All Seminars
| Title: A Method for Landscape Exploration in Global Optimization. |
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| Seminar: N/A |
| Speaker: Manuela Manetta of Emory University |
| Contact: Bree Ettinger, bettinger@mathcs.emory.edu |
| Date: 2017-03-16 at 1:00PM |
| Venue: MSC W303 |
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| Abstract: Finding global minima for a general smooth objective function is a fundamental yet challenging problem arising in applied mathematics. Nevertheless, the most reliable techniques to converge to a minimum are local (gradient descent and Newton's method), and remain trapped in the basins of attraction of the minima found, which could be either local or global. Even in optimization courses, the students are often left with questions, such as, "how do we know that we found the global minimum? How do we know that we have visited the interesting regions of configuration space?" The purpose of this talk is to present methods and ideas that could help the students formulate answers to the questions above. In particular, I will present a new descent technique and a way to explore the landscape of the objective function, with no pretense that this is the answer to the problem, but with the hope of engaging the students. Interested students can begin to take small steps in the right direction toward the development of their own methods. |
| Title: Curvature through Cubes |
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| Seminar: N/A |
| Speaker: Michael Carr of Emory University |
| Contact: Bree Ettinger, bettinger@mathcs.emory.edu |
| Date: 2017-03-15 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Everyone knows the shortest distance between two points in Euclidean space is a straight line, but what about in more exotic spaces? Mathematicians have been studying paths on curved spaces for as long as we have known we lived on one. More recently the work of Gromov showed that notions of curvature can be extended to spaces that seem to have no curves at all: complexes made from ordinary cubes glued together. We will look at applications of these spaces from robotics to chemistry to recent advances in topology. |
| Title: Bias and Uncertainty in Information Visualization |
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| Type: Computer Science |
| Speaker: Michael Correll of University of Washington |
| Contact: TBA |
| Date: 2017-03-13 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: We often turn to data to help us make sense of an uncertain world. However, the uncertainty in our data is often esoteric, complex, or counter-intuitive. It can be challenging to present this uncertainty, especially to audiences without backgrounds in statistics. Charts, graphs, and other visualizations of data address this issue by making people into “visual statisticians:” we can estimate statistical properties through visual inspection. However, just as statistical measures can be subject to bias, visualizations can also introduce bias. In this talk, I show how designers can intervene to create new visualizations that correct these biases, and improve the judgments of visual statisticians. From this perspective of designing for de-biasing, I focus on two common visualizations: error bars and thematic maps. I present visual alternatives for error bars that avoid “within-the-bar” bias while also promoting statistically grounded comparisons between means. I also present “Surprise Maps,” a technique for thematic maps that relies on Bayesian reasoning to highlight interesting regions that might otherwise be hidden in traditional maps. I conclude with a discussion of remaining challenges for visual de-biasing, and how we might use visualizations to encourage better, data-driven decision-making. |
| Title: The Distribution Of The Number Of Prime Factors With Restrictions - Variations Of The Classical Theme |
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| Seminar: Algebra |
| Speaker: Krishna Alladi of University of Florida |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2017-02-28 at 4:00PM |
| Venue: W306 |
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| Abstract: The study of $\nu(n)$ the number of prime factors of $n$ began with Hardy and Ramanujan in 1917 who showed that $\nu(n)$ has normal order $log\,log\,n$ regardless of whether the prime factors are counted singly or with multiplicity. Their ingenious proof of this utilized uniform upper bounds for $N_k(x)$, the number of integers up to $x$ with $\nu(n)=k$. Two major results followed a few decades later - the Erd\"os-Kac theorem on the distribution more generally of additive functions, and the Sathe-Selberg theorems on the asymptotic behavior of $N_k(x)$ as $k$ varies with $x$ - a significant improvement of Landau's asymptotic estimate for $N_k(x)$ for fixed $k$. We shall consider the distribution of the number of prime factors by imposing certain restrictions - such as (i) requiring all prime factors of $n$ to be $ |
| Title: Bounded colorings of graphs and hypergraphs |
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| Seminar: Combinatorics |
| Speaker: Jan Volec of McGill University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2017-02-27 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: A conjecture of Bollobas and Erdos from 1976 states that any coloring of edges of an n-vertex complete graph such that at each vertex no color appears more than (n/2)-times contains a properly-colored Hamilton cycle. This problem was motivation for the following more general question: Let c be a coloring of E(K_n) where at each vertex, no color appear more than k-times. What properly colored subgraphs does c necessarily contain? In this talk, we will be interested in spanning subgraphs of K_n that have bounded maximum degree or the total number of cherries, i.e., the paths on three vertices. We will also mention similar questions for hypergraphs, as well as analogous problems concerned with rainbow subgraphs in edge colorings of K_n, where the total number of appearances for each color is bounded. One of our main results confirms the following conjecture of Shearer from 1979: If G is an n-vertex graph with O(n) cherries and c is a coloring of E(K_n) such that at each vertex every color appears only constantly many times, then c contains a properly colored copy of G. The talk is based on a joint work with Nina Kamcev and Benny Sudakov. |
