Geometry and Physics Seminar

Professor I. Hambleton
McMaster University

will present

Conjugation Spaces and 4-manifolds

Wednesday, February 17, 2010, 4:00pm
Ungar Room 402


Abstract: A conjugation space is a space X with involution, where the cohomology mod 2 of the fixed set is the same as the cohomology of the space after doubling dimensions. The first example is X = complex projective space, with the involution given by complex conjugation. In the talk I will describe the relation between smooth conjugation 4-manifolds and knotted surfaces in mod 2 homology 4-spheres. This is joint work with Jean-Claude Hausmann.

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Combinatorics Seminar

Benjamin Braun
University of Kentucky

will present

Nowhere-Harmonic Colorings of Graphs

Tuesday, February 16, 2010, 5:00pm
Ungar Room 506


Abstract: Proper vertex colorings of a graph are related to its boundary map, also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, a natural extension of the boundary map, leads us to introduce nowhere-harmonic colorings and analogues of the chromatic polynomial and Stanley's theorem relating negative evaluations of the chromatic polynomial to acyclic orientations. Further, we discuss some examples demonstrating that nowhere-harmonic colorings are more complicated from an enumerative perspective than proper colorings. Our primary tool for these investigations is the theory of "inside-out polytopes," developed by M. Beck and T. Zaslavsky, and the theory of Ehrhart quasi-polynomials for rational polytopes. This is joint work with Matthias Beck of San Francisco State University.

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Geometry and Physics Seminar

Professor I. Itenberg
Université de Strasbourg

will present

On Real Determinantal Quartics

Wednesday, February 10, 2010, 4:00pm
Ungar Room 402


Abstract: Let A_0, A_1, A_2, and A_3 be real symmetric 4 x 4 matrices. One can associate to these four matrices a spectral surface in the three dimensional complex projective space CP^3 (the set of points (x_0 : x_1 : x_2 : x_3) in CP^3 such that the determinant of the matrix x_0 A_1 + x_1 A_1 + x_2 A_2 + x_3 A_3 is zero) and a spectrahedron in the three dimensional real projective space RP^3 (the set of points (x_0 : x_1 : x_2 : x_3) in RP^3 such that the matrix x_0 A_1 + x_1 A_1 + x_2 A_2 + x_3 A_3 is semidefinite).

In general, the spectral surface considered has 10 double points. We show that the boundary of the spectrahedron cannot contain more than 8 doubles points of the spectral surface. The proof is based on a study of period spaces of real K3-surfaces.

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Combinatorics Seminar

Michelle Wachs
University of Miami

will present

Eulerian Quasisymmetric Functions and Cyclic Sieving

Tuesday, February 9, 2010, 5:00pm
Ungar Room 506


Abstract: Certain q-analogs of classical combinatorial numbers exhibit the curious phenomenon of evaluating to a positive integer when q is set equal to an nth root of unity. A stronger phenomenon called the cyclic sieving phenomenon (of Reiner, Stanton and White) is exhibited when these positive integers can be interpreted as the number of fixed points of an element of a cyclic group acting on a set whose size is equal to the classical combinatorial number.

In this talk I will present an instance of the cyclic sieving phenomenon involving a q-analog of the Eulerian numbers and their cycle type refinement. The main tool in proving this result is the Eulerian quasisymmetric functions introduced a few years ago in joint work with Shareshian.

This is joint work with Bruce Sagan and John Shareshian.

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Geometry and Physics Seminar

Dima
University of Miami

will present

Motives

Thursday, February 4, 2010, 2:00pm
Ungar Room 547

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Combinatorics Seminar

Drew Armstrong
University of Miami

will present

Reduced Decompositions of Permutations

Tuesday, February 2, 2010, 5:00pm
Ungar Room 506


Abstract: Consider the group of permutations of {1,2,\ldots, n}, which is generated as a Coxeter group by the adjacent transpositions (i,i+1). The reduced S-decompositions for a permutation \pi are the ways of writing \pi as a product of the fewest adjacent transpositions. A nice result gives a bijection from the (essentially different) reduced S-decompositions of the longest permutation to *rhombic tilings of a regular 2n-gon*.

We will describe an analogous result for the reduced T-decompositions of a permutation (using all transpositions, not just the adjacent ones). We will give a bijection from the (essentially different) reduced T-decompositions of the long cycle to *quadrangulations of a regular 2n-gon*.

We will note some striking similarities between these two results.

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Geometry and Physics Seminar

Alexandr Usnich
Ludmil Katzarkov
Dima
University of Miami

will present

On the Work of Lurie

Tuesday, February 2, 2010, 4:00pm
Ungar Room 547

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Geometry and Physics Seminar

Ludmil Katzarkov
University of Miami

will present

Hodge Structures and Spectra

Tuesday, February 2, 2010, 2:00pm
Ungar Room 547

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Geometry and Physics Seminar

Alexandr Usnich
University of Miami

will present

A infty Categories

Monday, February 1, 2010, 11:00am
Ungar Room 547

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NSF-CSMS Project Industry-Liaison Seminar

Michael Goldberg
President and CEO
Flamingo Software

will present

A Career in Software Development, Web-Based Systems

Wednesday, January 27, 2010, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: Over 40 years ago, Michael Goldberg started a Miami software company called FDP (Financial Data Planning), employing many UM mathematics and computer science students over the years and eventually becoming the leading provider of software for the insurance and pension industries. After selling FDP, Michael started another company 5 years ago called Flamingo Software, specializing in web-based systems for insurance and financial services companies. Find out what a career in software development can be like and what it takes to run a successful software company.

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Geometry and Physics Seminar

Professor A. Dvorsky
University of Miami

will present

Realizations of Minimal Representation of O(p,q)

Wednesday, December 9, 2009, 3:00pm
Ungar Room 402


Abstract: The "smallest" unitary representation of a non-compact simple Lie group is a surprisingly rich object with many interesting analytic properties. Unlike the metaplectic representation of Sp(2n), which was studied extensively, the minimal representation for the orthogonal groups O(p,q) has not been analyzed in comparable detail. We will discuss the explicit models for this representation, constructed recently by Kobayashi and Orsted, and introduce some applications of these models.

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Geometry and Physics Seminar

Jeremy Van Horn-Morris
American Institute of Mathematics

will present

Symplectic Fillings of Contact Manifolds

Friday, December 4, 2009, 3:30pm
Ungar Room 402


Abstract: Work of Loi and Piergalini as well as Akbulut and Ozbagci allows us to create symplectic fillings of contact 3-manifolds from factorizations of the monodromy of a compatible open book decomposition. Recent results of Wendl complete this correspondence: every symplectic filling comes from such a factorization. We'll explain this correspondence in more detail and give some example applications including the rational blowdown operation and the uniqueness of symplectic fillings of certain Lens spaces. Some of this work is joint with Tom Mark and Hasaaki Endo and some is joint with Olga Plamenevskaya.

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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


Abstract: In this talk we will define the notion of spectrum of category and will compute it on the example of some Fukaya categories. Other applications will be discussed.

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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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NSF-CSMS Project Industry-Liaison Seminar

Dr. Arnaldo Horta
Applied Research Mathematician
National Security Agency
Fort Meade, Maryland

will present

Inside the Puzzle Palace:
Careers in Mathematics and Computer Science at the National Security Agency

Thursday, October 8, 2009, 5:00pm
Ungar Room 402

Refreshments at 4:30pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In this talk, I will discuss the role of mathematics and computer science at NSA and discuss hiring opportunities, including REUs (Research Experiences for Undergraduates) and programs for graduate students.

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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.