All Seminars
| Title: Designing lenses with help from geometry and optimal transport |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Vladimir Oliker of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2010-02-02 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: This is a continuation of the presentation started at the previous seminar |
| Title: Galois group actions over the integers |
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| Colloquium: Number theory |
| Speaker: George Pappas of Michigan State University |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2010-01-26 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: According to the ``normal basis theorem", if $L/K$ is a Galois extension of fields with finite Galois group $G$, then there is an element $x$ in $L$, such that the collection of all its conjugates, $g(x)$, for $g$ in $G$, forms a basis of $L$ as a vector space over $K$. This talk will describe a theme of ``integral" extensions of this classical fact to situations where a finite group acts on a system of polynomial equations with integer coefficients, i.e., when a finite group acts on a ``scheme over $\mathbf{Z}$". |
| Title: Designing lenses with help from geometry and optimal transport |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Vladimir Oliker of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2010-01-26 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Mirror and lens devices converting an incident plane wave of a given cross section and intensity distribution into an output plane wave irradiating at a given target set with prescribed intensity are required in many applications. Most of the known designs are restricted to rotationally symmetric mirrors/lenses. In this talk I will discuss designs with freeform lenses, that is, without a priori assumption of rotational symmetry. Assuming the geometrical optics approximation, it can be shown that the functions describing such freeform lenses satisfy Monge-Amp\`{e}re type partial differential equations. Because of strong nonlinearities analysis of these PDE's is difficult. Fortunately, many such problems can also be formulated geometrically and lead to problems in calculus of variations in which instead of solving the nonlinear PDE's one needs to find extrema of some Fermat-like functionals. Furthermore, discrete versions of such problems can be formulated and are useful for numerics. In this talk I will describe some of these results in the case of the lens design problem. This is work "in progress", so the presentation may be technical and require more than one seminar. |
| Title: Chow groups of quadrics |
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| Seminar: Algebra |
| Speaker: Asher Auel of Emory University |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2010-01-19 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: |
| Title: Unitary descent properties |
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| Seminar: Algebra |
| Speaker: Eva Bayer of Swiss Federal Institute of Technology, Lausanne (EPFL) |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2009-12-07 at 4:00PM |
| Venue: W306 |
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| Abstract: Let $k$ be a field of characteristic $\not = 2$, let $L/k$ be an odd degree extension and let $U$ be a unitary group defined over $k$. It is well--known that the natural map $H^1(k,U) \to H^1(L,U)$ is injective. Suppose that $L/k$ is Galois with group $G$. Is then $H^1(k,U) \to H^1(L,U)^G$ a bijection? This is true for orthogonal groups, and one of the main ingredients in the proof is a result of Rosenberg and Ware concerning a descent property for Witt rings of quadratic forms, namely that $W(L)^G \simeq W(k)$. This talk will present a generalization of the Rosenberg--Ware theorem to Witt groups of hermitian forms, as well as some applications of this result, in particular to the above mentioned Galois cohomology descent question. |
| Title: Learning With Changing Language Data |
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| Colloquium: Computer Science |
| Speaker: Mark Dredze of Johns Hopkins University and Human Language Technology Center of Excellence |
| Contact: Eugene Agichtein, eugene@mathcs.emory.edu |
| Date: 2009-12-04 at 2:00PM |
| Venue: MSC W301 |
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| Abstract: The information revolution has produced huge quantities of knowledge in the form of natural human language. This explosion of data has pushed natural language processing (NLP) research towards empirical data driven methods, which rely on statistical machine learning. This effort has produced numerous high quality tools for processing language, including knowledge extraction, information organization and automated translation of numerous languages. With more data and better statistical methods, the state of the art advances. Behind the success of this statistical movement is a reliance on statistical methods that are susceptible to changes in data, a particular problem for language data which naturally transitions between topical domains, genres, formats, dialects and languages. High performing systems fail with even subtle changes to language input, like a change in the topic domain. This talk will survey recent NLP successes in tackling complex natural language problems as well as challenges posed by changes in language data. I will present several approaches to solving domain change challenges that adapt a learned statistical model between one source domain and a new different target domain. I describe Confidence Weighted Learning, a streaming machine learning algorithm designed for the types of data distributions common in language tasks. I show how Confidence Weighted Learning both improves learning in NLP tasks and can be applied to confront the challenges associated with data shifts. BIO: Mark Dredze is as an Assistant Research Professor in the department of Computer Science and a Senior Research Scientist at the Human Language Technology Center of Excellence at The Johns Hopkins University. His research interests include machine learning, natural language processing and intelligent user interfaces. His focus is on novel applications of machine learning to solve language processing challenges as well as applications of machine learning and natural language processing to support intelligent user interfaces for information management. He earned his PhD from the University of Pennsylvania and has worked at Google, IBM and Microsoft. |
