All Seminars

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Title: On the Number of B_h Sets of a Given Size
Seminar: Combinatorics
Speaker: Domingos Dellamonica of Sao Paulo
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2014-10-27 at 4:00PM
Venue: W303
Abstract:
For an integer h bigger or equal to 2, a \$B_h\$ set is a set of integers with the property that every collection containing h of its elements yield a unique sum (and repetitions are allowed). For \$h = 2\$, such sets are also called Sidon sets. In this talk we will describe our recent results on estimating \$F(n, s, h)\$, which we define as the number of \$B_h\$ sets of cardinality s containing integers from \$[n] = {1, 2, ..., n}\$. It is not hard to see that for \$s > n^(1/h)\$, we have \$F(n, s, h) = 0\$. Indeed, in this case there are more h-sums than possible outcomes for the sums. On the other hand, there are constructions of B-h sets having cardinality \$c.n^(1/h)\$, (with c depending on h only) hence we shall estimate the behavior of \$F(n, s, h)\$ for s up to \$O( n^(1/h))\$. Our counting shows the existence of a surprising threshold function \$T(n)\$: for values of \$s << T(n)\$, the B-h sets are abundant while for \$s >> T(n)\$ the B-h sets become very rare. More precisely, we show that \$T(n) ~ n^{(1 + o(1))/(2h - 1)}\$ and establish fairly precise estimates of \$F(n, s, h)\$ for the entire range of s.
Title: Intermittence and Entropy-Equivalent Measures in Brain Function and Behavior
Colloquium: Ergodic Theory and Dynamical Systems
Speaker: Arnold Mandell of UCSD School of Medicine
Contact: Vaidy Sunderam, vss@emory.edu
Date: 2014-10-23 at 4:30PM
Venue: W201
Abstract:
TBA
Title: Tropical Independence and Algebraic Curves
Seminar: Algebra
Speaker: David Jensen of University of Kentucky
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-10-21 at 4:00PM
Venue: W306
Abstract:
Many questions about an algebraic curve concern the ranks of linear maps between linear series on the curve. Recent years have witnessed the development of a new, combinatorial approach to studying such questions via tropical geometry. We will discuss the basics of this theory, and how it can be used to gain new insight into the geometry of general curves. If time permits, we will discuss joint work with Sam Payne in which we use these techniques to provide a new proof of the Gieseker-Petri Theorem.
Title: Recent Advances and Open Problems in the Degree/Diameter Problem
Seminar: Combinatorics
Speaker: Mirka Miller of Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic; and School of Mathematical and Physical Sciences, University of Newcastle, Australia
Contact: Vojtech Rodl, rodl@mathcs.emory.edu
Date: 2014-10-20 at 4:00PM
Venue: W302
Abstract:
The degree/diameter problem is to find the largest possible graphs in terms of the number of vertices, given the maximum degree and diameter. The directed version is similar except that instead of the maximum degree constraint we are given the maximum out-degree. For both the undirected and directed versions of the problem there are general upper bounds on the number of vertices, called the Moore bounds. On the other hand, the best current lower bounds are obtained from constructions of ever larger graphs (given maximum degree and diameter).\\ \\ In this talk we will give an overview of the undirected, directed and mixed versions (allowing both undirected edges and directed arcs in the graph) of the problem and the most recent advances.\\ \\ The talk concludes with several open problems.
Title: Recent developments in rationality of cubic fourfolds
Seminar: Algebra
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-10-07 at 4:00PM
Venue: W306
Abstract:
Which cubic hypersurfaces in \$P^5\$ are rational? Certainly some, but conjecturally not all. The problem has classical roots, but it has seemed tractable since the 70s, when Clemens and Griffiths gave a beautiful solution to the analogous problem for cubic threefolds using Hodge theory. Hassett worked on adapting their argument to cubic fourfolds in the late 90s; Kuznetsov tried again around 2008, using derived categories in place of Hodge theory; Galkin and Shinder have gotten further this year using the Grothendieck ring of varieties. While none of these attempts has succeeded at solving the problem, each has brought new insights. My own contribution has been to explain how these three would-be rationality criteria are interrelated. In the course of the talk I'll pose an elementary number theory puzzle that might get a student a paper.
