All Seminars
| Title: Complex dynamics and adelic potential theory |
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| Seminar: Athens-Atlanta Number Theory |
| Speaker: Matthew Baker of Georgia Institute of Technology |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-02-01 at 5:00PM |
| Venue: MSC W201 |
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| Abstract: I will discuss the following theorem: for any fixed complex numbers a and b, the set of complex numbers c for which both a and b both have finite orbit under iteration of the map $z -->z^2 + c$ is infinite if and only if $a^2 = b^2$. I will explain the motivation for this result and give an outline of the proof. The main arithmetic ingredient in the proof is an adelic equidistribution theorem for preperiodic points over product formula fields, with non-archimedean Berkovich spaces playing an essential role. This is joint work with Laura DeMarco, relying on earlier joint work with Robert Rumely. |
| Title: A shape-based method for determining protein binding sites in a genome |
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| Colloquium: Topology |
| Speaker: Valerie Hower of University of California, Berkeley |
| Contact: Susan Guppy, sguppy@emory.edu |
| Date: 2011-01-31 at 4:30PM |
| Venue: MSC W201 |
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| Abstract: We present a new algorithm for the identification of bound regions from ChIP-Seq experiments. ChIP-Seq is a relatively new assay for measuring the interactions of proteins with DNA. The binding sites for a given protein in a genome are "peaks" in the data, which is given by an integer-valued height function defined on the genome. Our method for identifying statistically significant peaks is inspired by the notion of persistence in topological data analysis and provides a non-parametric approach that is robust to noise in experiments. Specifically, our method reduces the peak calling problem to the study of tree-based statistics derived from the data. The software T-PIC (Tree shape Peak Identification for ChIP-Seq) is available at http://math.berkeley.edu/~vhower/tpic.html and provides a fast and accurate solution for ChIP-Seq peak finding. |
| Title: Superfast and stable direct solutions of Toeplitz systems |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Jianlin Xia of Department of Mathematics, Purdue University |
| Contact: Jim Nagy, nagy@mathcs.emory.edu |
| Date: 2011-01-28 at 12:50PM |
| Venue: W306 |
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| Abstract: Toeplitz matrices arise in many applications such as signal and image processing, time series analysis, solution methods for PDEs, and regularization of inverse problems. In this talk, we will discuss some ideas of structured solutions of Toeplitz linear systems. These ideas can also be used to solve some other structured systems. With the displacement structure, our methods quickly solve a Cauchy-like system converted from the Toeplitz system, based on a fact that the Cauchy-like matrix is rank structured. Semiseparable structured factorizations are used to develop different versions of superfast (roughly O(n) cost) and stable Toeplitz solvers. These versions include: direct semiseparable matrix approximation, randomized sampling together with fast Toeplitz matrix-vector products, and multi-layer structured approximation. In particular, the last version uses two layers of structured representations to achieve high efficiency: an outer layer hierarchically semiseparable (HSS) structure, and an inner Cauchy-like structure for each dense HSS generator. Fast strong rank revealing LU factorizations are used in a hierarchical scheme for the structured approximation. We test the methods on various highly ill-conditioned examples to show both the efficiency and the stability. This is joint work with Ming Gu at UC Berkeley and Yuanzhe Xi at Purdue University. |
| Title: Information Discovery on Vertical Domains |
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| Seminar: Computer Science |
| Speaker: Vagelis Hristidis of Florida International University |
| Contact: Eugene Agichtein, eugene@mathcs.emory.edu |
| Date: 2011-01-28 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: As the amount of available data increases, the problem of information discovery, often referred to as finding the needle in the haystack problem, becomes more pressing. The most successful search applications today are the general purpose Web search engines and the well-structured database querying (e.g., SQL). Directly applying these two search models to specific domains is ineffective since they ignore the domain semantics -meaning of object associations- and the needs of the domain users -a biologist wants to see different results from a physician for the same query on PubMed. We present challenges and techniques to achieve effective information discovery on vertical domains by modeling the domain semantics and its users, and exploiting the knowledge of domain experts. Our focal domains are products marketplace, biological data, clinical data, bibliographic data, blogs and patents. This project is being funded by NSF.\\ \\Bio:\\ Vagelis Hristidis is an Associate Professor at the School of Computing and Information Sciences at Florida International University, in Miami. He received his PhD in Computer Science from the University of California, San Diego, in 2004. He has received funding from the National Science Foundation, the Department of Homeland Security, Google, IBM and the Kauffman Entrepreneurship Center, including the NSF CAREER Award. He has also received the FIU SCIS Excellence in Research Award twice, the FIU University Faculty Award, and the FIU University Service Award. His main research addresses the problem of bridging the gap between databases and information retrieval, with particular interest in the interdisciplinary directions of Healthcare and Disaster Management. His work has received more than 2,100 citations according to Google Scholar. He also recently edited and co-authored a book on “Information Discovery on Electronic Health Records”. For more information, please visit http://www.cis.fiu.edu/~vagelis/. |
| Title: The fractional version of Hedetniemi's Product Conjecture |
