All Seminars
| Title: Topics in Ramsey Theory |
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| Defense: Dissertation |
| Speaker: Domingos Dellamonica Jr. of Emory University |
| Contact: Domingos Dellamonica Jr., ddellam@emory.edu |
| Date: 2012-04-03 at 4:00PM |
| Venue: W304 |
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| Abstract: In this thesis we discuss two results in Ramsey Theory.\\ \\ Result I: the size-Ramsey number of a graph $H$ is the smallest number of edges a graph $G$ must have in order to force a monochromatic copy of $H$ in every $2$-coloring of the edges of $G$. In 1990, Beck studied the size-Ramsey number of trees: he introduced a tree invariant $\beta(\cdot)$, and proved that the size-Ramsey number of a tree $T$ is at least $\beta(T)/4$. Moreover, Beck showed an upper bound for this number involving $\beta(T)$, and further conjectured that the size-Ramsey number of any tree~$T$ is of order $\beta(T)$. We answer his conjecture affirmatively. Our proof uses the expansion properties of random bipartite graphs.\\ \\ Result II: We prove the following metric Ramsey theorem. For any connected graph $G$ endowed with a linear order on its vertex set, there exists a graph $R$ such that in every coloring of the $t$-sets of vertices of $R$ it is possible to find a copy $G'$ of $G$ inside $R$ satisfying the following two properties:\\ \begin{itemize} \item the distance between any two vertices $x, y \in V(G')$ in the graph $R$ is the same as their distance within $G'$; \item the color of each $t$-set in $G'$ depends only on the graph-distance metric induced in $G'$ by the ordered $t$-set. \end{itemize} |
| Title: On highly connected monochromatic subgraphs |
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| Seminar: Combinatorics |
| Speaker: Tomasz Luczak of Emory University and Adam Mickiewicz University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2012-03-30 at 4:00PM |
| Venue: W306 |
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| Abstract: |
| Title: Quasi Isometric Properties of Graph Braid Groups |
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| Defense: Dissertation |
| Speaker: Praphat Fernandes of Emory University |
| Contact: Praphat Fernandes, pxferna@emory.edu |
| Date: 2012-03-30 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: In my thesis I initiate the study of the quasi-isometric properties of the 2 dimensional graph braid groups. I do this by studying the behaviour of flats in the geometric model spaces of the graph braid groups, which happen to be CAT(0) cube complexes. I define a quasi-isometric invariant of these graph braid groups called the intersection complex. In certain cases it is possible to calculate the dimension of this intersection complex from the underlying graph of the graph braid group. And I use the dimension of the intersection complex to prove that the family of graph braid groups $B_2(K_n)$ are quasi-isometrically distinct for all $n$. I also show that the dimension of the intersection complex for a graph braid group takes on every possible non-negative integer value. |
| Title: Monkey fields |
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| Colloquium: N/A |
| Speaker: Brian Conrad of Stanford |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2012-03-29 at 3:00PM |
| Venue: W306 |
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| Abstract: Joseph Ritt spent his entire career working with the real and complex fields, and he reportedly referred to fields of positive characteristic as "monkey fields". The development of algebraic geometry and number theory during the second half of the 20th century showed the tremendous usefulness of the so-called monkey fields even in the service of problems whose formulation only involves fields of characteristic 0. Sometimes the implications go in the other direction, using results in characteristic 0 to prove theorems over finite fields. We illustrate both directions of this interaction. |
| Title: Riemann's zeros and the rhythm of the primes |
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| EUMMA Event: N/A |
| Speaker: David Borthwick of Emory University |
| Contact: Erin Nagle, erin@mathcs.emory.edu |
| Date: 2012-03-29 at 6:00PM |
| Venue: MSC W301 |
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| Abstract: |
| Title: CM lifting |
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| Seminar: Algebra and Number Theory |
| Speaker: Brian Conrad of Stanford |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2012-03-28 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: The classification of isogeny classes of simple abelian varieties over finite fields by Honda and Tate rests on the remarkable fact that, up to a finite ground field extension and isogeny, such abelian varieties admit lifts to CM abelian varieties in characteristic 0. Building on this, Tate proved that every abelian variety over a finite field is "of CM type". But this leaves open the question of whether characteristic-0 CM lifting can be done without introducing an isogeny or ground field extension. There are several precise versions of such a refined CM lifting question, and after reviewing some basics in CM theory I will formulate such problems and discuss positive and negative answers (and examples). This is joint work with C-L. Chai and F. Oort. |
