All Seminars
| Title: Splitting projective modules using Chern classes |
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| Seminar: Algebra and Number Theory |
| Speaker: Jean Fasel of LMU Munich |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-11-15 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: Let $X$ be a smooth affine variety of dimension $d$ over a field $k$ and let $E$ be a vector bundle of rank $r$. If $E$ splits off a free bundle of rank 1, then the Chern class $c_r(E)$ is trivial. If the base field $k$ is algebraically closed and $r=d$ then M.P.~Murthy (with N.~Mohan Kumar when $d=3$) proved that the converse statement holds. In this talk, we will discuss more general situations, namely $r=d$ over arbitrary fields and $r=d-1$ over algebraically closed fields. |
| Title: On Blow-ups of Compact Metrics and the Resulting Curvatures |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Pascal Philipp of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2011-11-15 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: On a compact Riemannian manifold with non-empty boundary, let a boundary defining function $\rho$ be given. Multiplying the compact metric by $\rho_{-2}$ defines a new metric. This conformal change, together with the interior of the original manifold, gives an infinite area Riemannian manifold $(M,g)$. The asymptotic behavior of the sectional curvatures of $g$ will be studied. The main result of these considerations will justify the use of asymptotically hyperbolic manifolds in fields of Mathematics and Physics. |
| Title: Querying Probabilistic Data |
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| Colloquium: Computer Science |
| Speaker: Dan Suciu of University of Washington |
| Contact: Li Xiong, lxiong@mathcs.emory.edu |
| Date: 2011-11-14 at 2:00PM |
| Venue: MSC W201 |
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| Abstract: A major challenge in data management to date is how to manage uncertainty in the data; uncertainty may exist because the data was extracted automatically from text, or was derived from the physical world such as RFID data, or was obtained by integrating several data sets using fuzzy matches, or may be the result of complex stochastic models. This has motivated research on probabilistic databases, where uncertainty is modeled using probabilities, and whose goal is to deliver predictable performance for queries on large probabilistic databases. Probabilistic inference is known to be intractable in general, but once we fix a query and considers only the database as variable input, it becomes a specialized problem, which requires a specialized analysis. I will show that Unions of Conjunctive Queries (also known as non-recursive datalog rules) admit a dichotomy: every query is either provably \#P hard, or can be evaluated in PTIME. For practical purposes, the most interesting part of this dichotomy is the PTIME algorithm, which relies on the inclusion/exclusion formula. Interestingly, the algorithm succeeds in evaluating in polynomial time some queries for which the underlying Boolean formula does not admit polynomial size OBDDs or FBDDs, or even (we conjecture) a polynomial size d-DNNF.\\ \\ Bio: \\ Dan Suciu is a Professor in Computer Science at the University of Washington. He received his Ph.D. from the University of Pennsylvania in 1995, then was a principal member of the technical staff at AT and T Labs until he joined the University of Washington in 2000. Professor Suciu is conducting research in data management, with an emphasis on topics that arise from sharing data on the Internet, such as management of semistructured and heterogeneous data, data security, and managing data with uncertainties. He is a co-author of two books Data on the Web: from Relations to Semistructured Data and XML, 1999, and Probabilistic Databases, 2011. He holds twelve US patents, received the 2000 ACM SIGMOD Best Paper Award, the 2010 PODS Ten Years Best paper award, and is a recipient of the NSF Career Award and of an Alfred P. Sloan Fellowship. Suciu's PhD students Gerome Miklau and Christopher Re received the ACM SIGMOD Best Dissertation Award in 2006 and 2010 respectively, and Nilesh Dalvi was a runner up in 2008. |
| Title: Complex iso-length-spectral arithmetic hyperbolic 3-manifolds |
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| Defense: Dissertation |
| Speaker: Sean Thomas of Emory University |
| Contact: Emily Hamilton, emh@mathcs.emory.edu |
| Date: 2011-11-11 at 2:00PM |
| Venue: MSC W303 |
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| Abstract: |
| Title: Equivariant pretheories and invariants of torsors |
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| Seminar: Algebra and Number Theory |
| Speaker: Kirill Zainoulline of University of Ottawa |
| Contact: Skip Garibaldi, skip@mathcs.emory.edu |
| Date: 2011-11-07 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: In this talk we introduce and study the notion of an equivariant pretheory. Basic examples of such pretheories are equivariant Chow groups, equivariant $K$-theory and equivariant algebraic cobordism. As a new example we define an equivariant version of the cycle (co)homology with coefficients in a Rost cycle module. We also provide a version of Merkurjev's spectral sequence for equivariant cycle homology. As an application we generalize the theorem of Karpenko-Merkurjev on $G$-torsors and rational cycles; to every $G$-torsor $E$ and a $G$-equivariant pretheory we associate a graded ring which serves as an invariant of $E$. In the case of Chow groups this ring encodes the information concerning the motivic $J$-invariant of $E$ and in the case of Grothendieck's $K_0$ it encodes the indexes of the respective Tits algebras. |
| Title: Assimilation of velocity data into fluid dynamics simulations, an application to computational hemodynamics |
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| Defense: Dissertation |
