All Seminars
| Title: Generalized Orbifolds in Conformal Field Theory |
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| Seminar: Algebra |
| Speaker: Marcel Bischoff of Vanderbilt University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-09-20 at 4:00PM |
| Venue: W306 |
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| Abstract: I will introduce the notion of a finite hypergroup. It turns out that certain subfactors (unital inclusions of von Neumann algebras with trivial center) can naturally be seen as such a fixed point. Chiral conformal field theory can be axiomatized as local conformal nets of von Neumann algebras.The orbifold of a conformal net is the fixed point with respect to a finite group of automorphisms. We define a generalized orbifold to be the fixed point of a conformal net under a proper hypergroup action. The fixed point is finite index subnet and it turns out that all finite index subnets are generalized orbifolds. A holomorphic conformal net is a conformal net with trivial representation category. For example, every positive even self-dual lattice gives such a conformal net. The representation category of a generalized orbifold of a holomorphic net is the Drinfeld center of a categorification of the hypergroup. Based on arXiv:1506.02606. |
| Title: Borcherds and Zagier Revisited: Divisors of Modular Forms |
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| Seminar: Algebra |
| Speaker: Ken Ono of Emory University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-09-13 at 4:00PM |
| Venue: W306 |
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| Abstract: |
| Title: Positive Polynomials and Varieties of Minimal Degree |
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| Seminar: Algebra |
| Speaker: Daniel Plaumann of Universitat Konstanz |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-09-06 at 4:00PM |
| Venue: W306 |
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| Abstract: A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of three squares of quadratic forms. We show more generally that every nonnegative quadratic form on a real projective variety X of minimal degree is a sum of dim(X) + 1 squares of linear forms. This provides a new proof for one direction of a recent result due to Blekherman, Smith, and Velasco. We explain the geometry behind this generalization and discuss what is known about the number of equivalence classes of sum-of-squares representations. (Joint work with G. Blekherman, R. Sinn, and C. Vinzant) |
| Title: Arithmetic Restrictions on Geometric Monodromy |
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| Seminar: Algebra |
| Speaker: Daniel Litt of Columbia University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-08-30 at 4:00PM |
| Venue: W306 |
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| Abstract: Let X be an algebraic variety over a field k. Which representations of pi_1(X) arise from geometry, e.g. as monodromy representations on the cohomology of a family of varieties over X? We study this question by analyzing the action of Gal(k/k) on pi_1(X), where k is a finite or p-adic field. As a sample application of our techniques, we show that if A is a non-constant Abelian variety over C(t), such that A[l] is split for some odd prime l, then A has at least four points of bad reduction. |
| Title: Harmonic measure, reduced extremal length and quasicircles |
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| Defense: Dissertation |
| Speaker: Huiqiang Shi of Emory University |
| Contact: Huiqiang Shi, huiqiang.shi@emory.edu |
| Date: 2016-08-10 at 12:00PM |
| Venue: W302 |
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| Abstract: This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In chapter 2, we mainly study two important conformal invariants: the extremal distance and the reduced extremal distance. Gives the estimate of extremal distance in the unit disk and the comparison of these two conformal invariants. In chapter 3 and 4, we give several necessary and sufficient conditions for the sewing homeomorphism of a Jordan domain to be bi-Lipschitz or bi-Holder, by using harmonic measure, extremal distance and reduced extremal distance. Furthermore, in chapter 5, we obtain some equivalent conditions for a Jordan curve to be a quasicircle. In chapter 6, we use the Robin capacity to define a new index and use this new index to characterize unit circle. |
| Title: Optimal Investment Strategies Based on Financial Crisis Indicators |
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| Seminar: Quantitative Finance |
| Speaker: Antoine Kornprobst of University of Paris I, Pantheon Sorbonne |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2016-06-15 at 1:00PM |
| Venue: MSC W303 |
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| Abstract: The main objective of this study is to build successful investment strategies and devise optimal portfolio structures by exploiting the power of forecast of our financial crisis indicators based on random matrix theory. While using daily data constituted of the components of a major equity index like the Standard and Poor’s 500 or the Shanghai-Shenzhen CSI 300, the financial crisis indicators used in this paper are of two kinds. Firstly we consider the financial crisis indicators based on measuring the Hellinger distance between the empirical distribution of the eigenvalues of the correlation matrix of those index components and a distribution of reference built to either reflect a calm or agitated market situation. Secondly, we consider the financial crisis indicators based on the study of the spectral radius of the correlation matrix of the index components where the coefficients have been weighted in order to give more importance to the stock components that satisfy a chosen characteristic related to the structure of the index, market conditions or the nature of the companies which are part of the index. For example, we will attempt to give more importance in the computation of the indicators to the most traded stocks, the stocks from the companies with the highest market capitalization or from the companies with an optimal debt to capital ratio (financial leverage). Our optimal investment strategies exploit the forecasting power of the financial crisis indicators described above in order to produce a ‘buy’, ‘sell’ or ‘stay put’ signal every day that is able to anticipate most of the market downturns while keeping the number of false positives at an acceptable level. Such tools are very valuable for investors who can use them to anticipate market evolution in order to maximize their profit and limit their losses as well as for market regulators who can use those tools to anticipate systemic events and therefore attempt to mitigate their effects. |