| Title: Privacy Preserving Medical Data Publishing |
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| Defense: Dissertation |
| Speaker: James Gardner of Emory University |
| Contact: James Gardner, jgardn3@emory.edu |
| Date: 2012-03-26 at 12:00PM |
| Venue: MSC E406 |
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| Abstract: There is an increasing need for sharing of medical information for public health research. Data custodians and honest brokers have an ethical and legal requirement to protect the privacy of individuals when publishing medical datasets. This dissertation presents an end-to-end Health Information DE-identification (HIDE) system and framework that promotes and enables privacy preserving medical data publishing of textual, structured, and aggregated statistics gleaned from electronic health records (EHRs). This work reviews existing de-identification systems, personal health information (PHI) detection, record anonymization, and differential privacy of multi-dimensional data. HIDE integrates several state-of-the-art algorithms into a unified system for privacy preserving medical data publishing. The system has been applied to a variety of real-world and academic medical datasets. The main contributions of HIDE include: 1) a conceptual framework and software system for anonymizing heterogeneous health data, 2) an adaptation and evaluation of information extraction techniques and modification of sampling techniques for protected health information (PHI) and sensitive information extraction in health data, and 3) applications and extension of privacy techniques to provide privacy preserving publishing options to medical data custodians, including de-identified record release with weak privacy and multidimensional statistical data release with strong privacy. |
| Title: Some Mathematical Problems in Design of Free-Form Mirrors and Lenses |
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| Defense: Dissertation |
| Speaker: Hasan Palta of Emory University |
| Contact: Hasan Palta, hpalta@emory.edu |
| Date: 2012-03-20 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: In this dissertation, we investigate several optics-related problems. The problems discussed in Chapters 1, 2, and 3 are concerned with the determination of surfaces reshaping collimated beams of light to obtain a priori given intensities on prescribed target sets. In optics, such transformations are performed by lenses and/or mirrors whose shapes need to be determined in order to satisfy the application requirements. These are inverse problems, which in analytical formulations lead to nonlinear partial differential equations of Monge-Amp\`{e}re type. In Chapter 4, we present several different designs of radiant energy concentrators. Our goal in these designs is to obtain a device that can capture solar rays with maximal efficiency. |
| Title: Multi-commodity distribution using PageRank |
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| Seminar: Combinatorics |
| Speaker: Paul Horn of Harvard University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2012-03-16 at 4:00PM |
| Venue: W306 |
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| Abstract: Discontent breaks out on a graph! Unhappiness, in the form of demand for various commodities spreads according to a variation of the contact process beginning with some initial seed. We wish to schedule shipments of goods in order to ensure that demand (and hence unhappiness) is squelched. On the other hand, shipments are expensive so we wish to limit the total amount of shipments we make and only ship to 'important' vertices. In this talk, we investigate a scheme which guarantees that all demand is met, and hence the contact process dies out, quickly (with high probability). When not all vertices are sent shipments, we get bounds on the 'escape probability' in terms of PageRank (and when there are multiple commodities, we get better bounds in terms of a vectorized version of PageRank). |
| Title: The Lagrangian of a hypergraph and its application to extremal problems |
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| Seminar: Combinatorics |
| Speaker: Yuejian Peng of Indiana State University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2012-03-09 at 4:00PM |
| Venue: W306 |
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| Abstract: In 1965 Motzkin and Straus established a connection between the maximum clique number and the Lagrangian of a graph, and provided a new proof of Turan's theorem. This new proof aroused interest in the study of Lagrangians of hypergraphs. In the 1980's, Frankl and Rodl disproved the well-known jumping constant conjecture of Erdos by using Lagrangians of hypergraphs as a tool. We present more applications of Lagrangians of hypergraphs in determining non-jumping numbers of hypergraphs. We also present some Motzkin-Straus type results for hypergraphs |