All Seminars
| Title: Fooling bounded depth circuits |
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| Seminar: Combinatorics |
| Speaker: Domingos Dellamonica of The University of Sao Paulo |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2016-11-14 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Abstract: We will present a very nice breakthrough result of Mark Braverman which establishes that polynomially sized bounded depth circuits are "fooled" by t-independent distributions (for polylogarithmic t). In simpler words, for any circuit C of size m in this class, given any distribution D of n-bit strings (elements in {0, 1}^n) such that the bits are t-wise independent (t = polylog(m)), the distribution of C(D) is practically identical to that of C(U), where U is the uniform distribution. This result was recently applied by E. Chattopadhyay and D. Zuckerman (2016) to essentially derandomize the Binomial Random Graph G(N, 1/2). As a corollary they now hold the record for the best bounds on Ramsey Graphs explicitly constructed by an algorithm. |
| Title: Efficient Search and Computation on Encrypted Data with Access Control |
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| Defense: Dissertation |
| Speaker: Michael Solomon of Emory University |
| Contact: Michael Solomon, msolo01@emory.edu |
| Date: 2016-11-08 at 2:30PM |
| Venue: W306 |
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| Abstract: Outsourcing data and processing to cloud environments often raises security and privacy concerns, which can be addressed through the use of encryption. But current approaches either provide all-or-nothing encryption, or rely on an omniscient third party to handle granular key management and make access control decisions to provide fine-grained access control, and introduce obstacles to searching over ciphertext. We explore the problem of efficiently searching encrypted data and simultaneously providing embedded fine-grained access control, first in a general setting, and then extended to location-based data. We first propose a new framework for generic database data that enforces access control for queries from different classifications of users, while still providing the capability to search over encrypted data. We then extend our research focus to location-based applications by implementing and assessing several existing location privacy solutions to produce concrete recommendations of the best technique for implementors to choose for specific use cases. And finally, we combine the first and second parts of our work to propose another new framework for mutually private proximity detection (MPPD) to efficiently support searching over encrypted data and enforcing fine-grained access control and privacy for data owners (DO) and users for location-based applications. The culmination of our work provides researchers and application developers with a viable framework that provides MPPD in a categorical setting, and is based on current architectures and technologies. |
| Title: The transformation laws of algebraic theta functions |
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| Seminar: Algebra |
| Speaker: Luca Candelori of Louisiana State University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-11-08 at 4:00PM |
| Venue: W306 |
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| Abstract: ABSTRACT: We present the algebro-geometric theory underlying the classical transformation laws of theta functions with respect to the action of symplectic matrices on Sigel's upper half-space. More precisely, we explain how the theta multiplier, the half-integral weight automorphy factor and the Weil representation occurring in the classical transformation laws all have a geometric origin, that is, they can all be constructed within a given moduli problem on abelian schemes. To do so, we introduce and study new algebro-geometric constructions such as theta multiplier bundles, metaplectic stacks and bundles of half-forms, which could be of independent interest. Applications include a geometric theory of modular forms of half-integral (in the sense of Shimura), and their generalizations to higher degree. |
| Title: Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points |
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| Seminar: Algebra |
| Speaker: Padmavathi Srinivasan of Georgia Institute of Technology |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-11-01 at 4:00PM |
| Venue: W306 |
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| Abstract: Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In the case of elliptic curves, the Ogg-Saito formula shows that (the negative of) the Artin conductor equals the minimal discriminant. In the case of genus two curves, equality no longer holds in general, but the two invariants are related by an inequality. We investigate the relation between these two invariants for hyperelliptic curves of arbitrary genus. |
| Title: A Ramsey Class of Steiner Systems |
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| Seminar: Combinatorics |
| Speaker: Christian Reiher of The University of Hamburg |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2016-10-24 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: We construct a Ramsey class whose objects are Steiner systems. In contrast to the situation with general r-uniform hypergraphs, it turns out that simply putting linear orders on their sets of vertices is not enough for this purpose: we also have to strengthen the notion of subobjects used from induced subsystems to something we call strongly induced subsystems. Moreover we study the Ramsey properties of other classes of Steiner systems obtained from this class by either forgetting the order or by working with the usual notion of subsystems. This leads to a perhaps surprising induced Ramsey theorem in which it designs get coloured. This is joint work with Vindya Bhat, Jaroslav Nevsetvril, and Vojtvech Rodl. |
