All Seminars
| Title: Infinitesimal Deformation Theory and Grothendieck Topologies |
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| Seminar: Algebra |
| Speaker: Jonathan Wise of CU Boulder |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2012-10-10 at 3:00PM |
| Venue: W306 |
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| Abstract: To probe the infinitesimal structure of a moduli space of geometric objects, one seeks to understand families of those objects over "fat points". Understanding such families frequently yields a great deal of information about the moduli space. Remarkably, these deformation problems tend to admit cohomological solutions of a common form: obstructions in H 2, deformations in H 1, and automorphisms in H 0. I will offer an explanation for this common form, coming from some exotic Grothendieck topologies. We will see how this point of view works in several examples. No prior knowledge about Grothendieck topologies or deformation theory will be assumed. |
| Title: KLR conjecture in Sparse Random Graphs |
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| Colloquium: N/A |
| Speaker: Mathias Schacht of University of Hamburg |
| Contact: Vojtech Rodl, rodl@mathcs.emory.edu |
| Date: 2012-10-05 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: The KLR conjecture of Kohayakawa, Luczak, and Rödl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph G(n,p) satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and Rödl. We prove a variant of this conjecture which is sufficient for most applications to random graphs. In particular, our result implies a number of recent probabilistic threshold results. We also discuss several further applications. This joint work with Conlon, Gowers, and Samotij. |
| Title: Periods of Modular Forms and Identities between Eisenstein Series |
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| Seminar: Algebra |
| Speaker: Wissam Raji of American University of Beirut |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2012-10-03 at 3:00PM |
| Venue: W306 |
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| Abstract: Borisov and Gunnels observed in 2001 that certain linear relations between products of two holomorphic weight 1 Eisenstein series had the same structure as the relations between periods of modular forms. We give a conceptual reason for this and for similar phenomena in all weights. This involves an unconventional way of expanding the Rankin-Selberg convolution of a cusp form with an Eisenstein series. (Joint with Kamal Khuri-Makdisi). |
| Title: Optimal partitions of measures |
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| Colloquium: N/A |
| Speaker: Gershon Wolansky of Technion - Israel Institute of Technology |
| Contact: Professor Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2012-09-27 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Let $X$ be a probability measure space and $\psi_1....\psi_N$ measurable, real valued functions on $X$. Consider all possible partitions of $X$ into $N$ disjoint subdomains $X_i$ on which $\int_{X_i}\psi_i$ are prescribed. I'll address the question of characterizing the set $(m_1,,,m_N) \in \mathbb{R}^N$ for which there exists a partition $X_1, \ldots X_N$ of $X$ satisfying $\int_{X_i}\psi_i= m_i$ and discuss some optimization problems on this set of partitions. The relation of this problem to semi-discrete version of optimal mass transportation is discussed, as well as applications to game theory. |
| Title: Syzygies and Boij--Soederberg Theory |
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| Seminar: Algebra and Number Theory |
| Speaker: Daniel Erman of University of Michigan |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2012-09-26 at 3:00PM |
| Venue: W306 |
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| Abstract: For a system of polynomial equations, it has long been known that the relations (or syzygies) among the polynomials provide powerful insights into the properties and invariants of the corresponding projective varieties. Boij--Soederberg Theory provides a powerful perspective on syzygies, and in particular reveals a surprising duality between syzygies and cohomology of vector bundles. I will describe some new results on this duality and on the properties of syzygies. |
| Title: Modeling Rich Interactions for Web Search Intent Inference, Ranking and Evaluation |
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| Defense: Dissertation |
| Speaker: Qi Guo of Emory University |
| Contact: Qi Guo, qguo3@emory.edu |
