All Seminars
| Title: Set families with a forbidden induced subposet |
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| Seminar: Combinatorics |
| Speaker: Tao Jiang of Miami university |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-11-15 at 4:00PM |
| Venue: W306 |
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| Abstract: Sperner’s theorem asserts that the largest antichain in a Boolean lattice Bn has size n n/2 . A few years ago, Bukh obtained a substantial asymptotic extension of Sperner’s theorem by proving that for any poset H whose Hasse diagram is a tree of height k, the largest size of a n subfamily of Bn not containing H is asymptotic to (k − 1) n/2 . We establish an induced version of Bukh’s result, namely that the largest size of a subfamily of Bn not containing H as an induced n subposet, is also asymptotic to (k −1) n/2 . This is an old result (2012). I will focus on presenting the ideas of the proof. This is joint work with Ed Boenhlein. |
| Title: The minimum number of nonnegative edges in hypergraphs |
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| Seminar: Combinatorics |
| Speaker: Hao Huang of Institute for Advanced Study and DIMACS |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-11-14 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: An r-unform n-vertex hypergraph H is said to have the Manickam-Miklos-Singhi (MMS) property if for every assignment of weights to its vertices with nonnegative sum, the number of edges whose total weight is nonnegative is at least the minimum degree of H. In this talk I will show that for $n>10r^3$, every r-uniform n-vertex hypergraph with equal codegrees has the MMS property, and the bound on n is essentially tight up to a constant factor. An immediate corollary of this result is the vector space Manickam-Miklos-Singhi conjecture which states that for $n \geq 4k$ and any weighting on the 1-dimensional subspaces of $F_q^n$ with nonnegative sum, the number of nonnegative k-dimensional subspaces is at least ${n-1 \brack k-1}_q$. I will also discuss two additional generalizations, which can be regarded as analogues of the Erdos-Ko-Rado theorem on k-intersecting families. This is joint work with Benny Sudakov. |
| Title: Unramified Brauer classes on cyclic covers of the projective plane |
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| Seminar: Algebra |
| Speaker: Andrew Obus of University of Virginia |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-11-12 at 4:00PM |
| Venue: W306 |
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| Abstract: Brauer groups on schemes have many applications, for example, giving obstructions to existence of rational points. After reviewing different ways of presenting Brauer groups of fields and schemes, we will give a method to exhibit p-torsion Brauer classes on a p-cyclic cover of the projective plane, branched over a smooth curve of degree divisible by d. This extends earlier work of van Geemen for degree 2 K3 surfaces. In the case p=2, our method gives all the 2-torsion classes, and is equivalent to another (more geometric) method of Catanese. This is joint work with Colin Ingalls, Ekin Ozman, and Bianca Viray. |
| Title: Characterization of Quasiconformal Mapping and Extremal Length Decomposition and Its Application |
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| Defense: Dissertation |
| Speaker: Wenfei Zou of Emory University |
| Contact: Wenfei Zou, wzou3@emory.edu |
| Date: 2013-11-12 at 4:00PM |
| Venue: W302 |
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| Abstract: My defense includes two parts. The first part is about the characterization of Quasiconformal mapping. It is known that Conformal mapping preserves the measure of angle. The Quasiconformal mapping is a natural generalization of the conformal mapping. Some measure of angle named topological angle could be defined to characterize Quasiconformal mappings. I will discuss these results in higher dimensional Euclidean space.\\ \\ The second part is about extremal length decomposition and its application. Quasiextremal distance domains (QED) are a class of domains introduced by Gehring and Martio in connection with Quasiconformal mapping theories. I will discuss a decomposition theorem about the extremal length of a curve family within the finitely connected QED domain. Moreover, I will discuss its application, a result of sharp upper bound for QED constant of finitely connected domain on the complex plane. |
| Title: SOUTHEAST GEOMETRY SEMINAR (SGS XXIII) |
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| Type: N/A |
| Speaker: . of . |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2013-11-10 at 8:00AM |
| Venue: MSC W201 |
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| Abstract: |
| Title: Thresholds for Random Geometric k-SAT |
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| Seminar: Combinatorics |
| Speaker: Will Perkins of Georgia Tech |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-11-08 at 4:00PM |
