All Seminars

Title: Finding a role for structural graph theory in real-world network analysis
Seminar: The SIAM Student Chapter
Speaker: Blair Sullivan of Oak Ridge National Laboratory
Contact: Alexis Aposporidis, aapospo@emory.edu
Date: 2012-10-23 at 4:00PM
Venue: W306
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Abstract:
Network science is a rapidly growing interdisciplinary field with methods and applications drawn from across the natural, social, and information sciences. Perhaps surprisingly, very few approaches use techniques from the rich literature of structural graph theory. In this talk, we discuss some first steps towards integrating what have been predominantly theoretical results into tools for scalable network analysis.\\ \\ Tree-like structures arise extensively in network science - for example, hierarchical structures in biology, hyperbolic routing in the internet, and core-periphery behavior in social networks. As such, this talk focuses on ways to use tree decompositions, key combinatorial objects used in graph minor theory, in Tandem with k-cores and Gromov hyperbolicity to provide structural characterization of and improve inference on complex networks. We also discuss new algorithms using tree decompositions to enable scalable solution of certain graph optimization problems in a high performance computing environment.
Title: Resonances on hyperbolic surfaces
Seminar: Analysis and Differential Geometry
Speaker: Professor David Borthwick of Emory University
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2012-10-23 at 4:00PM
Venue: MSC W301
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Abstract:
The spectral theory of compact hyperbolic surfaces is a classical topic with many interesting results, most of which originate in Atle Selberg's approach to the study of automorphic forms. At first glance, Selberg's techniques do not appear to extend to non-compact surfaces of infinite area. However, in the last 15 years, thanks to breakthroughs in geometric scattering theory and the theory of resonances, we have developed a much more complete picture of the spectral theory in the infinite-area case. Many results of the Selberg theory turn out to have surprisingly close analogs in this setting, despite the radically different character of the spectral theory.\\ \\ In this talk we will try to give an accessible introduction to the spectral theory of hyperbolic surfaces, with our main goal being to introduce recent developments in the infinite-area setting.
Title: Tropical complexes
Seminar: Algebra
Speaker: Dustin Cartwright of Yale University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-23 at 5:00PM
Venue: W306
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Abstract:
A tropical complex is a simplicial complex together with some additional numerical, which come from a semistable degeneration of a variety. Tropical complexes generalize to higher dimensions some of the analogies between curves and graphs which has been studied in tropical geometry. I will introduce tropical complex and talk about some of the connections to classical algebraic geometry.
Title: Combinatorics of splice graphs
Colloquium: N/A
Speaker: Dustin Cartwright of Yale University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-22 at 4:00PM
Venue: W302
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Abstract:
A splice graph is a way of modeling the alternative splicings of a gene, which are different ways of forming related proteins from the same genetic building blocks. The characterization of this alternative splicing is a major area of study in contemporary biology. I will talk about some of the combinatorics relevant to splice graphs. Also, I will talk about some of the implications for inferring splice graphs from data.
Title: Upper bounds for Euclidean minima of abelian fields
Seminar: Algebra
Speaker: Eva Bayer of EPFL
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-17 at 3:00PM
Venue: W306
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Abstract:
The Euclidean division is a basic tool when dealing with the ordinary integers. It does not extend to rings of integers of algebraic number fields in general. It is natural to ask how to measure the 'deviation' from the Euclidean property, and this leads to the notion of Euclidean minimum. The case of totally real number fields is of especial interest, in particular because of a conjectured upper bound (conjecture attributed to Minkowski). The talk will present some recent results, obtained jointly with Piotr Maciak.
Title: Quantum Modular Forms
Seminar: Number Theory
Speaker: Ken Ono of Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-17 at 4:00PM
Venue: W306
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Abstract:
Title: Infinitesimal Deformation Theory and Grothendieck Topologies
Seminar: Algebra
Speaker: Jonathan Wise of CU Boulder
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-10 at 3:00PM
Venue: W306
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Abstract:
To probe the infinitesimal structure of a moduli space of geometric objects, one seeks to understand families of those objects over "fat points". Understanding such families frequently yields a great deal of information about the moduli space. Remarkably, these deformation problems tend to admit cohomological solutions of a common form: obstructions in H 2, deformations in H 1, and automorphisms in H 0. I will offer an explanation for this common form, coming from some exotic Grothendieck topologies. We will see how this point of view works in several examples. No prior knowledge about Grothendieck topologies or deformation theory will be assumed.
Title: KLR conjecture in Sparse Random Graphs
Colloquium: N/A
Speaker: Mathias Schacht of University of Hamburg
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2012-10-05 at 4:00PM
Venue: MSC W201
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Abstract:
The KLR conjecture of Kohayakawa, Luczak, and Rödl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph G(n,p) satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and Rödl. We prove a variant of this conjecture which is sufficient for most applications to random graphs. In particular, our result implies a number of recent probabilistic threshold results. We also discuss several further applications. This joint work with Conlon, Gowers, and Samotij.
Title: Periods of Modular Forms and Identities between Eisenstein Series
Seminar: Algebra
Speaker: Wissam Raji of American University of Beirut
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2012-10-03 at 3:00PM
Venue: W306
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Abstract:
Borisov and Gunnels observed in 2001 that certain linear relations between products of two holomorphic weight 1 Eisenstein series had the same structure as the relations between periods of modular forms. We give a conceptual reason for this and for similar phenomena in all weights. This involves an unconventional way of expanding the Rankin-Selberg convolution of a cusp form with an Eisenstein series. (Joint with Kamal Khuri-Makdisi).
Title: Optimal partitions of measures
Colloquium: N/A
Speaker: Gershon Wolansky of Technion - Israel Institute of Technology
Contact: Professor Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2012-09-27 at 4:00PM
Venue: MSC W301
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Abstract:
Let $X$ be a probability measure space and $\psi_1....\psi_N$ measurable, real valued functions on $X$. Consider all possible partitions of $X$ into $N$ disjoint subdomains $X_i$ on which $\int_{X_i}\psi_i$ are prescribed. I'll address the question of characterizing the set $(m_1,,,m_N) \in \mathbb{R}^N$ for which there exists a partition $X_1, \ldots X_N$ of $X$ satisfying $\int_{X_i}\psi_i= m_i$ and discuss some optimization problems on this set of partitions. The relation of this problem to semi-discrete version of optimal mass transportation is discussed, as well as applications to game theory.