All Seminars

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Title: Analysis of Monge-Ampere functions
Seminar: Analysis and Differential Geometry
Speaker: Joseph Fu of University of Georgia
Contact: Vladmir Oliker, oliker@mathcs.emory.edu
Date: 2015-11-24 at 4:00PM
Venue: W301
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Abstract:
The notion of Monge-Ampere (MA) function, introduced by the speaker around 1989 and subsequently generalized by R. Jerrard around 2005, relaxes the strong positivity properties enjoyed by convex functions while preserving the integrality of their derivatives. For example, just as for a convex function there is a natural notion of the Hessian determinant measure for any MA function, with the added flexibility that in the MA case this measure may be signed. In this talk we will give the basic definitions and discuss the main properties and central open questions of this class.
Title: Control of oscillators, temporal homogenization, and energy harvest by super-parametric resonance
Seminar: Numerical Analysis and Scientific Computing
Speaker: Molei Tao of Georgia Institute of Technology
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2015-11-20 at 1:00PM
Venue: W302
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Abstract:
We show how to control an oscillator by periodically perturbing its stiffness, such that its amplitude follows an arbitrary positive smooth function. This also motivates the design of circuits that harvest energies contained in infinitesimal oscillations of ambient electromagnetic fields. To overcome a key obstacle, which is to compensate the dissipative effects due to finite resistances, we propose a theory that quantifies how small/fast periodic perturbations affect multidimensional systems. This results in the discovery of a mechanism that we call super-parametric resonance, which reduces the resistance threshold needed for energy extraction based on coupling a large number of RLC circuits.
Title: K3 Surfaces, Mock Modular Forms and the Conway Group
Seminar: Algebra and Number Theory
Speaker: John Duncan of Emory University
Contact: Michael H. Mertens, michael.mertens@emory.edu
Date: 2015-11-17 at 4:00PM
Venue: White Hall 112
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Abstract:
In their famous Monstrous Moonshine paper of 1979, Conway Norton also described an association of modular functions to the automorphism group of the Leech lattice (a.k.a. Conways group). In analogy with the monstrous case, there is a distinguished vertex operator superalgebra that realizes these functions explicitly. More recently, it has come to light that this Conway moonshine module may be used to compute equivariant enumerative invariants of K3 surfaces. Conjecturally, all such invariants can be computed in this way. The construction attaches explicitly computable mock modular forms to automorphisms of K3 surfaces.
Title: Local-to-global principle for rational points on conic and quadric bundles over curves
Seminar: Algebra and Number Theory
Speaker: Alexei Skorobogatov of Imperial College London
Contact: Michael H. Mertens, michael.mertens@emory.edu
Date: 2015-11-17 at 5:15PM
Venue: White Hall 112
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Abstract:
One expects the Brauer-Manin obstruction to control rational points on 1-parameter families of conics and quadrics over a number field when the base curve has genus 0. Results in this direction have recently been obtained as a consequence of progress in analytic number theory. On the other hand, it is easy to construct a family of 2-dimensional quadrics over a curve with just one rational point over Q, which is a counterexample to the Hasse principle not detected by the etale Brauer-Manin obstruction. Conic bundles with similar properties exist over real quadratic fields, though most certainly not over Q.
Title: On Large Scale Inverse Problems that Cannot be Solved
Seminar: Numerical Analysis and Scientific Computing
Speaker: Eldad Haber of The University of British Columbia
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2015-11-13 at 1:00PM
Venue: W302
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Abstract:
In recent years data collection systems have improved and we are now able to collect large volume of data over vast regions in space. This lead to large scale inverse problems that involve with multiple scales and many data. To invert this data sets, we must rethink our numerical treatment of the problems starting from our discretization, to the optimization technique to be used and the efficient way we can parallelize these problems. In this talk we introduce a new multi-scale asynchronous method for the treatment of such data and apply it to airborne Electromagnetic data.
Title: Upper tails for arithmetic progressions in random sets
Seminar: Combinatorics
Speaker: Lutz Warnke of The University of Cambridge
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2015-11-13 at 4:00PM
Venue: W303
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Abstract:
We study the upper tail {\mathbb P}(X \ge (1+\varepsilon) {\mathbb E} X) of the number of arithmetic progressions of a given length in a random subset of [n]=\{1, \ldots, n\}, establishing exponential bounds for which are best possible up to constant factors in the exponent (improving results of Janson and Ruci{\'n}ski). The proof also extends to Schur triples, and, more generally, to the number of edges in random induced subhypergraphs of `almost linear' k-uniform hypergraphs.
