All Seminars

Title: Riemann's zeros and the rhythm of the primes
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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Title: CM lifting
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
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
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
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
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
Title: Experiences with Model Reduction and Interpolation
Seminar: Numerical Analysis and Scientific Computing
Speaker: Paul Constantine of Sandia National Laboratory
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2012-03-07 at 12:50PM
Venue: W306
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Abstract:
Modern physical simulations can be remarkably expensive, often requiring extensive time on massive supercomputers. The simulated models typically depend on a set of input parameters -- e.g., material properties, boundary conditions, etc. Unfortunately, the cost of the simulations makes it difficult to study the effects of the parameters on model outputs; thorough sensitivity analysis, uncertainty quantification, and design optimization studies are often infeasible.\\ \\ In this talk, I'll examine methods for constructing cheaper reduced order models (ROMs) with input/output relationships that are comparable to the full physical simulation. These ROMs can be used in place of the expensive simulation to study the effects of the input parameters on the model outputs.\\ \\ The essential idea behind the construction of the ROM is to run a few expensive simulations, and to use their outputs to tune the parameters of the ROM. This tuning procedure involves a singular value decomposition (SVD) on the matrix of outputs from the expensive simulations, which may be very large. I will discuss a MapReduce implementation of the communication-avoiding QR factorization for tall matrices that allows us to scale the SVD computation to matrices with billions of rows.
Title: Integral points on pencils of homogeneous spaces
Seminar: Algebra and Number Theory
Speaker: Jean-Louis Colliot-Thelene of University of Paris-Sud, Orsay
Contact: TBA
Date: 2012-03-06 at 3:00PM
Venue: W306
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Abstract:
In this seminar talk I shall first go into details of my work with Fei Xu on integral solutions of the diophantine equation $q(x,y,z)=P(t)$, where $q$ is an indefinite integral ternary quadratic form and $P(t)$ is a polynomial with integral coefficients. I shall then explain the extent to which David Harari and I may currently extend the result to pencils of homogeneous spaces of linear algebraic groups.
Title: Questions in the algebraic topology of Galois theory
Colloquium: N/A
Speaker: Kirsten Wickelgren of Harvard University
Contact: Emily Hamilton, emh@mathcs.emory.edu
Date: 2012-03-01 at 4:00PM
Venue: MSC W201
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Abstract:
One of Vladimir Voevodsky's beautiful results is the proof of the Milnor conjecture, which imports powerful techniques from algebraic topology into algebraic geometry, and computes the mod 2 etale cohomology ring of a field in terms of the field arithmetic of k. This talk will begin with a broad discussion of this work, and then replace the cohomology ring with its underlying differential graded algebra and obtain field arithmetic identities generalizing the relation in Milnor and Voevodksy's description of the cohomology ring.
Title: 3-Connected, Claw-Free, Generalized Net-Free Graphs are Hamiltonian
Defense: Dissertation
Speaker: Susan Janiszewski of Emory University
Contact: Susan Janiszewski, sjanisz@emory.edu
Date: 2012-02-29 at 3:00PM
Venue: W306
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Abstract:
Given a family $\mathcal{F} = \{H_1, H_2, \dots, H_k\}$ of graphs, we say that a graph is $\mathcal{F}$-free if $G$ contains no subgraph isomorphic to any $H_i$, $i = 1,2,\dots, k$. The graphs in the set $\mathcal{F}$ are known as {\it forbidden subgraphs}. The main goal of this dissertation is to further classify pairs of forbidden subgraphs that imply a 3-connected graph is hamiltonian. First, the number of possible forbidden pairs is reduced by presenting families of graphs that are 3-connected and not hamiltonian. Of particular interest is the graph $K_{1,3}$, also known as the {\it claw}, as we show that it must be included in any forbidden pair. Secondly, we show that 3-connected, $\{K_{1,3}, N_{i,j,0}\}$-free graphs are hamiltonian for $i,j \ne 0, i+j \le 9$ and 3-connected, $\{K_{1,3}, N_{3,3,3}\}$-free graphs are hamiltonian, where $N_{i,j,k}$, known as the {\it generalized net}, is the graph obtained by rooting vertex-disjoint paths of length $i$, $j$, and $k$ at the vertices of a triangle. These results combined with previous known results give a complete classification of generalized nets such that claw-free, net-free implies a 3-connected graph is hamiltonian.