All Seminars

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Title: What to expect when you're unexpecting: The distribution of consecutive prime biases
Seminar: Algebra
Speaker: Robert Lemke Oliver of Tufts University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-01-10 at 5:00PM
Venue: W306
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Abstract:
In recent work with Soundararajan, we conjectured that the are large biases in the distribution of consecutive primes in arithmetic progressions to a fixed modulus. Here, we review this conjecture, and we discuss the distribution of the terms involved. This proves to be surprisingly subtle and connected to classical problems in analytic number theory.
Title: Ramsey and Anti-Ramsey Multiplicities
Seminar: Combinatorics
Speaker: Michael Young, PhD of Iowa State University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2016-12-02 at 4:00PM
Venue: W301
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Abstract:
A classic problem in Ramsey theory is determining, for a given graph G, the largest value of n such that there exist an edge coloring of the complete graph on n vertices that does not contain a monochromatic subgraph that is isomorphic to G. This talk will discuss, asymptotically, how many monochromatic copies of G must exist in an edge coloring of the complete graph on n vertices. This value is known as the Ramsey Multiplicity. A graph is rainbow if each edge of the graph is distinctly colored. We will also discuss Anti-Ramsey Multiplicities, which is the asymptotic maximum number of rainbow copies of a graph G that can exist in an edge coloring of the complete graph on n vertices.
Title: New forms of moonshine
Seminar: Algebra
Speaker: Jeff Harvey of University of Chicago
Contact: John Duncan, john.duncan@emory.edu
Date: 2016-11-29 at 4:00PM
Venue: W306
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Abstract:
I will give an overview of some recent developments in moonshine including umbral moonshine and its connection to K3 surfaces and Niemeier lattices. I will then discuss a new form of moonshine related to skew-holomorphic Jacobi forms and discuss briefly some of the relations between these new moonshines and the original moonshine associated to the Monster sporadic group.
Title: On the number of cliques in graphs with a forbidden clique minor
Seminar: Combinatorics
Speaker: Fan Wei of Stanford University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2016-11-28 at 4:00PM
Venue: W301
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Abstract:
Abstract: Reed and Wood and, independently, Norine, Seymour, Thomas, and Wollan, showed that for each t there is c(t) such that every graph on n vertices with no Kt minor has at most c(t)n cliques. Wood asked in 2007 if c(t) < ct for some absolute constant c. This problem was recently solved by Lee and Oum. In this paper, we determine the exponential constant. We prove that every graph on n vertices with no Kt minor has at most 32t=3+o(t)n cliques. This bound is tight for n ≥4t/3. We use the similiar idea to give an upper bound on the number of cliques in an n-vertex graph with no Kt-subdivision. Easy computation will give an upper bound of 23t+o(t)n; a more careful examination gives an upper bound of 21.48t+o(t)n. We conjecture that the optimal exponential constant is 32/3 as in the case of minors. This is a joint work with Jacob Fox.
Title: Differentially private data release and learning mechanisms
Defense: Dissertation
Speaker: Haoran Li of Emory University
Contact: Haoran Li, hli57@emory.edu
Date: 2016-11-17 at 1:45PM
Venue: E408
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Abstract:
Nowadays data sharing is important for application domain, such as scientific discoveries, business strategies, commercial interests, and social goods, especially when there are not enough local samples to test a hypothesis. However, data in its raw format are sensitive as they essentially contains individual specific information, and publishing such data without proper protection may disclose personal privacy. Netflix canceled their recommendation system contest because the released customers data can identify special individuals with high probability. In order to promote data sharing, it is important to develop privacy-preserving algorithms that respect data confidentiality while present data utility. In this dissertation, we address the privacy concerns in publishing high-dimensional data and dynamic datasets, releasing support vector machine classification model, and optimizing utility on data with records of various privacy preferences. It can be shown that all of our privacy preserving algorithms satisfy a rigorous privacy guarantee known as differential privacy, which has been the de facto standard for privacy protection. Extensive empirical studies confirm that they will enable privacy-preserving data release and analytical tasks in a broad range of application domains.
Title: Patient Specific Modeling and the Predictive Paradigm in Cardiovascular Medicine
Colloquium: Numerical Analysis and Scientific Computing
Speaker: Thomas J. R. Hughes, PhD of The University of Texas at Austin
Contact: Alessandro Veneziani, ale@mathcs.emory.edu
Date: 2016-11-16 at 4:00PM
Venue: W201
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Abstract:
https://www.ices.utexas.edu/people/339/
Title: Asymptotic stabilization of point counts for moduli spaces
Seminar: Algebra
Speaker: Joseph Gunther of CUNY
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-11-15 at 4:00PM
Venue: W306
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Abstract:
A common theme in different areas of mathematics is that natural sequences of moduli spaces often stabilize in certain respects: homological stability in topology, convergence of motives in algebraic geometry, finite field point counts in number theory. I'll explain recent point-counting results on Hurwitz spaces parametrizing covers of curves, and moduli spaces of hypersurfaces. Time willing, I'll discuss motivic convergence in the Grothendieck ring of varieties.
Title: Fooling bounded depth circuits
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: 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
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
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.