Title: Two Methods for Easing Video Consumption
Seminar: Computer Science
Speaker: Amanda Stent of Yahoo Labs
Contact: Eugene Agichtein, eugene@mathcs.emory.edu
Date: 2015-11-11 at 1:30PM
Venue: W302
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Abstract:
Content on the world wide web increasingly takes the form of video; consequently, it is important both to analyze and to summarize video in order to facilitate search, personalization, browsing, etc. In this talk I will present two projects from Yahoo Labs devoted to different aspects of video processing. First, I will present a method for automatic creation of a well-formatted, readable transcript for a video from closed captions or ASR output. Readable transcripts are a necessary precursor to indexing, ranking and content-based summarization of videos. Our approach uses acoustic and lexical features extracted from the video and the raw transcription/caption files. Empirical evaluations of our approach show that it outperforms baseline methods. Second, I will present a method for video summarization that uses title-based image search results to find visually important shots. A video title is often carefully chosen to be maximally descriptive of the video’s main topic, and hence images related to the title can serve as a proxy for important visual concepts of the main topic. However, images searched using the title can contain noise (images irrelevant to video content) and variance (images of different topics). Our approach to video summarization is a novel co-archetypal analysis technique that learns canonical visual concepts shared between video and images, but not in either alone, by finding a joint-factorial representation of the two data sets. Experimental results show that our approach produces superior quality summaries compared to several recently proposed approaches. I will conclude the talk with some ideas for future work on video summarization using multimodal representations.
Title: A reexamination of the Birch and Swinnerton-Dyer cubic surfaces
Seminar: Algebra and Number Theory
Speaker: Mckenzie West of Emory University
Contact: Michael H. Mertens, michael.mertens@emory.edu
Date: 2015-11-10 at 4:00PM
Venue: W304
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Abstract:
The Hasse principle asks whether solutions to an equation in a local field extend to those in a global field. This does not always happen, the Brauer-Manin obstruction being a common explanation. A conjecture of Colliot-Thelene and Sansuc implies that a Brauer-Manin obstruction exists for every cubic surface which fails to satisfy the Hasse principle. In 1975, Birch and Swinnerton-Dyer gave some early examples of cubic surfaces which have a Brauer-Manin obstruction: (cubic norm) = (linear) (quadratic norm). They make a rough number theoretic argument for the Brauer-Manin obstruction in the case that the Hasse principle fails, focusing on the particular fields and constants. We make use of advancements in arithmetic geometry, taking a geometric look at these objects and utilizing the correspondence between the Brauer group and the Picard group of a surface in order to update and generalize their arguments.
Title: Truncating low-rank preconditioner updates for sequences of linear systems
Seminar: Numerical Analysis and Scientific Computing
Speaker: Eric de Sturler of Virginia Tech
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2015-11-09 at 4:00PM
Venue: E408
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Abstract:
In many applications, we need to solve sequences of large linear systems. If good preconditioners are required for fast convergence, we may need to compute many preconditioners. This can be very expensive. One could compute a single preconditoner for all systems or recompute the preconditioner infrequently, but this may lead to very large number of iterations. An alternative is to update the preconditioner in some efficient manner while maintaining the quality of the preconditioner. One such approach is to update the preconditioner by low-rank updates, typically applied in a multiplicative way, which can be done very cheaply. However, this has the problem that applying the preconditioner (during the iterative solve) gets increasingly expensive. We discuss two methods to truncate such low-rank updates while maintaining good preconditioner quality. We give applications from solid state physics and nonlinear partial differential equations.
Title: Algebraic Iterative Reconstruction Methods - A Users' Guide
Seminar: Numerical Analysis and Scientific Computing
Speaker: Per Christian Hansen of Technical University of Denmark and Silvia Gazzola, Hariot Watt University
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2015-11-06 at 1:00PM
Venue: W302
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Abstract:
Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising, for example, in tomographic image reconstruction. This includes both the Algebraic Reconstruction Techniques (ART) and the Simultaneous Iterative Reconstruction Techniques (SIRT), both of which rely on semi-convergence. Hybrid Krylov subspace methods have also become popular in recent years, which are used to stabilize the semi-convergence behavior. We survey these methods and explain their convergence properties, and we discuss some practical issues such as stopping rules and the choice of the relaxation parameter. We finish with some examples that illustrates our MATLAB implementation of these methods.