Geometry and Physics Seminar

Professor L. Katzarkov
University of Miami

will present

Spectra of Categories and Applications to Low Dimensional Topology

Tuesday, December 1, 2009, 5:00pm
Ungar Room 402

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Applied Math Seminar

Dr. Orou Gaoue
ITME Post Doc
Department of Biology
University of Miami

will present

Modeling the Impact of Non-timber Forest Product Harvest in Variable Environments

Friday, November 20, 2009, 4:30pm
Ungar Room 402


Abstract: Harvesting wild plants for non-timber forest products is an important source of income, food and medicine for millions of people around the world. Over-exploitation of these plant resources may lead to species extinction and impair their availability for future use by people who depend on them for their livelihoods. Yet, our knowledge of the way harvesting some non-timber forest products may affect population dynamics is still limited. I will use the case study of Khaya senegalensis (Meliaceae) foliage and bark harvest by indigenous Fulani people in Africa, to demonstrate that harvesting reduces population growth rate even further if environmental conditions vary stochastically. I will show how using harvest-specific elasticity analysis provides in-depth understanding of the management options that are available to mitigate the negative effects of harvest at the population level. I suggest that the temporal sequence of harvest intensity matters when modeling the impact of wild plant harvest.

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Geometry and Physics Seminar

Professor N. Saveliev
University of Miami

will present

Seiberg-Witten Equations and End-periodic Dirac Operators

Wednesday, November 18, 2009, 4:00pm
Ungar Room 402


Abstract: Let X be a smooth spin 4-manifold with homology of S^1 x S^3. In our joint project with Tom Mrowka and Daniel Ruberman, we study the Seiberg-Witten equations on X. The count of their solutions, called the Seiberg-Witten invariant of X, depends on choices of Riemannian metric and perturbation. A similar dependency issue is resolved in dimension 3 by relating the jumps in the Seiberg-Witten invariant to the spectral flow of the Dirac operator; the resulting invariant is then the Casson invariant. In dimension 4, we use Taubes' theory of end-periodic operators to relate the jumps in the Seiberg-Witten invariant to the index theory of the Dirac operator on a manifold with periodic end modeled on the infinite cyclic cover of X. The resulting invariant is then a smooth invariant of X whose reduction is the Rohlin invariant. Some calculations and applications of this invariant will be discussed.

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Applied Math Seminar

Professor Gaetano Zampieri
Dipartimento di Informatica
Universita di Verona

will present

A Class of Integrable Hamiltonian Systems and Weak Lyapunov Stability

Friday, November 13, 2009, 4:30pm
Ungar Room 402


Abstract: The aim of the talk is to introduce a class of Hamiltonian autonomous systems which are completely integrable and their dynamics is described in all details. In particular we show explicit examples of Hamiltonian systems with an unstable equilibrium where the eigenvalues of the linearization are imaginary and no motion is asymptotic to the equilibrium in the past, namely no solution has the equilibrium as limit point as time goes to minus infinity.

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Combinatorics Seminar

Professor Eric Gottlieb
Rhodes College

will present

A Combinatorial Optimization Problem from Genomics

Friday, November 13, 2009, 3:00pm
Ungar Room 506


Abstract: Biologists often wish to locate the gene controlling for a specific feature in a given species. One approach is to use recombinant inbred lines (RILs) from that species. RILs are homozygous, with genetic material alternating between a parent having the trait in question and a parent not having the trait. The break points in the genetic contributions from the parents occur at different points in different RILs. Biologists typically select a (usually large) subset of the RILs that visually appears to have sufficiently varied break points to ensure that the location of the controlling gene can be resolved by comparing which RILs have the trait with the parental contribution at each gene.

Unfortunately, this subjective approach does not guarantee the ability of the selected subset to resolve the gene location as well as the full set of RILs. In addition, the experiments that must be performed to determine whether a given RIL has the trait in question can be intensive with respect to time, money, and laboratory space. For this reason, it is desirable to minimize the size of the set of RILs selected for analysis. The typical approach makes little or no effort to select a smallest set.

We describe a Mathematica program we have written to find sets of RILs that are as small as possible subject to the constraint of being able to resolve the location of any gene the full set of RILs can resolve.

This is joint work with Jonathan Fitz Gerald, Department of Biology, Rhodes College.

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Applied Math Seminar

Professor Neil Johnson
Department of Physics
University of Miami

will present

Insurgent Wars, Pandemics, Global Emissions and Market Crises:
One Model Fits All?