| Date: 2012-09-21 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: The thesis aims to enable more intelligent Web search engines by modeling and interpreting a wide range of searcher interactions, including queries, clicks, time, and finer grained interactions such as mouse cursor movements and scrolling behavior (or pinching, zooming and sliding with a touch screen). The thesis spans three key areas in Web search, namely, understanding information needs, ranking result documents, and evaluating search experience.\\ \\ First, the thesis developed techniques for inferring the immediate searcher information needs through mining the rich interactions and context in a search session. The developed techniques improve the prediction of general search intent, commercial search intent and future ad clickthrough over the state-of-the-art methods that only exploit query and click signals.\\ \\ Second, the thesis developed techniques for estimating document relevance to improve search result ranking. The Post-Click Behavior (PCB) relevance prediction model was introduced, which focuses on estimating the "intrinsic" document relevance from a rich set of fine-grained interactions on the viewed result documents in a search session, outperforming the state-of-theart methods that are based on the time information.\\ \\ Third, the thesis developed techniques for automatically evaluating search experience or search engine performance at different levels. The first level is the query-level, where techniques for predicting query performance were developed, enabling evaluation and diagnostic for particular queries or query classes. The second level is the session-level, where techniques for predicting search success were developed, which include a principled framework to study Web search success, and fine-grained interaction models that improve prediction accuracies for both desktop and mobile settings. The third level is the level of using multiple search engines, where the developed techniques focus on understanding and predicting the rationales of engine switching in a search session. |
| Title: Almost harmonic Maass forms and Kac-Wakimoto characters |
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| Seminar: Algebra and Number Theory |
| Speaker: Amanda Folsom of |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2012-09-19 at 3:00PM |
| Venue: W306 |
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| Abstract: We address a question Kac, and explain the modular properties of certain characters due to Kac and Wakimoto pertaining to $sl(m|n)^$, where $n$ is a positive integer. We prove that these characters are essentially holomorphic parts of new automorphic objects we call "almost harmonic Maass forms," which generalize both weak Maass forms and almost holomorphic modular forms. By new methods involving meromorphic Jacobi forms, this generalizes prior works of Bringmann-Ono and Bringmann-Folsom, which treat only the case $n=1$. This is joint work with Kathrin Bringmann (University of Cologne). |
| Title: Estimation of a semiparametric mixture of regression models: application to the ChipMIX model |
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| Seminar: Computer Science and Informatics |
| Speaker: Pierre Vandekerkhove of Visiting professor, Department of Materials Science and Engineering, Georgia Institute of Technology |
| Contact: Alfredo Tirado-Ramos, atirado@emory.edu |
| Date: 2012-09-14 at 3:00PM |
| Venue: MSC W301 |
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| Abstract: In this talk we will present a new mixture of regression models which is a generalization of the semiparametric two-component mixture model, which can be used as an exploratory and complementary tool for the modeling of two-color ChIP-chip datasets. An implementation and numerical performances for this method is discussed, using several simulated datasets and one real microarray dataset, the ChipMIX model. |
| Title: Minimum Degree and Disjoint Cycles in Generalized Claw-free Graphs |
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| Colloquium: N/A |
| Speaker: Ralph Faudree of The University of Memphis |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2012-09-14 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: For $s \geq 3$ a graph is $K_{1,s}$-free, if it does not contain an induced subgraph isomorphic to $K_{1,s}$. For $s = 3$, such graphs are called claw-free graphs. Results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions will be be discussed, such as if $G$ is claw-free of sufficiently large order $n = 3k$ with $\delta (G) \geq n/2$, then $G$ contains $k$ disjoint triangles. Also, the extension of results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions to $K_{1,s}$-free graphs for $s > 3$ will be presented. These results will be used to prove the existence of minimum degree conditions that imply the existence of powers Hamiltonian cycle in generalized claw-free graphs. |
| Title: Minimum Degree and Disjoint Cycles in Generalized Claw-free Graphs |
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| Seminar: Combinatorics |
| Speaker: Ralph Faudree of The University of Memphis |
| Contact: Dwight Duffus, dwight@math.cs.emory.edu |
| Date: 2012-09-14 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: For $s \geq 3$ a graph is $K_{1,s}$-free, if it does not contain an induced subgraph isomorphic to $K_{1,s}$. For $s = 3$, such graphs are called claw-free graphs. Results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions will be be discussed, such as if $G$ is claw-free of sufficiently large order $n = 3k$ with $\delta (G) \geq n/2$, then $G$ contains $k$ disjoint triangles. Also, the extension of results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions to $K_{1,s}$-free graphs for $s > 3$ will be presented. These results will be used to prove the existence of minimum degree conditions that imply the existence of powers Hamiltonian cycle in generalized claw-free graphs. |