All Seminars

Title: Representing polynomials as products of two values of a quadratic form
Seminar: Algebra
Speaker: Alexander Sivatski of St. Petersburg Electrotechnical University
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2008-10-21 at 4:00PM
Venue: MSC W303
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Abstract:
Title: A SQL Database System for Solving Constraints
Seminar: Computer Science
Speaker: Sebastien Siva of Emory University
Contact: James Lu, jlu@mathcs.emory.edu
Date: 2008-10-17 at 3:00PM
Venue: MSC W201
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Abstract:
It has long been recognized that practical contexts for constraint satisfaction problems (CSP) often involve large relational databases (RDB). Early attempts to marry constraint solving systems and relational database systems include deductive and constraint databases that reuse important ideas from logic programming. These techniques required knowledge outside the scope of traditional database users. The recent proposal by Cadoli and Mancini, CONSQL, shows that a simple extension to SQL provides a viable basis for modeling CSP. This opens the possibility for transparently integrating CSP with databases using SQL the most widely known and popular database language. Such an extension brings the power of constraint problem solving to SQL knowledgeable users. Towards that end, the current research describes a case study in the engineering details of designing and implementing such a prototype.
Title: Pretentiousness in Analytic Number Theory
Colloquium: N/A
Speaker: Andrew Granville of Universite de Montreal
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2008-10-09 at 4:00PM
Venue: MSC W201
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Abstract:
Inspired by the "rough classification" ideas from additive combinatorics, Soundararajan and I have recently introduced the notion of pretentiousness into analytic number theory. Besides giving a more accessible description of the ideas behind the proofs of several well- known difficult results of analytic number theory, it has allowed us to strengthen several results, like the Polya-Vinogradov inequality, the prime number theorem, etc. In this talk we will introduce these ideas and gave some flavour of these developments.
Title: Models of Scientific Communication from Large-Scale Usage Data
Seminar: Computer Science
Speaker: Dr. Johan Bollen of Los Alamos National Lab
Contact: Joan A. Smith, jsmit52@emory.edu
Date: 2008-10-08 at 3:00PM
Venue: MSC W201
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Abstract:
Scientific communication can be modeled on the basis of citation networks in which the flow of ideas is expressed by citations that point from one scientific publication to another. A number of graph-theoretical methods can be brought to bear on such citation networks to determine the status of particular publications and infer general properties of the scientific communication process. However, as scientific activity increasingly moves online, it becomes possible to study scientific relationships and processes from online usage patterns. In this colloquium I will present two applications of the analysis of large-scale usage data logs now commonly collected by scholarly web portals, namely modeling and mapping of the structure of scientific activity, and determining the components of scientific impact.
Title: From the Circle method to the Circular Law
Colloquium: Number Theory
Speaker: Van Vu of Rutgers University
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2008-10-02 at 4:00PM
Venue: MSC W201
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Abstract:
A starting point of the theory of random matrices is Wigner's semi-circle law obtained in the 1950s, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random hermitian matrix with iid (upper diagonal) entries follows the semi-circle law. The non-hermitian case is the famous Circular Law Conjecture, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random matrix with iid entries is uniform in the unit circle. Despite several important partial results (Ginibre-Mehta, Girko, Bai, Edelman, Gotze-Tykhomirov, Pan-Zhu etc) the conjecture remained open for more than 50 years. This summer, T. Tao and I confirmed the conjecture in full generality. I am going to give an overview of this proof, which relies on rather surprising connections between various fields: combinatorics, probability, number theory and theoretical computer science. In particular, tools from additive combinatorics and Hardy-Littlewood circle method from analytic number theory play crucial roles.
Title: The Algebraists and the Analysts Should be Friends
Graduate Student Seminar: Algebra
Speaker: Victoria Powers of Emory University
Contact: Victoria Powers, vicki@mathcs.emory.edu
Date: 2008-10-01 at 4:00PM
Venue: MSC W303
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Abstract:
In the last 15 years or so connections between questions in real algebraic geometry and functional analysis were discovered and exploited. By working together, algebraists and analysts were able to make progress on important problems in both areas. In this talk we discuss connections between a topic from algebra -- the representation of positive polynomials -- and two problems from analysis -- the classical moment problem and the Bessis-Moussa-Villani conjecture from quantum physics. The talk will be accessible to anyone who knows what polynomials, matrices, and integration are.
Title: On the inertia set of a graph
Seminar: Combinatorics
Speaker: Hein van der Holst of Eindhoven University of Technology
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2008-09-29 at 4:00PM
Venue: MSC W301
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Abstract:
Title: Graphs on Affine or Linear Points
Seminar: Combinatorics
Speaker: Hanno Lefmann of
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2008-09-26 at 4:00PM
Venue: W306
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Abstract:
Motivated by a question of Hajnal on independent finite sum-sets in triangle-free graphs with vertex sets being the set of positive integers we consider the following problem: Given are fixed integers k,l > 0 and a finite field F. Given is any graph G = (V, E) with vertex set being the set of all affine or linear points of an n-dimensional affine or linear vector space over F, where G does not contain a complete graph on l vertices. Is it possible to find a k-dimensional subspace, such that the set of all its affine or linear points forms an independent set in G? Having answered this questions, we give some applications to the corresponding problem for the set of solutions of partition regular systems of linear equations over Abelian groups. This is some joint work with D. Gunderson.
Title: Mass formulas for mod p Galois representations
Colloquium: N/A
Speaker: Chandrashekhar Khare of UCLA
Contact: Parimala Raman, parimala@mathcs.emory.edu
Date: 2008-09-25 at 4:00PM
Venue: MSC W201
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Abstract:
The recent proof of Serre's conjecture allows one to prove the finiteness of certain types of Galois representations (2-dimensional mod $p$, odd, semisimple respresentations of the absolute Galois group of the rationals with bounded prime to $p$ Artin conductor). One may ask for quantitative refinements of this. It seems hard to get a grip on this, although one can formulate a natural expectation. This is in the spirit of the theorem of Hermite-Minskowski which asserts that there are only finitely many extensions of the rationals of bounded discriminant. One can ask for quantitative versions of this: a precise count is again unknown.
Title: A Reflector Design Problem for a Collimated Source
Seminar: N/A
Speaker: Tobias Graf of Emory University
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2008-09-23 at 5:00PM
Venue: MSC W301
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Abstract:
We will discuss the following reflector problem. Given a parallel light beam emitted from a bounded domain in a hyperplane of n+1 dimensional Euclidean space and a receiver surface as well as prescribed in advance intensities for the source domain and the receiver, can we design a reflector surface that redistributes the emitted light accordingly?