Friday, November 6, 2009, 4:30pm
Ungar Room 402


Abstract: For complex real-world problems, it seems that there are (at least) as many models in the literature as there are researchers in the field. In this seminar, I will attempt the opposite approach: One model, stretched in various directions, to encompass four major issues. The model is a coalescence-fragmentation model in which clusters are continually playing the 'El Farol' bar attendance game. In certain limits, analytic solutions are obtainable which seem to capture the stylized statistical facts of each of these problems. Generalizations of the model, and their implications in each real-world scenario, are discussed.

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Geometry and Physics Seminar

Professor Bruno de Oliveira
University of Miami

will present

Closed Symmetric Differentials of Degree 2 and the Geometry of Complex Surfaces

Wednesday, November 4, 2009, 4:00pm
Ungar Room 402


Abstract: It is well understood how holomorphic differential p-forms reflect the topology of a given complex manifold. On the other hand, little is known about the relationship between the topology and the algebra of holomorphic symmetric differentials of complex manifolds. In this talk we will give results about the impact of the presence of closed symmetric 2-differentials on the topology and geometry of complex surfaces.

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Geometry and Physics Seminar

Professor Ken Baker
University of Miami

will present

Rational Open Books, Cabling, and Contact Structures

Wednesday, October 28, 2009, 4:00pm
Ungar Room 402


Abstract: The Giroux Correspondence is a one-to-one correspondence between contact structures up to isotopy and open book decompositions up to positive stabilization. An open book decomposition of a 3-manifold is a link with a fibration of its exterior such that each fiber is a Seifert surface for the link. Cabling a link component produces a new open book decomposition (with few exceptions). We will describe how the contact structure supported by an open book changes under cabling, generalizing Hedden's result for open books in S^3. We'll also define rational open books and discuss their cablings. This is joint work in progress with John Etnyre and Jeremy Van Horn-Morris.

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Applied Math Seminar

Juan Gutierrez
University of Miami

will present

Extinction-proof Sperm Parasites

Friday, October 23, 2009, 4:30pm
Ungar Room 402


Abstract: It has been observed that feminization has deleterious effects on fish populations. In this talk we will discuss the case of Poecilia formosa, a unisexual fish (parasite) that can cause local extinction of Poecilia mexicana and Poecilia latipinna (hosts) through sexual parasitism conducive to population feminization. We will also show that once the parasite population surpasses the host female population, the system is highly sensitive to perturbations. We will show that stochasticity is a stabilizing force in that case, which explains the very high variability of field data. With a time of origination estimated in more than 100,000 years, it is remarkable that P. Formosa has avoided extinction. In this talk we will offer a solution to this 80-year old puzzle.

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Applied Math Seminar

Juan Gutierrez
University of Miami

will present

Biostructural Classification Database Case Study:
Shape Analysis for Automated Sulcal Classification and Parcellation of MRI Data

Friday, October 9, 2009, 4:30pm
Ungar Room 402


Abstract: The cortical surface of the brain can be represented by a triangulated mesh obtained from magnetic resonance imaging (MRI) data. Each ridge (gyrus) and fissure (sulcus) of the cerebral cortex can be represented by a polygonal curve. In this talk I will describe a set of geometric features that can characterize the shape of such curves and surfaces in 3D space: curvature, Gauss integrals and moments. In a experiment conducted in the Biostructural Classification Database (BCD), these geometric features were successfully used to classify sulcal curves into sulcal and hemispheric classes. These results suggest application of the BCD to neuroscientific data as a diagnosis tool for brain conditions that cause structural changes.

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Geometry and Physics Seminar

Professor G. Grancharov
Florida International University

will present

Pseudo-Hermitian Metrics on Complex Surfaces

Wednesday, October 7, 2009, 4:00pm
Ungar Room 402


Abstract: In this work, joint with J. Davidov, O. Mushkarov and M. Yotov, we consider an indefinite analog of hypercomplex and hyperhermitian structures on compact complex surfaces. Based on Kodaira's classification there is a list of surfaces which could admit such structures and some examples will be provided. Relations with generalized geometry and pseudo-bihermitian structures will be mentioned.

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Applied Math Seminar

Juan Gutierrez
University of Miami

will present

Trojan Y Chromosomes as Means of Eradication of Invasive Species

Friday, October 2, 2009, 4:30pm
Ungar Room 402


Abstract: Invasive species are considered second only to habitat destruction as a threat to biodiversity. The economic loss due to invasive species is a trillion dollar figure every year worldwide. This talk presents a theoretical method of eradication of invasive species through the use of Trojan Y chromosomes. The mathematical analysis of the Trojan Y chromosome eradication strategy is presented for the ODE case and the PDE case in R. It is shown that is possible to cause local extinction of species that have XY sex determination systems as long as they are susceptible to sex reversal.

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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.

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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.