All Seminars
| Title: The Riemann Hypothesis for Period Polynomials |
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| Seminar: Algebra |
| Speaker: Ken Ono of Emory University |
| Contact: David Zureick-Brown, dab@mathcs.emory.edu |
| Date: 2016-01-12 at 4:00PM |
| Venue: W304 |
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| Abstract: |
| Title: The 1729 K3 surface |
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| Seminar: Algebra and Number Theory |
| Speaker: Sarah Trebat-Leder of Emory University |
| Contact: Michael H. Mertens, michael.mertens@emory.edu |
| Date: 2015-12-08 at 4:00PM |
| Venue: W304 |
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| Abstract: We revisit the mathematics that Ramanujan developed in connection with the famous "taxi-cab" number 1729. A study of his writings reveals that he had been studying Euler's diophantine equation a^3+b^3=c^3+d^3. It turns out that Ramanujan's work anticipated deep structures and phenomena which have become fundamental objects in arithmetic geometry and number theory. We find that he discovered a K3 surface with Picard number 18, one which can be used to obtain infinitely many cubic twists over Q with rank >= 2. |
| Title: Torsion in Odd Degree |
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| Seminar: Algebra |
| Speaker: Abbey Bourdon of University of Georgia |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2015-12-01 at 4:00PM |
| Venue: W304 |
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| Abstract: Let E be an elliptic curve defined over a number field F. It is a classical theorem of Mordell and Weil that the collection of points of E with coordinates in F form a finitely generated abelian group. We seek to understand the subgroup of points with finite order. In particular, given a positive integer d, we would like to know precisely which abelian groups arise as the torsion subgroup of an elliptic curve defined over a number field of degree d. I will discuss recent progress on this problem for the special class of elliptic curves with complex multiplication (CM). In particular, if d is odd, we now have a complete classification of the groups that arise as the torsion subgroup of a CM elliptic curve defined over a number field of degree d. This is joint work with Paul Pollack. |
| Title: Analysis of Monge-Ampere functions |
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| 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: MSC 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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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 |
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| 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. |