| Title: Can Compressed Sensing Accelerate High-Resolution Photoacoustic Tomography? |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Dr. Felix Lucka of University College London |
| Contact: Lars Ruthotto, lruthotto@emory.edu |
| Date: 2016-05-20 at 1:00PM |
| Venue: W306 |
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| Abstract: The acquisition time of current high-resolution 3D photoacoustic tomography (PAT) devices limits their ability to image dynamic processes in living tissue (4D PAT). In our work, we try to overcome this limitation by combining recent advances in spatio-temporal sub-sampling schemes, variational regularization and convex optimization with the development of tailored data acquisition systems. We first show that images with good spatial resolution can be obtained from suitably sub-sampled PAT data if sparsity-constrained image reconstruction techniques such as total variation regularization enhanced by Bregman iterations are used. A further increase of the dynamic frame rate can be achieved by exploiting the temporal redundancy of the data through the use of sparsity-constrained dynamic models. While simulated data from numerical phantoms will be used to illustrate the potential of the developed methods, we will also discuss the results of their application to different measured data sets. Furthermore, we will outline how to combine GPU computing and state-of-the-art optimization approaches to cope with the immense computational challenges imposed by 4D PAT.. Joint work with Marta Betcke, Simon Arridge, Ben Cox, Nam Huynh, Edward Zhang and Paul Beard. |
| Title: Improving PDE approximation via anisotropic mesh adaptation |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Simona Perotto of MOX, Dept. Mathematics, Politecnico di Milano, Italy |
| Contact: Alessandro Veneziani, ale@mathcs.emory.edu |
| Date: 2016-05-06 at 1:00PM |
| Venue: W306 |
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| Abstract: Anisotropic meshes have proved to be a powerful tool for improving the quality and the efficiency of numerical simulations in scientific computing, especially when dealing with phenomena characterized by directional features such as, for instance, sharp fronts in aerospace applications or steep boundary or internal layers in viscous flows around bodies. In these contexts, standard isotropic meshes often turn out to be inadequate since they allow one to tune only the size of the mesh elements while completely missing the directional features of the phenomenon at hand. On the contrary, via an anisotropic mesh adaptation it is possible to control the size as well as the orientation and the shape of the mesh elements. In this presentation we focus on an anisotropic setting based on the concept of metric. In particular, to generate the adapted mesh, we derive a proper metric stemming from an error estimator. This procedure leads to optimal grids which minimize the number of elements for an assigned accuracy. After introducing the theoretical context, several test cases will be provided to emphasize the numerical benefits led by an anisotropic approach. An overview of the ongoing research will complete the presentation. |
| Title: Geometrically unfitted finite elements for PDEs posed on surfaces and in the bulk |
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| Seminar: Numerical Analysis and Scientific Computing |
| Speaker: Maxim Olshanskii of University of Houston |
| Contact: Michele Benzi, benzi@mathcs.emory.edu |
| Date: 2016-04-28 at 4:00PM |
| Venue: W306 |
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| Abstract: Geometrically unfitted finite element methods are known in the literature under different names, e.g., XFEM, cut FEM, trace FEM, etc. These discretizations are mainly developed for efficient numerical treatment of differential equations posed in domains of complex geometry and/or having propagating interfaces. Unlike immersed boundary methods these discretizations typically treat interfaces in a `sharp' way, but avoid fitting the mesh. The talk will discuss some recent analysis and developments of unfitted FEM. |
| Title: The Kolchin Irreducibility Theorem |
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| Seminar: Algebra |
| Speaker: Taylor Dupuy of University of Vermont |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2016-04-26 at 4:00PM |
| Venue: W304 |
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| Abstract: A jet bundle is a higher order version of a tangent bundle (one for each positive integer) and the points correspond to truncated power series on your original variety. It turns out that if you have a singular variety these spaces get all messed up---they have extra irreducible components above the singular locus (and encode interesting singularity invariants). Magically, if we take the limit of these spaces, where the points correspond to full power series, these spaces become irreducible again! This is Kolchin's Irreducibility theorem. We will talk about this theorem and what happens when power series are replaced by Witt vectors. This talk is based on joint work with Lance Edward Miller and James Freitag. |