All Seminars
| 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 |
| Download Flyer |
| 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 |
| Download Flyer |
| 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 |
| Download Flyer |
| 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 |
| Download Flyer |
| 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: MSC W303 |
| Download Flyer |
| 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 |
| Download Flyer |
| 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 |
| Download Flyer |
| 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: MSC E408 |
| Download Flyer |
| 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 |
| Download Flyer |
| 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. |
| Title: Fusion system and classifying spaces |
|---|
| Seminar: Algebra and Number Theory |
| Speaker: Justin Lynd of University of Montana |
| Contact: John Duncan, john.duncan@emory.edu |
| Date: 2015-11-06 at 3:00PM |
| Venue: MSC E406 |
| Download Flyer |
| Abstract: Given a finite group, one can form its classifying space, and then its reduced integral cohomology. This cohomology is a finite abelian group in each degree and so is a product of its p-primary components, as p ranges over the prime divisors of the group order. There are corresponding "p-local" constructions at the group and space level that reflect the p-primary part of group cohomology. At the level of the group, one is led to a category called the p-fusion system. At the space level, one has p-completion in the sense of Bousfield and Kan. That these two constructions preserve essentially the same data is known as the Martino-Priddy conjecture, which was first proved in 2004 (p odd) and 2006 (p=2) by B. Oliver. I'll give an introduction to fusion systems and the broad outline of a proof of a generalization of this conjecture, due to A. Chermak, B. Oliver, and G. Glauberman and myself. |