# Seminars archive

 Search keyword Select type Any typeGeneral interest (colloquium, job talks, ...)AlgebraAnalysis and Differential GeometryCombinatoricsComputer ScienceNumber TheoryNumerical Analysis and Scientific ComputingTopologyOther
 Upcoming Seminars Mon04/27/201511:15am Defense: DissertationRamsey Theorem and Ramsey Tur\'an Type Results for HypergraphsVindya Bhat, Emory UniversityContact: Vindya Bhat, vbhat@emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 58.6 kB)Show abstract{This thesis defense includes Ramsey Theorem type results and Ramsey-Tur\'an type results. Both topics involve finding substructures within hypergraphs under certain conditions.} \\ \noindent{\textbf{Ramsey Theorem type results:}} \\ The Induced Ramsey Theorem (1975) states that for $c,r \geq 2$ and every $r$-graph $G$, there exists an $r$-graph $H$ such that every $c$-coloring of the edges of $H$ contains a monochromatic induced copy of $G$. A natural question to ask is what other subgraphs $F$ (besides edges) of $G$ can be partitioned and have the $F$-Ramsey property. We give results on the $F$-Ramsey property of two types of objects: hypergraphs or partial Steiner systems. We find that while the restrictions on the Ramsey properties of hypergraphs are lifted by any linear ordering of the vertex set, the Ramsey properties for partial Steiner systems (with vertex set linearly ordered or unordered) are quite restricted. \\ \noindent{\textbf{Ramsey-Tur\'an type results:}} \\ Tur\'an's Theorem (1941) states that for $1 < k \leq n$, every graph $G$ on $n$ vertices not containing a $K_{k+1}$ has at most $|E(T_{k}(n))|$ edges, where $T_{k}(n)$ is the graph on $n$ vertices obtained by partitioning $n$ vertices into $k$ classes of each size $\lfloor{\frac{n}{k}}\rfloor$ or $\lceil{\frac{n}{k}}\rceil$ and joining two vertices if and only if they are in two different classes. In 1946, Erd\H{o}s and Stone showed that any sufficiently large dense graph will contain $T_k(n)$. Nearly 75 years later, in spite of considerable interest and effort, no generalization of Tur\'an's Theorem or Erd\H{o}s-Stone Theorem for hypergraphs is known. Instead, we consider a variant of this question where we restrict to quasi-random hypegraphs and prove some partial results in this direction. Past Seminars Thu04/23/20154:00pm Colloquium: DepartmentExtremal Problems In CombinatoricsMathias Schacht, University of HamburgContact: Steve Batterson, sb@mathcs.emory.eduVenue: MSC E208Download printable flyer (PDF, 270 kB) Tue04/21/20154:00pm Seminar: AlgebraTropical schemes and the Berkovich analytificationNoah Giansiracusa, UGAContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W304Download printable flyer (PDF, 38.3 kB)Show abstractIn “Equations of tropical varieties,” J.H.Giansiracusa and I introduced a scheme-theoretic framework for tropicalization and tropical geometry. In this talk I’ll discuss recent developments in this program. Specifically, we introduce a canonical embedding of any scheme in an F1-scheme (in essence, a non-finite type toric variety) such that the corresponding tropicalization is the inverse limit of all tropicalizations and its T-points form the space underlying Berkovich’s analytification. This is related to Payne’s topological inverse limit result. Mon04/20/20154:00pm Seminar: CombinatoricsProof of the Middle Levels ConjectureTorsten Muetze, Georgia TechContact: Dwight Duffus, dwight@mathcs.emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 50.1 kB)Show abstractDefine 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. Fri04/17/20154:00pm Seminar: CombinatoricsExtending Partial Geometric Representations of GraphsJan Kratochvil, Charles University, PragueContact: Dwight Duffus, dwight@mathcs.emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 39.5 kB)Show abstractIntersection-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. Mon04/13/20154:00pm Colloquium: DepartmentA relative Szemer\'edi theoremDavid Conlon, The University of OxfordContact: Dwight Duffus, Dwight@mathcs.emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 49.8 kB)Show abstractThe 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 Szemer\'edi 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 Szemer\'edi 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 Szemer\'edi 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. Fri04/10/20154:00pm Seminar: AlgebraKnots and Brauer groups of curvesTed Chinburg, PennContact: David Zureick-Brown, dzb@mathcs.emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 35.5 kB)Show abstractThere 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. Fri04/10/20153:00pm Colloquium: DepartmentMusic Information RetrievalDavide Fossati, Carnegie Mellon University in QatarContact: Ken Mandelberg, km@mathcs.emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 37.3 kB)Show abstractWhat 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. Thu04/09/20154:00pm Seminar: AlgebraAthens-Atlants joint number theory seminarDick Gross and Ted Chinburg, Harvard and PennVenue: At UGADownload printable flyer (PDF, 22.3 kB) Wed04/08/20154:30pm Defense: DissertationAn $\epsilon$ improvement to the asymptotic density of $k$-critical graphsVictor Larsen, Emory UniversityContact: Victor Larsen, vlarsen@emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 67.1 kB)Show abstractGiven 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. Fri04/03/20153:00pm Colloquium: DEPARTMENTCloud Computing: Just a buzzword or already a reality?Gongbing Hong, William and MaryContact: Ken Mandelberg, KM@mathcs.emory.eduVenue: Mathematics and Science Center, Room W303Download printable flyer (PDF, 38.2 kB)Show abstractIn 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.
 « Previous page 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Next page »