All Seminars
| Title: Moonshine beyond the Monster |
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| Seminar: Algebra |
| Speaker: Michael Mertens of Max-Planck-Institut für Mathematik |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2017-01-17 at 4:00PM |
| Venue: W306 |
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| Abstract: Over the last 35 years, Moonshine has been an intriguing subject in mathematics, providing a still somewhat mysterious connection among Number Theory, especially the theory of modular forms, Representation Theory of finite groups, and Mathematical Physics. In the first part of my talk, I explain the general phenomenon of Moonshine at the historically first instance of so-called Monstrous Moonshine, as well as the more recent case of Umbral Moonshine. In the second part of the talk, I intend to talk in a bit more detail on recent joint work with M. J. Griffin proving a conjecture by J. Harvey and B. Rayhaun on Moonshine for Thompson’s sporadic simple group and some joint work in progress with J. F. R. Duncan and K. Ono. |
| Title: Quantum Symmetry |
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| Colloquium: Algebra |
| Speaker: Chelsea Walton of Temple University |
| Contact: Victoria Powers, vicki@mathcs.emory.edu |
| Date: 2017-01-12 at 4:00PM |
| Venue: W304 |
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| Abstract: Like Hopf algebras? You will after this talk! The aim of this lecture is to motivate and discuss "quantum symmetries" of quantum algebras (i.e. Hopf co/actions on noncommutative algebras). All basic terms will be defined, examples will be provided, along with a brief survey of recent results. |
| Title: p-torsion in class groups of number fields of arbitrary degree |
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| Seminar: Algebra |
| Speaker: Lillian Pierce of Duke |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2017-01-10 at 4:00PM |
| Venue: W306 |
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| Abstract: Fix a number field K of degree n over the rationals, and a prime p, and consider the p-torsion subgroup of the class group of K. How big is it? It is conjectured that this p-torsion subgroup should be very small (in an appropriate sense), relative to the absolute discriminant of the field. But it has so far proved difficult even to beat the trivial bound, that is, to show that the p-torsion subgroup is noticeably smaller than the full class group. In 2007, Ellenberg and Venkatesh shaved a power off the trivial bound by assuming GRH. This talk will discuss several new methods that recover this bound for certain families of fields, without assuming GRH. |
| Title: What to expect when you're unexpecting: The distribution of consecutive prime biases |
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| 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 |
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| 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: MSC 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 |
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| 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 |
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| Seminar: Combinatorics |
| Speaker: Fan Wei of Stanford University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2016-11-28 at 4:00PM |
| Venue: MSC 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 |
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| Defense: Dissertation |
| Speaker: Haoran Li of Emory University |
| Contact: Haoran Li, hli57@emory.edu |
| Date: 2016-11-17 at 1:45PM |
| Venue: MSC 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 |
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| 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: MSC W201 |
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| Abstract: https://www.ices.utexas.edu/people/339/ |
| Title: Asymptotic stabilization of point counts for moduli spaces |
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| 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. |