All Seminars

Title: Extremal Problems In Combinatorics
Evans Hall Awards Ceremony and Lecture: Combinatorics
Speaker: Mathias Schacht of University of Hamburg
Contact: Steve Batterson, sb@mathcs.emory.edu
Date: 2015-04-23 at 4:00PM
Venue: MSC E208
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Abstract:
Title: Tropical schemes and the Berkovich analytification
Seminar: Algebra
Speaker: Noah Giansiracusa of UGA
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-04-21 at 4:00PM
Venue: W304
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Abstract:
See downloadable flyer.
Title: Proof of the Middle Levels Conjecture
Seminar: Combinatorics
Speaker: Torsten Muetze of Georgia Tech
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2015-04-20 at 4:00PM
Venue: W302
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Abstract:
Define the middle layer graph as the graph whose vertex set consists of all bitstrings of length $2n+1$ that have exactly $n$ or $n+1$ entries equal to 1, with an edge between any two vertices for which the corresponding bitstrings differ in exactly one bit. The middle levels conjecture asserts that this graph has a Hamilton cycle for every $ n \ge 1$. This conjecture originated probably with Havel, Buck and Wiedemann, but has also been (mis)attributed to Dejter, Erdos, Trotter and various others, and despite considerable efforts it remained open during the last 30 years. In this talk I present a proof of the middle levels conjecture. In fact, I show that the middle layer graph has $2^{2^{\Omega(n)}}$ different Hamilton cycles, which is best possible.
Title: Extending Partial Geometric Representations of Graphs
Seminar: Combinatorics
Speaker: Jan Kratochvil of Charles University, Prague
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2015-04-17 at 4:00PM
Venue: MSC W303
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Abstract:
Intersection-defined classes of graphs are intensively studied for their applications and interesting properties. Many of them allow polynomial-time algorithms for otherwise computationally hard problems such as independent set, clique or coloring problems. And many of them can be recognized in polynomial time. In fact the polynomial-time algorithms often need a representation to be given or constructed as the initial step. The rather natural question of extending a partial representation has been studied only recently. It falls into the more general paradigm of extending a partial solution of a problem. Sometimes a global solution can be reached by incremental steps from a partial one in polynomial-time, but in many cases an otherwise easy problem may become hard. Examples of such behavior can be found for instance in graph colorings (e.g., deciding if a partial edge-coloring of a cubic bipartite graph can be extended to a full 3-coloring of it is NP-complete, though it is well known that every cubic bipartite graph is 3-edge-colorable and such a coloring can be found in polynomial time). In this talk we survey the known results about the computational complexity of extending partial geometric representations of graphs.
Title: A relative Szemeredi theorem
Colloquium: Department
Speaker: David Conlon of The University of Oxford
Contact: Dwight Duffus, Dwight@mathcs.emory.edu
Date: 2015-04-13 at 4:00PM
Venue: MSC W303
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Abstract:
The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the primes. The proof has two parts. The first part is a relative Szemeredi theorem which says that any subset of a pseudorandom set of integers of positive relative density contains long arithmetic progressions, where a set is pseudorandom if it satisfies two conditions, the linear forms condition and the correlation condition. The second part is in finding a pseudorandom set in which the primes have positive relative density. In this talk, we will discuss a simple proof for a strengthening of the relative Szemeredi theorem, showing that a weak linear forms condition is sufficient for the theorem to hold. By removing the correlation condition, our strengthened version can be applied to give a relative Szemeredi theorem for $k$-term arithmetic progressions in pseudorandom subsets of $\mathbb{Z}_N$ of density $N^{-c_k}$. It also simplifies the deduction of the Green-Tao theorem by removing the need for certain number theoretic estimates in the second part of their proof. Joint work with Jacob Fox and Yufei Zhao.
