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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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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
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