All Seminars

Title: The O-Z Conjecture and Ono's Fundamental Problem Number 1
Job Talk: N/A
Speaker: Zachary Kent of The University of Hawaii at Manoa
Contact: Susan Guppy, sguppy@emory.edu
Date: 2010-05-18 at 1:00PM
Venue: MSC W303
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Abstract:
The study of mock modular forms and mock theta functions is one of the hottest areas in number theory with important works by Bringmann, Ono, Zagier, and Zwegers, among many others. The theory, which is still in its infancy, has many applications: additive number theory, elliptic curves, mathematical physics, representation theory, etc. Despite this high level of activity, many fundamental problems remain open. The first of Ono's "Fundamental Problems" is: Find a direct method for relating the coefficients of Zagier shadows and mock modular forms. Here I will announce a solution to this problem, and along the way will announce a proof of the O-Z Conjecture.
Title: Combinatorial approach to an interpolation method and scaling limits for sparse random graphs
Seminar: Combinatorics
Speaker: Prasad Tetali of Georgia Institute of Techonology
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2010-05-06 at 4:00PM
Venue: MSC W301
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Abstract:
We establish the existence of free energy limits for several sparse random hypergraph models corresponding to certain combinatorial models on Erdos-Renyi graph G(N,c/N) and random r-regular graph G(N,r). For a variety of models, including independent sets, MAX-CUT, Coloring and K-SAT, we prove that the free energy both at a positive and zero temperature, appropriately rescaled, converges to a limit as the size of the underlying graph diverges to infinity. In the zero temperature case, this is interpreted as the existence of the scaling limit for the corresponding combinatorial optimization problem. For example, as a special case we prove that the size of a largest independent set in these graphs, normalized by the number of nodes converges to a limit w.h.p., thus resolving an open problem mentioned by several experts: Wormald '99, Aldous-Steele 2003, Bollobas-Riordan 2008, as well as Janson-Thomason 2008. Our approach is based on extending and simplifying the Guerra-Toninelli interpolation method, as well as extending the work of Franz-Leone and Montanari. We provide a simpler combinatorial approach and work with the zero temperature case (optimization) directly both in the case of Erdos-Renyi graph G(N,c/N) and random regular graph G(N,r), while the previous authors handled the zero temperature case (for other models) by taking limits of positive temperature models. In addition we establish the large deviations principle for the satisfiability property for constraint satisfaction problems such as Coloring, K-SAT and NAE-K-SAT. This is joint work with D. Gamarnik (MIT) and M. Bayati (Stanford).
Title: Georges de Rham's work and life before 1945
Colloquium: N/A
Speaker: Manuel Ojanguren of Swiss Federal Institute of Technology, Lausanne
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2010-04-30 at 3:00PM
Venue: MSC W303
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Abstract:
The talk will deal with the following aspects of de Rham's life and mathematics: \begin{enumerate} \item ``How a duel in Strasbourg changed mathematics in Lausanne" \item Studies in Lausanne \item Thesis in Paris, de Rham's theorems in 1930 \item The idea of currents \item Rotations and Reidemeister torsion \item The war years \end{enumerate}
Title: Solar Concentration at the Interface between Optics and Thermodynamics
Colloquium: Joint MathCS and Physics
Speaker: Professor Roland Winston of University of California, Merced
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2010-04-27 at 3:00PM
Venue: MSC Center, Planetarium
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Abstract:
I show how the interface between optics and thermodynamics organizes and informs the design of solar concentrators. This extends from ultra-high concentrating systems of ~ 100,000 suns to stationary systems of ~ 4 X concentrations. Luminescent systems which rely on a Stokes shift to concentrate even diffuse sunlight are discussed
Title: Mathematical Modeling in Biology and a Problem in Phylogenetics
Lecture Series: Evans/Hall
Speaker: Elizabeth Housworth of Indiana University
Contact: Steve Batterson, sb@mathcs.emory.edu
Date: 2010-04-27 at 4:00PM
Venue: Mathematics and Science Center E208
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Abstract:
The study of planetary motion leading to Newton's theory of gravity is the epitome of the success of mathematics in the sciences. How does the role of mathematics in biology compare to the role of mathematics in physics?\\ \\ The theory of evolution is arguably of the same caliber as the theory of planetary motion. What is the role of mathematics in this theory? We will discuss an open mathematical problem that should be accessible to most members of the audience.