Title: Music Information Retrieval
Colloquium: Department
Speaker: Davide Fossati of Carnegie Mellon University in Qatar
Contact: Ken Mandelberg, km@mathcs.emory.edu
Date: 2015-04-10 at 3:00PM
Venue: MSC W303
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Abstract:
What does it take to build a search engine for sound and music? How can computers "listen" to music and understand what you are playing? Currently, the most successful and widespread technologies for organizing and searching for information are based on text. Instead, the emerging field of Music Information Retrieval focuses on technology that operates directly on audio signals without relying on textual annotation. In this presentation I will give a brief overview of Music Information Retrieval: foundational ideas, methodology, and applications. We will see how sound can be represented, segmented, converted into a set of features, and classified.
Title: Knots and Brauer groups of curves
Seminar: Algebra
Speaker: Ted Chinburg of Penn
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-04-10 at 4:00PM
Venue: W302
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Abstract:
There has been a great deal of research over the last 20 years on invariants of knots on one hand and on Brauer groups of curves on the other. The goal of this talk is to link these two subjects. This is joint work with Alan Reid and Matt Stover.
Title: Athens-Atlants joint number theory seminar
Seminar: Algebra
Speaker: Dick Gross and Ted Chinburg of Harvard and Penn
Contact: TBA
Date: 2015-04-09 at 4:00PM
Venue: At UGA
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Abstract:
Title: An epsilon improvement to the asymptotic density of k-critical graphs
Defense: Dissertation
Speaker: Victor Larsen of Emory University
Contact: Victor Larsen, vlarsen@emory.edu
Date: 2015-04-08 at 4:30PM
Venue: MSC W303
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Abstract:
Given a graph $G$ the \emph{chromatic number}, denoted $\chi(G)$, is smallest number of colors necessary to color $V(G)$ such that no adjacent vertices receive the same color. A graph $G$ is $k$-critical if $\chi(G)=k$ but every proper subgraph has chromatic number less than $k$. As $k$-critical graphs can be viewed as minimal examples of graphs with chromatic number $k$, it is natural to ask how small such a graph can be. Let $f_k(n)$ denote the minimum number of edges in a $k$-critical graph on $n$ vertices. The Ore construction, used to build larger $k$-critical graphs, implies that \[f_k(n+k-1)\leq f_k(n)+(k-1)\left(\frac{k}{2}-\frac{1}{k-1}\right).\] A recent paper by Kostochka and Yancey provides a lower bound for $f_k(n)$ which implies that the asymptotic density $\phi_k:=\lim_{n\to\infty}f_k(n)/n = \frac{k}{2}-\frac{1}{k-1}$. In this work, we use the method of discharging to prove a lower bound on the number of edges which includes structural information about the graph. This lower bound shows that the asymptotic density of a $k$-critical graph can be increased by $\epsilon>0$ by restricting to $(K_{k-2})$-free $k$-critical graphs.\\ \\ We also prove that the graphs constructible from the Ore construction and $K_k$, called \emph{$k$-Ore} graphs, are precisely the graphs which attain Kostochka and Yancey's bound. Moreover, we also provide results regarding subgraphs which must exist in $k$-Ore graphs. For the discharging argument, carried out in two stages, we also prove results regarding the density of nearly-bipartite subgraphs in $k$-critical graphs.
Title: Cloud Computing: Just a buzzword or already a reality?
Colloquium: DEPARTMENT
Speaker: Gongbing Hong of William and Mary
Contact: Ken Mandelberg, KM@mathcs.emory.edu
Date: 2015-04-03 at 3:00PM
Venue: MSC W303
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Abstract:
In this talk, we will give a brief introduction to Cloud Computing. First, we will provide a few definitions for cloud computing and discuss the big ideas of this new computing paradigm. Then we will talk about the services provided by cloud computing as seen today along with examples as offered by big players in the industry. We will also talk about how clouds are being deployed and the future of the clouds. At the end, we will discuss the impacts, issues, and the challenges of cloud computing.