All Seminars
| Title: Tensor products of division algebras |
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| Seminar: Algebra and Number Theory |
| Speaker: David J. Saltman of CCR Princeton |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2011-10-25 at 4:00PM |
| Venue: MSC E406 |
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| Abstract: If $F$ is algebraically closed, and $F_i \supset F$ are field extensions, then $F_1 \otimes_F F_2$ is always a domain. It thus makes sense to conjecture that if $D_i/F_i$ are division algebras (meaning $F_i$ is the center of $D_i$ and $D_i/F_i$ is finite dimensional), then $D_1 \otimes_F D_2$ is a (noncommutative) domain. We will show that this is often true, but not always. We will concentrate on the case that $F$ has characteristic 0 and that the $D_i/F_i$ have prime degree. We also hope to draw attention to the interesting properties of $F_1 \otimes_F F_2$ and how they relate to our problem. Along the way we will make use of Picard varieties and elliptic curves. |
| Title: Recommendation Services for Location-Based Social Networks |
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| Seminar: Computer Science |
| Speaker: Wang-Chien Lee of The Pennsylvania State University |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2011-10-21 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: With the rapid development of mobile devices, wireless networks and Web 2.0 technology, a number of location-based social networking services (LBSNs), e.g., Foursquare, Whrrl, Facebook Place, Google Latitude, Loopt, and Brightkite, have emerged in recent years. These LBSNs allow users to establish cyber links to their friends or other users, and share tips and experiences of their visits to plentiful point-of-interests (POIs), e.g., restaurants, stores, cinema theaters, etc. Recommendation services, e.g., POI recommendation service that suggests new POIs to users in order to help them explore new places and know their cities better, are essential for LBSNs and thus receiving a lot of research interests. In this talk, I will introduce some recommendation services for LBSNs and present our research effort and results for enabling some of these recommendation services.\\ \\ Bio: \\ Wang-Chien Lee is an Associate Professor of Computer Science and Engineering at Pennsylvania State University, where he leads the Pervasive Data Access (PDA) Research Group to pursue cross-area research in database systems, pervasive/mobile computing, and networking. He is particularly interested in developing data management techniques (including accessing, routing, indexing, caching, aggregation, dissemination, and query processing) for supporting complex queries and location-based services in a wide spectrum of networking and mobile environments such as peer-to-peer networks, mobile ad-hoc networks, wireless sensor networks, and wireless broadcast systems. Meanwhile, he also works on XML, security, information integration/retrieval, and object-oriented databases. He has published more than 200 technical papers on these topics. |
| Title: First-Fit is Linear on $(r+s)$-free Posets |
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| Seminar: Combinatorics |
| Speaker: Kevin Milans of The University of South Carolina |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-10-21 at 4:00PM |
| Venue: W306 |
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| Abstract: First-Fit is an online algorithm that partitions the elements of a poset into chains. When presented with a new element $x$, First-Fit adds $x$ to the first chain whose elements are all comparable to $x$. In 2004, Pemmaraju, Raman, and Varadarajan introduced the Column Construction Method to prove that when $P$ is an interval order of width $w$, First-Fit partitions $P$ into at most $10w$ chains. This bound was subsequently improved to $8w$ by Brightwell, Kierstead, and Trotter, and independently by Narayanaswamy and Babu. The poset $r+s$ is the disjoint union of a chain of size $r$ and a chain of size $s$. A poset is an interval order if and only if it does not contain $2+2$ as an induced subposet. Bosek, Krawczyk, and Szczypka proved that if $P$ is an $(r+r)$-free poset of width $w$, then First-Fit partitions $P$ into at most $3rw^2$ chains and asked whether the bound can be improved from $O(w^2)$ to $O(w)$. We answer this question in the affirmative. By generalizing the Column Construction Method, we show that if $P$ is an $(r+s)$-free poset of width $w$, then First-Fit partitions $P$ into at most $8(r-1)(s-1)w$ chains. This is joint work with Gwena\"el Joret. |
| Title: Galois algebras, Hasse principle and induction-restriction methods |
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| Seminar: Algebra and number theory |
| Speaker: Eva Bayer-Fluckiger of Swiss Federal Institute of Technology, Lausanne |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-10-18 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: The aim of this talk is to prove a local-global principle for the existence of self-dual normal bases for Galois algebras. The proof involves a restriction-induction result for $G$-quadratic forms (provided $G$ has the ``odd determinant property") that is of independent interest. |
| Title: Angles and quasiconformal mappings in space |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Wenfei Zou of Emory University |
| Contact: Wenfei Zou, wzou3@emory.edu |