| Speaker: Marta D'Elia of Emory University |
| Contact: Marta D'Elia, mdelia2@emory.edu |
| Date: 2011-11-04 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Cardiovascular applications recently gave a strong impulse to numerical methods for fluid dynamics. Furthermore, thanks to new precise measurement devices and efficient image processing techniques, medicine is experiencing a tremendous increment of available data, inevitably affected by noise. Beyond validation, these data can be combined with numerical simulations in order to develop mathematical tools, known as data assimilation (DA) methods, of clinical impact. In the context of hemodynamics accuracy and reliability of assimilated solutions are particularly crucial in view of possible applications in the clinical routine. Hence, it is of central relevance to quantify the uncertainty of numerical results.\\ \\ We propose a robust DA technique for the inclusion of noisy velocity measures, collected from magnetic resonance imaging, into the simulation of hemodynamics equations, namely the incompressible Navier-Stokes equations (NSE). The technique is formulated as a control problem where a weighted misfit between velocity and data is minimized under the constraint of the NSE; the optimization problem is solved with a discretize then optimize approach relying on the finite element method. The control variable is the normal stress on the inflow section of the vessel, which is usually unknown in real applications. We design deterministic and statistical estimators (the latter based on a Bayesian approach to inverse problems) for the estimation of the blood velocity and its statistical properties and of related variables of medical relevance, such as the wall shear stress. We also derive conditions on data location that guarantee the existence of an optimal solution.\\ \\ Numerical simulations on 2-dimensional and axisymmetric 3-dimensional geometries show the consistency and accuracy of the method with synthetic noise-free and noisy data. Simulations on 2-dimensional geometries approximating blood vessels demonstrate the applicability of the approach for hemodynamics applications. |
| Title: Blind Image Restoration in Modern Ground-Based Astronomy |
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| Colloquium: Numerical Analysis and Scientific Computing |
| Speaker: Stuart Jefferies of Department of Physics and the Institute for Astronomy, University of Hawaii |
| Contact: Jim Nagy, nagy@mathcs.emory.edu |
| Date: 2011-11-03 at 4:00PM |
| Venue: MSC W201 |
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| Abstract: Driven by the never-ending quest for better resolution, ground-based astronomy continues its march toward using telescopes with larger and larger apertures. Current “large aperture” (8m-10m) telescopes will soon be eclipsed by 30m-50m behemoths. However, as with any telescope with an aperture of more than about 0.3m, realizing the full resolving power of these telescopes requires the combined use of adaptive optics compensation and image restoration (due to turbulence in the Earth’s atmosphere). Because the characteristics of the image blur are typically unknown, blind deconvolution, where both the target object and the blurring function are estimated from the observed data, is the restoration technique of choice. I will give an overview of blind deconvolution and describe some recent advances that allow us to obtain high-quality imagery under turbulence conditions which, up until now, have been thought unsuitable for high-resolution imaging. |
| Title: Quadratic forms over the rational function field of a field having cohomological dimension 1 |
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| Seminar: Algebra and number theory |
| Speaker: David Leep of University of Kentucky |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-11-01 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: In 2003, Colliot-Thelene and Madore constructed a system of two quadratic forms in 5 variables defined over a field of cohomological dimension 1 having no nontrivial common zero lying in the field. This gave the first counterexample to a claim Armand Brumer made in a 1978 paper. I will briefly explain their counterexample, then greatly generalize the counterexample using techniques from the algebraic theory of quadratic forms, and then give a far simpler proof for the wider class of counterexamples. |
| Title: List colorings of infinite graphs |
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| Seminar: Combinatorics |
| Speaker: Peter Komjath of Eotvos Lorand University and Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2011-10-28 at 4:00PM |
| Venue: W306 |
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| Abstract: After a short reminder of things like alephs and well ordering, we consider the notions of coloring number and list-chromatic number for infinite graphs and compare them with the chromatic number and each other, and calculate the list chromatic number for some complete bipartite graphs. We state some theorems essentially saying that, for uncountable graphs, the list chromatic number can be equal to the coloring number, to the chromatic number, but not both. |
| Title: The Rost invariant for groups of type $A$ |
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| Seminar: Algebra and Number Theory |
| Speaker: Anne Queguiner-Mathieu of Paris XIII and Paris-Est |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2011-10-25 at 3:00PM |
| Venue: MSC E406 |
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| Abstract: We discuss an invariant due to Rost for torsors under simple simply connected groups with values in degree three Galois cohomology. We will explain how one can provide an exact formula to compute the Rost invariant of a torsor under the group $SL_1(A)$ of norm 1 elements in a central simple algebra. This talk is based on a joint work with Philippe Gille. |