Geometry and Physics Seminar

Bruno de Oliveira
University of Miami

will present

Closed Symmetric Differentials on Surfaces

Wednesday, December 10, 2008, 3:00pm
Ungar Room 506


Abstract: In general symmetric differentials $w \in H^0(X,S^m\Omega^1_X)$ behave like analytic objects on families, i.e they will appear and dissappear along a family. On the other hand, as we well know symmetric differentials of degree one, i.e. holomorphic 1-forms, on compact Kahler manifolds are preserved along families because they are tied to the topology of the manifold. A key element is the fact that holomorphic one forms are closed on kahler manifolds. This talk will be about generalizing the notion of closed symmetric differentials to higher order. We will then describe the topological significance of closed symmetric differentials.

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Geometry and Physics Seminar

Eric Harper
University of Miami

will present

Casson-Lin Type Invariant for Links

Thursday, December 4, 2008, 4:00pm
Ungar Room 506


Abstract: Andrew Casson defined an invariant for oriented homology 3-spheres, M, which essentially counts conjugacy classes of representations of the fundamental group of M into SU(2). Xiao-Song Lin similiarly defined a knot invariant which counts conjugacy classes of representations of the fundamental group of the complement of the knot in S^3 into SU(2). Lin's invariant is the knot signature. In this talk, we will define a (2-component) link invariant using a construction similiar to Lin's, then we will show our invariant gives the linking number.

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Geometry and Physics Seminar

K. Baker
University of Miami

will present

Small Seifert Fibered Spaces and Surgery

Wednesday, October 15, 2008, 4:00pm
Ungar Room 506


Abstract: Generically, a small Seifert fibered space may be viewed as a thrice-punctured sphere cross S^1 with three solid tori attached along the boundary tori. Sometimes an embedded solid torus may be excised from S^3 and then reattached along the resulting boundary torus in a different manner to produce one of these small Seifert fibered spaces; i.e. Dehn surgery on a knot in S^3 sometimes produces a small Seifert fibered space. The classification of such knots and Dehn surgeries remains open. We'll talk about the context for this problem, what's known, and some of our current on-going joint research with Cameron Gordon and John Luecke.

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Geometry and Physics Seminar

N. Saveliev
University of Miami

will present

Real Moduli Spaces over M-curves

Wednesday, October 8, 2008, 4:00pm
Ungar Room 506


Abstract: Let F be a genus g curve with a real structure having the maximal possible number of fixed circles. We study the moduli space M of stable holomorphic vector bundles of rank 2 over F with fixed non-trivial determinant, and its real counterpart M' defined as the fixed point set of the induced real structure on M. The cohomology groups of M were computed by Atiyah and Bott; we compute cohomology of M' for g = 2 and conjecture the answer for all g (joint project with Shuguang Wang, University of Missouri).

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Geometry and Physics Seminar

L. Katzarkov
University of Miami

will present

Uniformization Results

Thursday, October 2, 2008, 4:00pm
Ungar Room 506


Abstract: We will discuss the universal coverings of smooth projective varieties.

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Geometry and Physics Seminar

F. Donzelli
University of Miami

will present

Density Property for Algebraic Varieties

Friday, September 19, 2008, 4:00pm
Ungar Room 402


Abstract: An affine algebraic manifold has the algebraic density property if the Lie algebra generated by integrable algebraic vector fields coincides with the set of all vector fields.

In this talk we show the algebraic density property for (1) homogeneous affine algebraic varieties equipped with sufficiently many fixed point free SL_2 actions, and (2) Zariski locally trivial fibrations with fiber having the algebraic density property.

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Geometry and Physics Seminar

Professor C. Guttikar
University of Miami

will present

Recovering Algebraic Varieties from Their Derived Categories

Thursday, September 11, 2008, 4:00pm
Ungar Room 506


Abstract: We prove that a fibration of projective Fano/Anti-Fano varieties over a smooth projective base is determined by the bounded derived category of coherent sheaves on the total space, a Torelli type of result for fibrations. This extends the result of Bondal-Orlov about fano varieties.

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Geometry and Physics Seminar

Professor S. Kaliman
University of Miami

will present

C^*-actions on Affine Algebraic Surfaces

Friday, August 29, 2008, 4:00pm
Ungar Room 506


Abstract: We give a classification of conjugacy classes of algebraic C^*-actions on smooth affine algebraic surfaces (in their groups of algebraic automorphisms). The main part of the talk will be about the most difficult case of quasi-homogeneous (or so-called Gizatullin) surfaces. We describe moduli spaces for a class of special Gizatullin surfaces which is a generalization of the following Danilov-Gizatullin theorem: an isomorphism class of the complement to an ample section of a Hirzebruch surfaces is completely determined by the selfintersection number of this section.

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Applied Math Seminar

James D. Englehardt, Ph.D., P.E.
Professor, Environmental Engineering
University of Miami

will present

Why Does North America Have the Highest Cancer Rate in the World?
A Suggested Alternative to the Central Limit Theorem in Nonlinear Correlated Systems and Networks and Its Use in Dose-response Assessment

Friday, April 25, 2008, 4:30pm
Ungar Room 402


Abstract: The magnitudes of hurricanes, solar flares, citation rates, web connections, illness severities, and many other complex system outcomes are observed to have asymptotic power law distributions. However, power laws typically require truncation or empirical cutoff, often requiring additional parameters. The Weibull form on the other hand has been shown to model a broad range of complex system outcome sizes directly. Weibull-form distributions, continuous and proposed discrete, will be shown in this talk to be stable, attracting distributions of outcome size in multiplicative, correlated systems. Multiplicative systems are considered zeroth order models of many complex systems, and system outcome causes are typically inter-related and correlated. And while power laws are also multiplicatively stable in correlated systems, the Weibull emerges naturally from finite-mean, exponentially-distributed cause sizes. Also, in well-correlated systems even sums tend towards the parent distribution. Thus, the Weibull form may have generality in nonlinear correlated systems analogous to that of the Gaussian in linear independent systems. Accordingly, the Weibull is suggested with simple models to simulate nonlinear system outcomes such as simulated illness severities. A corresponding emergent multivariate dose-response function for chemical mixtures is then derived, accounting for covariance structure. The result is validated versus data on chloroform-induced liver necrosis in mice, and toluene/benzene-induced embryo mortality in Japanese medaka. Further empirical verification is suggested, with the goal of timely predictive Bayesian dose-response assessments based on available and possibly conflicting information, to shed light on chemical drivers of cancer and other disease.

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Combinatorics Seminar

Professor Eric Gottlieb
Rhodes College

will present

Fair Division, Voting Theory, and Posets

Thursday, March 6, 2008, 2:00pm
Ungar Room 411


Abstract: We describe a way to use posets to bring techniques from voting theory to bear on the problem of fairly distributing indivisible items. One of the posets that plays an important role is isomorphic to the quotient of a Coxeter group by a maximal parabolic subgroup. We will also mention a number of practical obstacles to the implementation of this program.

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Geometry and Physics Seminar

Professor N. Saveliev
University of Miami

will present

Asymptotics for End-periodic Dirac Operators

Wednesday, March 5, 2008, 4:00pm
Ungar Room 411