| Date: 2011-10-18 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Quasiconformal mappings are natural generalizations of conformal mappings. Angles are preserved under conformal mappings. It is interesting to investigate how angles interact with quasiconformal mappings. In the complex plane, Agard and Gehring studied how angles change under quasiconformal mappings and how angles are used to characterize quasiconformal mappings. In this talk I will discuss how to generalize these results to higher dimension. |
| Title: Abelian varieties with big monodromy |
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| Seminar: Algebra and Number Theory |
| Speaker: David Zureick-Brown of Emory University |
| Contact: TBA |
| Date: 2011-10-13 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: Serre proved in 1972 that the image of the adelic Galois representation associated to an elliptic curve E without complex multiplication has open image; moreover, he also proved that for an elliptic curve over Q the index of the image is always divisible by 2 (and in particular never surjective). More recently, Greicius in his thesis gave criteria for surjectivity and gave an explicit example of an elliptic curve E over a number field K with surjective adelic representation. Soon after, Zywina, building on earlier work of Duke, Jones, and others, proved that the adelic image `random' elliptic curve is maximal. In this talk I will explain recent work with David Zywina in which we generalize these theorems and prove that a random abelian variety in a family with big monodromy has maximal image of Galois. I'll explain the analytic and geometric techniques used in previous work and the new geometric ideas -- in particular, Nori's method of semistable approximation-- needed to generalized to higher dimension. |
| Title: Computerized Image Analysis for Biomedical Translational Research |
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| Seminar: Computer Science |
| Speaker: Jun Kong of Emory University |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2011-10-07 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: Abstract: In biomedical research, availability of an increasing array of high-throughput and high-resolution instruments has given rise to large datasets of "omics" data - such as genomics, proteomics, metabolomics - and imaging data - such as radiology and microscopy imaging. These datasets provide highly detailed views of biological systems and functions. The Emory In Silico Brain Tumor Research Center (EISBTRC), a National Cancer Institute In Silico Research Center of Excellence, has focused on the analysis of Glioblastoma (GBM), a deadly form of brain cancer with a median survival of six months. We are now carrying out large-scale in silico experiments with pubic datasets for Glioblastoma (GBM) brain tumor research for a better understanding of the biological underpinnings that drive the rapid progression of this devastating disease.. In this talk, I will discuss our work on large-scale micro-anatomic feature extraction and integration with genomics and patient survival.\\ \\ Bio:\\ \\ Jun Kong is a research scientist in the Center for Comprehensive Informatics at Emory University. Dr. Kong received his Ph.D. degree in the Dept. of Electrical and Computer Engineering at Ohio State University in 2008. Dr. Kong's research interests include computer vision, statistical machine learning, and medical/microscopy image analysis. He developed Computer-aided Diagnosis (CAD) systems for analyzing a large volume of microscopy images of histologic specimens with intensive use of computer vision and pattern recognition techniques. |
| Title: Turan's problem for odd cycles in pseudorandom graphs |
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| Seminar: Combinatorics |
| Speaker: Mathias Schacht of University of Hamburg |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-10-07 at 4:00PM |
| Venue: W306 |
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| Abstract: We consider the generalized extremal function $ex(G,F)$, defined to be the largest number of edges that an $F$-free subgraph of $G$ may have. Owing to the work of Mantel, Turan, Erd\"os and Stone this function is well understood for any graph F when $G$ is the complete graph $K_n$. Over the last two decades the problem was investigated and solved when $G$ is the binomial random graph {\bf G(n,p)}. For pseudorandom graphs $G$ only a few results are known. We will discuss recent progress for one of the simplest cases, when F is an odd cycle of fixed length. Roughly speaking, in joint work with Aigner-Horev and Han we obtained almost best possible conditions on the pseudorandom graph $G$ such that $ex(G,C_l)=(1/2+o(1)e(G)$ holds. |
| Title: A characterization of the polarity transform for reflectors |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Anastasia Svishcheva of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2011-10-04 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Convex reflectors arise as solutions to nonlinear second order elliptic partial differential equations (PDE's) of Monge-Amp\`{e}re type expressing conservation laws in geometrical optics. Previously it was shown by V. Oliker that this transform can be viewed as duality with respect to the form $Q(X,Y):=|X||Y|-\langle X, Y \rangle,~X, Y \in \mathbb{R}^{n+1}$. A natural and interesting geometric question is to find a minimal set of properties characterizing such duality transform between reflectors. I will speak about sufficient conditions for this transformation to be such duality. |
| Title: Math in Marriage: Don't Call the Lawyers Yet |
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| EUMMA Event: N/A |
| Speaker: Ron Gould of Emory University |
| Contact: Erin Nagle, erin@mathcs.emory.edu |
| Date: 2011-10-04 at 6:00PM |
| Venue: MSC W301 |
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| Abstract: |