| Title: On $K_t$-saturated Graphs |
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| Seminar: Combinatorics |
| Speaker: Kinnari Amin of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2009-12-04 at 4:00PM |
| Venue: W306 |
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| Abstract: Let $H$ be a graph. An $H$-free graph $G$ is called $H$-saturated if the addition of any new edge to $G$ results in a subgraph isomorphic to $H$. The minimum size of an $H$-saturated graph on n vertices is denoted by sat($n$, $H$). The edge spectrum for the family of graphs with property $P$ is the set of all sizes of graphs with property $P$. In this talk, I will present new results about the edge spectrum of $ K_t$-saturated graphs. This is joint work with Jill Faudree and Ronald Gould. |
| Title: Meet Lie groups (and some of their applications and misapplications in physics) |
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| Graduate Student Seminar: N/A |
| Speaker: Skip Garibaldi of Emory University |
| Contact: Pascal Philipp, pphilip@emory.edu |
| Date: 2009-12-02 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: You've met Lie groups already in your sophomore linear algebra class, in the sense that the n-by-n invertible matrices make up a Lie group. This talk will give some more examples of Lie groups, describe one of their classic applications to physics, and mention how they are being applied today. As part of the graduate student seminar series, this talk will be understandable to all mathematics graduate students. The talk should also be understandable by physics graduate students. |
| Title: From Droplets to Cloud: Towards Privacy-Preserving Integration of Distributed Heterogeneous Data |
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| Defense: Dissertation |
| Speaker: Pawel Jurczyk of Emory University |
| Contact: Pawel Jurczyk, pjurczy@emory.edu |
| Date: 2009-12-01 at 3:00PM |
| Venue: MSC W201 |
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| Abstract: With the trend of cloud computing, data and computing are moved away from desktop and are instead provided as a service from the cloud. Data-as-a-service enables access to a wealth of data across distributed and heterogeneous data sources in the cloud. It remains a challenge, however, to ensure the privacy, interoperability, and scalability for such services.\\ \\ We designed and developed DObjects, a general-purpose P2P-based query and data operations infrastructure that can be deployed in the cloud and provides access to heterogeneous data sources. The system builds on top of a distributed mediator-wrapper architecture where individual system nodes serve as mediators and/or wrappers and interact with each other in a P2P fashion what guarantees good scalability. As an analogy, the system nodes can be considered as droplets, small elements that provide similar functionality in the cloud. Just as thousands or millions of droplets form a single drop in nature, in cloud computing, groups of droplets that provide similar functionality can form a micro-cloud. Micro-clouds are an integral part of the whole cloud computing system and can provide specific services to users.\\ \\ The dissertation also discusses the novel dynamic query execution engine within the data query infrastructure that dynamically adapts to network and node (or droplet) conditions. The query processing is capable of fully benefiting from all the distributed resources to minimize the query response time and maximize system throughput. In addition to leveraging the traditional distributed query optimization techniques, the (sub)queries are deployed and executed on droplets in a dynamic and iterative manner in order to guarantee the best reaction to network and resource dynamics.\\ \\ Finally, the dissertation presents an extension to the basic DObjects model that enables access to private data that is distributed and needs anonymization. The extension enables droplets to form virtual groups in order to addresses two important privacy issues for the sensitive data: privacy of data subjects and confidentiality of data providers. The dissertation discusses decentralized protocols that enable data sharing for horizontally partitioned databases given these constraints. These protocols can be run by the groups of droplets. Concretely, given a query spanning multiple databases, the query results do not contain individually identifiable information. In addition, institutions do not reveal their databases to each other apart from the query results. |
| Title: Brauer-Manin obstructions on K3 surfaces |
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| Seminar: Algebra |
| Speaker: Patrick Corn of Emory University |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2009-12-01 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: There has been a great deal of recent research on the arithmetic of K3 surfaces, some of which has centered around the Brauer-Manin obstruction to the Hasse principle. In this talk, I'll give some background and discuss some of the results and open questions in this area. |