |
| Venue: E208 |
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| Abstract: The Georgia Algebraic Geometry Symposium is a conference series, jointly organized by the University of Georgia, Emory University and Georgia Tech. The conference will begin Friday afternoon and end Sunday, afternoons. See gags.torsor.org for more information. Confirmed speakers: Valery Alexeev (University of Georgia), Brian Conrad (Stanford University), Brian Lehman (Boston College), Max Lieblich (University of Washington), Alexander Merkurjev (UCLA), Alena Pirutka (École Polytechnique), Aaron Pixton (Harvard University), Tony Várilly-Alvarado (Rice University), Olivier Wittenberg (CNRS - École Normale Superieure) |
| Title: Rational points of rationally connected varieties over number fields, an overview (part 3) |
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| Seminar: Algebra |
| Speaker: Olivier Wittenberg of École normale supérieure |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2015-10-22 at 4:00PM |
| Venue: W304 |
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| Abstract: This will be a short course (3 lectures) aimed at graduate students. |