Title: Some Old and New Results on an Elimination Game
Seminar: Numerical Analysis and Scientific Computing
Speaker: Esmond G. Ng of Lawrence Berkeley National Laboratory
Contact: James Nagy, nagy@mathcs.emory.edu
Date: 2014-10-06 at 12:00AM
Venue: W301
Abstract:
Sparse matrix problems arise at the heart of many large-scale scientific and engineering applications. State-of-the-art algorithms for solving these problems involve not only numerical techniques, but may also require knowledge of data structures, graph theory, algorithm design, complexity analysis, and computer architectures. This is particularly true for factorization-based algorithms, such as those for solving sparse systems of linear equations, in which the nonzero entries of a matrix are eliminated according to certain prescribed rules. However, the order in which the nonzero entries are eliminated can have a dramatic effect on the overall performance of the solution process. This is referred to as the ordering problem, which is often posed as an elimination game on a graph. In this talk, an overview of the elimination game will be presented. In particular, previously known results and some recently work will be described.
Title: Wall crossing in moduli problems and semi-orthogonal decompositions
Seminar: Algebra
Speaker: Matt Ballard of USC
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-30 at 4:00PM
Venue: W306
Abstract:
We discuss how the derived category of a smooth algebraic stack of finite type changes as one removes certain types of closed substacks. As an application, we show how wall-crossing in moduli of stable sheaves and Bridgeland stable objects yields semi-orthogonal decompositions of relating their derived categories.
Title: Modeling Temporal Dynamics of User Generated Content
Defense: Dissertation
Speaker: Yu Wang of Emory Unviersity
Contact: Yu Wang, yu.wang@emory.edu
Date: 2014-09-29 at 10:15AM
Venue: PAIS 561
Abstract:
The evolving nature of user generated content (UGC) lays the key characteristics of Web 2.0. The evolution process in UGC offers valuable evidence to explain the content dynamics in the past and predict trends in the future. In this thesis, we design models to analyze content evolution patterns of UGC in three granularities: words, topics and sentiment. More specifically, this thesis investigates content evolution in the following aspects: (1) on word-level dyanmics: analyzing word frequency change in collaboratively generated content and using historical word frequencies to better weigh the words in ranking functions; (2) on topic-level dynamics: learning temporal transition patterns of topics in microblog streams and predict future topics according to historical posts; (3) on sentiment-level dynamics: estimating and understanding different sentiment change patterns of popular political topics across different user groups. We show that the developed models enable new applications in UGC, such as improving content-based ranking, anticipating future popular topics and visualizing and interpreting sentiment dynamics.
Title: Computing free surface flows of viscoplastic fluids
Seminar: Numerical Analysis and Scientific Computing
Speaker: Maxim Olshanskii of University of Houston
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2014-09-26 at 12:00AM
Venue: W301
Abstract:
Free surfaces flows of yield stress fluids are common in nature and in engineering applications. Viscoplastic models, such as the Herschel-Bulkley model, are often used to describe the complex rheology of such fluids and predict fluids dynamics with reasonable accuracy. The numerical modeling and analysis of the phenomena is a challenging task due to the non-trivial coupling of complex fluid dynamics and free surface evolution.\\ \\ In this talk we discuss an approach for numerical simulation of free surface flows of viscoplastic incompressible fluids. The approach features adaptive Cartesian grids and a splitting technique for numerical time integration. We shall point to several open problems in the mathematical and numerical analysis of equations governing free surface flows of viscoplastic fluids.
Title: An algebraic approach to enumerating field extensions
Seminar: Algebra
Speaker: Frank Thorne of University of South Carolina
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-09-22 at 4:00PM
Venue: W302
Abstract:
Building on previous work of Cohen and several of his collaborators, I will discuss the use Kummer theory and class field theory to enumerate field extensions of low degree. We obtain an explicit Dirichlet series representation, in the form of a finite sum of Euler products, for the set of field extensions with Galois group \$S_3, A_4, S_4\$, or \$D_l\$ (l an odd prime) with fixed resolvent. This has a variety of interesting consquences, including results on the Shintani zeta function as well as an extension of the Scholz reflection principle, which I will describe. Most of this is joint work with Henri Cohen, and one part is also joint with Simon Rubinstein-Salzedo.