| Title: Uncertainty Quantification and Numerical Analysis: Interactions and Synergies |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Daniela Calvetti of Case Western Reserve University |
| Contact: James Nagy, nagy@mathcs.emory.edu |
| Date: 2017-02-24 at 1:00PM |
| Venue: MSC W301 |
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| Abstract: The computational costs of uncertainty quantification can be challenging, in particular when the problems are large or real time solutions are needed. Numerical methods appropriately modified can turn into powerful and efficient tools for uncertainty quantification. Conversely, state-of-the-art numerical algorithms reinterpreted from the perspective of uncertainty quantification can becomes much more powerful. This presentation will highlight the natural connections between numerical analysis and uncertainty quantification and illustrate the advantages of re-framing classical numerical analysis in a probabilistic setting. |
| Title: Optical Design from Art to Car Mirrors |
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| Seminar: N/A |
| Speaker: Sarah Rody of Drexel University |
| Contact: Bree Ettinger, bree.d.ettinger@emory.edu |
| Date: 2017-02-24 at 3:00PM |
| Venue: MSC W201 |
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| Abstract: In order to design a mirror, we must first decide how to write the problem mathematically. I will start by looking at the historical use of perspective and mirrors in art. Then I will discuss how we can trace individual rays of light to describe how a mirror should work. I will show previous examples of optical design such as a non-reversing mirror and a panoramic mirror. Finally, I will turn to the specific example of a car mirror and show one optical design technique that I use. The standard passenger side mirror on a car has a limited field of view which results in a blind spot. Other mirrors, such as spherical mirrors, reduce the blind spot but distort the image. My goal is to find a construction for a passenger side mirror that reduces the blind spot and but creates less distortion than a spherical mirror. The idea central to our construction is the concept of an eigensurface. In general, if a surface is viewed in a curved mirror, it appears distorted. However, there could exist a surface that appears invariant in a particular curved mirror. I will show how I use this idea of eigensurfaces to find a mirror that could work as a passenger side car mirror. |
| Title: Good and Bad Reduction of Dynatomic Modular Curves |
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| Seminar: Algebra |
| Speaker: Andrew Obus of University of Virginia |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2017-02-21 at 4:00PM |
| Venue: W306 |
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| Abstract: The dynatomic modular curves parameterize one-parameter families of dynamical systems on $P^1$ along with periodic points (or orbits). These are analogous to the standard modular curves parameterizing elliptic curves with torsion points (or subgroups). For the family $x^2 + c$ of quadratic dynamical systems, the corresponding modular curves are smooth in characteristic zero. We give several results about when these curves have good/bad reduction to characteristic $p$, as well as when the reduction is irreducible. These results are motivated by uniform boundedness conjectures in arithmetic dynamics, which will be explained.\\ (This is joint work with John Doyle, Holly Krieger, Rachel Pries, Simon Rubinstein-Salzedo, and Lloyd West.) |
| Title: Quantum Kostka and the rank on problem for $sl_{2m}$ |
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| Seminar: Algebra |
| Speaker: Natalie Hobson of University of Georgia |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2017-02-14 at 4:00PM |
| Venue: W306 |
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| Abstract: In this talk we will define and explore an infinite family of vector bundles, known as vector bundles of conformal blocks, on the moduli space $M_{0,n}$ of marked curves. These bundles arise from data associated to a simple Lie algebra. We will show a correspondence (in certain cases) of the rank of these bundles with coefficients in the cohomology of the Grassmannian. This correspondence allows us to use a formula for computing "quantum Kostka" numbers and explicitly characterize families of bundles of rank one by enumerating Young tableaux. We will show these results and illuminate the methods involved. |
| Title: Torsion subgroups of elliptic curves over quintic and sextic number fields |
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| Seminar: Algebra |
| Speaker: Maarten Derickx of University of Bayreuth |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2017-02-09 at 4:00PM |
| Venue: W306 |
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| Abstract: The determination of which finite abelian groups can occur as the torsion subgroup of an elliptic curve over a number field has a long history starting with Barry Mazur who proved that there are exactly 15 groups that can occur as the torsion subgroup of an elliptic curve over the rational numbers. It is a theorem due to Loïc Merel that for every integer d the set of isomorphism classes of groups occurring as the torsion subgroup of a number field of degree d is finite. If a torsion subgroup occurs for a certain degree, then one can also ask for how many distinct pairwise non-isomorphic elliptic curves this happens. The question which torsion groups can occur for infinitely many non-isomorphic elliptic curves of a fixed degree is studied during this talk. The main result is a complete classification of the torsion subgroups that occur infinitely often for degree 5 and 6. This is joint work with Andrew Sutherland and heavily builds on previous joint work with Mark van Hoeij. |