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| Seminar: Combinatorics |
| Speaker: Dwight Duffus of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-01-28 at 4:00PM |
| Venue: W306 |
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| Abstract: Hedetniemi's Product Conjecture -- that the chromatic number of the categorical product of n-chromatic graphs is n-chromatic -- was made in 1967 and remains open. The fractional version of this has recently been proved by Xuding Zhu. We would like to present this, beginning with an introduction to fractional parameters and past work on the conjecture and related problems. We will also show how Zhu's result settles a conjecture of Burr, Erdos and Lovasz on chromatic Ramsey numbers. It will likely take a few presentations to get through the background material and Zhu's proof, so this will be the first of a series of seminars on this topic. |
| Title: The Euler-Kronecker constant of a number field |
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| Colloquium: N/A |
| Speaker: V. Kumar Murty of University of Toronto |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-01-27 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: Following Ihara, we define an invariant $g(K)$ for each algebraic number field which for the rational numbers is Euler's constant and for imaginary quadratic fields is a constant studied by Kronecker. This invariant reflects subtle aspects of the arithmetic of the field, and also is (conjecturally) related to periods of Abelian varieties with complex multiplication. |
| Title: The field of Fourier coefficients of a modular form |
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| Seminar: Algebra and Number Theory |
| Speaker: V. Kumar Murty of University of Toronto |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-01-26 at 4:00PM |
| Venue: W306 |
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| Abstract: Let $f$ be a holomorphic cusp form of level $N$ which is a normalized Hecke eigenform. The Fourier coefficients of $f$ generate a number field. If $N$ is squarefree, we show that in fact, this field is generated by a single Fourier coefficient. The result is effective. |
| Title: Gauge Theory in Four Dimensions and Mock Modular Forms |
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| Seminar: Algebra and number theory |
| Speaker: Andreas Malmendier of Colby College |
| Contact: Zachary Kent, kent@mathcs.emory.edu |
| Date: 2011-01-25 at 3:00PM |
| Venue: W306 |
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| Abstract: In physics, the moduli space of vacua for the topological N = 2 supersymmetric pure gauge theories with gauge group SO(3) is the universal elliptic curve for the modular group of level 2. Moreover, the supersymmetric gauge theory associates to each four-manifold a not necessarily holomorphic modular form of level two. I will explain why for the complex projective plane this modular form is a Mock theta function - in fact, it is one of the examples listed in Ramanujan's letter to Hardy to undermine a notoriously obscure definition. In joint work with Ken Ono, we then proved that its cusp contributions are the Donaldson invariants of $CP^2$, a conjecture made by Moore and Witten. Time permitting, I will also sketch how string theory suggests a connection of this construction to a generalized elliptic genus. |
| Title: Integrating Formalism and Pragmatism to Build Real Data Privacy Solutions |
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| Seminar: Computer Science |
| Speaker: Brad Malin of Vanderbilt University |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2011-01-21 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: Organizations collect personal information while providing an ever-expanding set of services. The collected data can support various “secondary” uses and to protect privacy, various law requires information be rendered “de-identified” before it is repurposed. However, a growing body of evidence suggests data can be “re-identified” and the viability of such laws have been questioned. I will review how and why re-identification occurs, but also push the discussion from a deterministic view (i.e., re-identification can or cannot occur) toward a probabilistic view (i.e., the likelihood of re-identification). In doing so, I will illustrate how to construct efficient de-identification algorithms that mitigate risks without precluding the secondary endeavors. This work will draw upon experience and case studies from with multiple medical centers around the United States. Brad Malin is an Assistant Professor of Biomedical Informatics and Computer Science at Vanderbilt University, where he directs the Health Information Privacy Laboratory (HIPLab). The HIPLab is funded through grants from the NSF and NIH and its research artifacts have received awards of distinction from the American and International Medical Informatics Associations. In 2010, Dr. Malin received the Presidential Early Career Award for Scientists and Engineers (PECASE), the highest honor bestowed by the U.S. government on outstanding scientists and engineers beginning their independent careers. He completed his education at Carnegie Mellon University, where he received a bachelor’s in biological sciences, a master’s in data mining and knowledge discovery, a master’s in public policy and management, and a doctorate in computer science. |
| Title: Adding and Counting |
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| Special Lecture: Number Theory |
| Speaker: Ken Ono of Emory University |
| Contact: Susan Guppy, sguppy@mathcs.emory.edu |
| Date: 2011-01-21 at 8:00PM |
| Venue: Oxford Road Building |
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| Abstract: Professor Ono will explain how the simple task of adding and counting has fascinated many of the world's leading mathematicians. As is typical in number theory, many of the most fundamental questions have remained unsolved. In 2010, Ono, with the support of the AIM and the NSF, assembled an international team of distinguished researchers to attack some of the problems in partition numbers. He will announce their findings: new theories which solve some of these famous questions. |