Title: Enumerating Tree Orbits - an Application to Viral Caspid Assembly
Seminar: Combinatorics
Speaker: Andrew Vince of University of Florida
Contact: Andrzej Rucinski, andrzej@mathcs.emory.edu
Date: 2010-04-26 at 4:00PM
Venue: W302
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Abstract:
Combinatorial methods (permutations, Mobius inversion, generating functions) are used to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the shell is fairly well understood in terms of its constituent subunits, the assembly process is not. Our approach involves the enumeration of certain labeled trees called assembly trees.
Title: Towards Accessible IR: Helping children search the Web
Seminar: Computer Science
Speaker: Pavel Serdyukov of Delft University of Technology
Contact: Eugene Agichtein, eugene@mathcs.emory.edu
Date: 2010-04-23 at 3:00PM
Venue: MSC W301
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Abstract:
Developing children's abilities to find and understand information is a key to their development as young adults. The Internet offers children exciting new ways to meet people, learn about different cultures and develop their creative potential. However, children's ability to use the Internet is severely hampered by the lack of appropriate search tools. Most Information Retrieval (IR) systems are designed for adults: they return information in a form that is unsuitable for children and they do not provide enough assistance to make the search for appropriate content rewarding and fun. The talk will present the state-of-the-art and recent research on children’s search behavior and describe problems and challenges that lie ahead, with regard to adapting current IR systems for children. It will also give an overview of the current studies being conducted in the scope of the EU-funded research project “PuppyIR”: on finding web-content appropriate for children, on analyzing query logs to understand children’s information needs and on providing query assistance functionality. \\ Pavel Serdyukov is a researcher at the Multimedia Information Retrieval Lab, Delft University of Technology, the Netherlands. He received his PhD in Computer Science from Twente University in 2009. His research interests include expert/entity search in enterprises, accessible search, geographical multimedia search and search in social media. He is currently leading a research effort aimed at studying how to modify traditional views on relevance ranking to satisfy children's information needs on the Web. He is also a co-organizer of the Entity track at TREC 2010 and SIGIR 2010 Workshop on Accessible Search Systems. More information and publication record can be found at http://dmirlab.tudelft.nl/users/pavel-serdyukov.
Title: Levels and sublevels of rings
Colloquium: N/A
Speaker: Detlev Hoffmann of University of Nottingham
Contact: Skip Garibaldi, skip@mathcs.emory.edu
Date: 2010-04-23 at 4:00PM
Venue: MSC W303
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Abstract:
The level (resp.\ sublevel) of a ring is the smallest number $n$ such that $-1$ (resp.\ $0$) can be written as a sum of $n$ (resp.\ $n+1$) nonzero squares in the ring if such an $n$ exists, otherwise it is defined to be infinity. A famous result by Pfister from the 1960s states that the level of a field, if finite, is always a $2$-power, and each $2$-power can in fact be realized as the level of a suitable field. This answered a question posed by van der Waerden in the 1930s. In the case of fields, level and sublevel coincide, but this need not be true for other types of rings. We will give a survey of various known results about levels and sublevels of rings and mention some open problems.
Title: Edge Partitions of Graphs by Trees
Seminar: Combinatorics
Speaker: Grant Zhang of University of Alabama Huntsville
Contact: Ron Gould, rg@mathcs.emory.edu
Date: 2010-04-23 at 4:00PM
Venue: W302
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Abstract:
Let tp(G) denote the minimum number of subsets into which the edge set of a graph G can be partitioned so that each subset induces a tree. For a connected graph G of order n, it is known that tp(G) <= (n+1)/2. The clique number of a graph G is the maximum t such that G contains a complete subgraph of order t. In this talk we consider the problem of determining tp(G) for a connected graph G of order n and clique number t.
Title: Simulating a Pipelined CPU
Undergraduate Honors Thesis Defense: N/A
Speaker: Aaron Bush of Emory University
Contact: Shun Yan Cheung,
Date: 2010-04-21 at 3:00PM
Venue: MSC W303
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Abstract:
The CS355 course in Computer Architecture teaches both entry-level and advanced pipelined CPU technology. For most of the computer components discussed in lectures, the course uses a circuit simulation program that allows students to gain an interactive experience with basic computer technology. However, the course has always lacked a simulation program for the pipelined CPU. Due to the complex nature of pipelining and the success with using the simulation software for other circuits, we have developed two versions of the pipelined CPU using the simulation program. By offering students a hands-on understanding of instruction pipelining, our simulated processors will greatly enhance the course.