| Venue: W306 |
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| Abstract: Random $k-SAT$ is a distribution over boolean formulas studied widely in combinatorics, statistical physics, and theoretical computer science for its intriguing behavior at its phase transition. I will present results on the satisfiability threshold in a geometric model of random $k-SAT$: labeled boolean literals are placed uniformly at random in a d-dimensional cube, and for each set of k contained in a ball of radius r, a k-clause is added to the random formula. For all $k$ we show that the satisfiability threshold is sharp, and for $k=2$ we find the location of the threshold as well. I will also discuss connections between this model and the random geometric graph. |
| Title: Regularization by Krylov Subspace Methods |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Silvia Gazzola of University of Padova |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2013-11-01 at 12:00PM |
| Venue: W302 |
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| Abstract: Iterative methods have always played a central role in the regularization of large-scale linear discrete ill-posed problems. These kind of problems arise in a variety of scientific and engineering applications: we are particularly interested in the image deblurring and denoising issues. Historically, the first Krylov subspace methods to be extensively used with regularization purposes were the CGLS and the LSQR methods. In the last three decades, many other Krylov subspace methods have been analyzed and employed to solve linear discrete ill-posed problems and, very recently, some modifications of the usually involved Krylov subspaces have been proposed: we cite the smoothing preconditioning, the augmentation, and the range-restricted techniques. In addition to a purely iterative approach to regularization, some hybrid methods have also been derived: hybrid methods merge an iterative and a variational (Tikhonov-like) approach to regularization. The purpose of this talk is to survey some classical iterative regularization methods and to present some original ones, comparing their performance on some meaningful test problems. Particular emphasis will be posed on the hybrid methods and on the strategies to be employed to set the regularization parameters. |
| Title: Some problems in Anti-Ramsey Theory |
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| Seminar: Combinatorics |
| Speaker: Sogol Jahanbekam of The University of Colorado, Denver |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-11-01 at 4:00PM |
| Venue: W306 |
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| Abstract: In this talk we introduce some new lower bounds for the matching number of bipartite graphs and general graphs. We apply these results to Anti-Ramsey numbers of some families of graphs including disjoint spanning disjoint spanning cycles, disjoint perfect matchings, and graphs with bounded diameter. |
| Title: Progressions with a pseudorandom step |
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| Seminar: Combinatorics |
| Speaker: Elad Aigner-Horev of Hamburg University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2013-10-28 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: An open problem of interest in combinatorial number theory is that of providing a non-ergodic proof to the so called polynomial Szemerédi theorem. So far, the landmark result in this venue is that of Green who considered the emergence of 3-term arithmetic progressions whose gap is a sum of two squares (not both zero) in dense sets of integers. In view of this we consider the following problem. Given two dense subsets A and S of a finite abelian group G, what is the weakest "pseudorandomness assumption" which, once put on S, implies that A contains a 3-term arithmetic progression whose gap is in S? We answer this question for $G = Z_n$ and $G = F_p^n$. To quantify pseudorandomness we use Gowers norms. |
| Title: Numerical Tilting and Derived Equivalence |
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| Seminar: Algebra |
| Speaker: Morgan Brown of University of Michigan |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2013-10-23 at 4:00PM |
| Venue: W306 |
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| Abstract: The derived category of an algebraic variety is a categorical invariant which is coarser than the category of coherent sheaves. There are many interesting examples in geometry and representation theory of varieties or algebras with different categories of sheaves or modules but equivalent derived categories. For example, if $G$ is a finite subgroup of $SL(3, \mathbb{C})$, Bridgeland, King, and Reid showed there is a derived equivalence between $G$ equivariant sheaves on $\mathbb{C}^3$ and sheaves on a minimal resolution of the quotient. I will show how in many cases one can understand these equivalences by factoring them into simple equivalences called tilts. |