| Title: Athens-Atlanta Joint Number Theory Seminar |
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| Seminar: Algebra |
| Speaker: Florian Pop and Ben Bakker of UPenn and UGA |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-10-18 at 4:00PM |
| Venue: AT UGA |
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| Abstract: AT UGA |
| Title: Centrality measures and contagion on temporal networks |
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| Defense: Dissertation |
| Speaker: Isabel Chen of Emory University |
| Contact: Isabel Chen, imchen@emory.edu |
| Date: 2016-10-17 at 4:00PM |
| Venue: W302 |
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| Abstract: The objective of this dissertation is to study the relationship between network-based centrality measures and epidemic outcome. Determining the key players in contagion processes can inform disease-prevention strategies. We analyze a time-stamped, person-to-person contact network based on human mobility movements within a busy, urban hospital. Movement patterns identified a small number of locations as hubs of activity. Linear algebraic techniques were used to compute a recently proposed temporal centrality measure applied to the empirical network; comparisons with traditional centrality measures were performed to determine if the inclusion of temporal information provides additional insights. Linear regression techniques were employed to describe the relationships between the quantities of interest. We find that while temporal centrality can at times identify key players not captured by traditional measures, it does not necessarily outperform non-temporal measures with respect to predicting epidemic outcome. Strategic removal of connections between highly central nodes resulted in an exponential decrease in the structural connectivity of the network, but this did not translate to a reduction in epidemic outcome. We conclude that contagion on temporal networks is extremely robust to changes in the network, and while network-based centrality can help to identify key players in an epidemic process, more work needs to be done to build an epidemic-containment strategy based on the information afforded by network-based analyses. |
| Title: CANCELED! Mathematical models for the correspondence problem |
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| Seminar: General interest for MathCS and Radiology |
| Speaker: Jan Modersitzki of University of Lubeck |
| Contact: Lars Ruthotto, lruthotto@emory.edu |
| Date: 2016-10-06 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: THIS SEMINAR HAS BEEN CANCELED. WE APOLOGIZE FOR THE SHORT NOTICE. We introduce the fascinating correspondence problem also known as image registration. Roughly spoken, the goal is to automatically establish correspondences between points in different projections of a scene. In particular, in medical imaging, this problem is very important and used for applications such as motion correction or data fusion. Several examples displaying different facets of the problem are discussed. A mathematical framework for the correspondence problem is outlined. Starting point is a variational formulation, where a joint energy is to be minimized on an appropriate set. Modular building blocks such as distance measures and regularizers are briefly discussed and related to particular applications. Finally, a brief outlook on constrained image registration is presented. Constraints are used to improve the modeling by restricting the admissible set in a smart way. |
| Title: Bounding torsion in geometric families of abelian varieties |
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| Seminar: Algebra |
| Speaker: Ben Bakker of UGA |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-10-04 at 4:00PM |
| Venue: W306 |
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| Abstract: A celebrated theorem of Mazur asserts that the order of the torsion part of the group of rational points of an elliptic curve over Q is absolutely bounded; it is conjectured that the same is true for abelian varieties over number fields K, though very little progress has been made in proving it. The natural geometric analog where K is replaced by the function field of a complex curve---known as the geometric torsion conjecture---is equivalent to the nonexistence of low genus curves in congruence towers of Siegel modular varieties. In joint work with J. Tsimerman, we prove the conjecture for abelian varieties with real multiplication. We'll discuss a general method for bounding the genus of curves in locally symmetric varieties using hyperbolic geometry to bound Seshadri constants and apply it to some related problems. |
| Title: Decomposing the Complete r-Graph |
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| Seminar: Combinatorics |
| Speaker: Imre Leader of The University of Cambridge |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2016-09-28 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: The Graham-Pollak theorem states that, if we wish to decompose the complete graph Kn into complete bipartite subgraphs, then we need at least n-1 of them. What happens for hypergraphs? In other words, if we wish to decompose the complete r-graph on n vertices into complete r-partite r-graphs, how many do we need? In this talk we report on recent progress on this question. This is joint work with Luka Milicevic and Ta Sheng Tan. |