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Friday, 8 May 2015
2:00pm – 3:00pm. Monroe 267 (Seminar Room).
Speaker: Svetlana Roudenko
Title: Creating a Good CV
Tuesday, 28 April 2015 (note special day and time)
4:00pm – 5:00pm. Monroe 267 (Seminar Room).
Speaker: Changkai Sun (GWU undergraduate)
Title: Thresholds for Solutions Existence in the Focusing Nonlinear Schroedinger equation
Abstract: We study the nonlinear Schroedinger equation with focusing nonlinearity in various space dimensions. We consider finite energy and finite variance initial data in the so called mass-supercritical regime. One of the goals in such studies is to understand whether solutions evolved by the nonlinear Schroedinger evolution exist globally in time, or could form a singularity, and thus, `break down' (in a certain sense) in finite time. There have been much research done in this direction recently, and there are various theoretical thresholds available now. However, all of them lack the full picture, i.e., there are theoretical gaps in classification of the above initial data. In this numerical work, we consider Gaussian and super Gaussian initial data, we let it evolve by the nonlinear Schroedinger flow with power nonlinearities p=3,5,7 and we are able to obtain numerical thresholds which identify the borderline between the globally existing solutions and solutions which blow up in finite time. We then compare our results with the known theoretical ones and show how the "gaps" in long-time existence of solutions should be addressed.
Friday, 24 April 2015
3:00pm – 4:00pm. Monroe 267 (Seminar Room).
Speaker: Jiajun Lu (GWU)
Title: Finite Element Method in Two Dimensional Poisson's Equation with Dirichlet/Neumann BC
Abstract: Finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It uses subdivision of a whole problem domain into simpler parts, called finite elements, and variational methods from the calculus of variations to solve the problem by minimizing an associated error function. I will focus on the FEM in two dimensional problems, particularly on Poisson's equation with both Dirichlet and Neunmann boundary condition.
Friday, 20 March 2015
3:00pm – 4:00pm. Monroe 267 (Seminar Room).
Speaker: Lara El-Sherif (GWU)
Title: Finding the maximum genus of a graph: a topic in topological graph theory
Abstract: For any graph G and an orientable surface S_g (a surface of genus g), whether G can be cellularly embedded in S_g creates an interesting problem for many topological graph theorists. The ``genus range'' of a graph G, denoted GR(G), is defined to be the set of numbers g such that the graph G can be cellularly embedded in surface S_g. We call the minimum number g in the genus range, the ``minimum genus'' of G and the largest number in the range, the ``maximum genus'' respectively. Whereas the study of minimum genus dates back into the 19th century, interest in maximum genus began in the 1970s. The main contributors to the theory behind finding the maximum genus of a graph are Xuong and Nebesky, among others. In this talk we will introduce the methods used by both Xuong and Nebesky in solving the maximum genus problem and its equivalent notion in non-orientable and pseudo-surfaces (which turn out to be much easier to determine). We will (time permitting) also talk about the polynomial time algorithms available for finding a maximum genus embedding of a graph and the problems that lie in those algorithms.
Friday, 6 March 2015
3:00pm – 4:00pm. Monroe 267 (Seminar Room).
Speaker: Chong Wang (GWU)
Title: The Existence of the Global Minimizer in the Ternary System
Abstract: The first part will focus on the theory of bounded variations. Here I will introduce some basic concepts, such as bounded variation, perimeter, sets of finite perimeter, lower semicontinuity, compactness and minimizing sequences.
In the second part, I will talk about elliptic PDE and the ternary inhibitory system. Elliptic operators, regularity hypotheses, boundary operators, regularity of solutions, existence of solutions and an energy functional J of the ternary system will be talked here.
In the third part, I will show how to prove the existence of the global minimizer in the inhibitory ternary system.
Friday, 27 February 2015
3:30pm – 4:30pm. Monroe 267 (Seminar Room).
Speaker: Yeyao Hu (GWU)
Title: Stationary Disk Assemblies on Inhibitory Vesicles
Abstract: PDF
Wednesday, 19 November 2014
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Speaker: Thomas J. Savitsky (GWU)
Title: Basis-Exchange Properties of Matroids and Laplace Expansion
Abstract: I will review Laplace expansion of determinants and show how it motivates the basis-exchange axioms of a matroid. Next, I will introduce base-orderable and strongly base-orderable matroids and discuss some of my current research along these lines.
NB: Thomas Savitsky's talk was originally scheduled for October 1, 2014, then rescheduled for October 22, 2014.
Thursday, 13 November 2014 (note special day and time)
3:00pm – 4:00pm. Monroe 267 (Seminar Room).
Speaker: Sam Mendelson (George Mason Univ.)
Title: Some Special Matrix Algebra Presentations
Abstract: PDF
Wednesday, 12 November 2014
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Monday, 3 November 2014 (note special day and time)
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Speaker: Seung Yeop Yang
Title: Torsion of a finite quasigroup quandle is annihilated by its order
Abstract: Niebrzydowski and Przytycki proved that the torsion subgroup of $H_{n}^{Q}(T(\mathbb(Z)_{3}))$ is annihilated by $3$, for $n > 1$, and Nosaka generalized this result, p annihilates the torsion of $H_{n}^{Q}(T(\mathbb(Z)_{p}))$ when $p$ is odd. Our goal is to extend the result of Niebrzydowski, Nosaka, and Przytycki about the torsion subgroup of quandle homology groups of Takasaki quandles.
Wednesday, 29 October 2014
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Speaker: David Shoup (GWU)
Title: Unmasking Laplace's Equation, the Heat Equation, and the Wave Equation
Abstract: Halloween may almost be upon us, but there is no need to be fearful of these canonical PDE and their general intuition. All graduate students should at least be familiar with Laplace's Equation, the Heat Equation, and the Wave Equation as well as the results that follow them. I will present several examples of each of these and their uses, and I hope to explain these equations in a way that students who are not studying differential equations can understand them.
Wednesday, 22 October 2014
2:30pm – 3:30pm. Monroe 250 (note special location).
Speaker: NSA
Title: The NSA's SPORT program
Abstract: The National Security Agency will be visiting
George Washington University to speak to U.S. Citizen Graduate Students
about the Summer Program for Operations Research Technology (SPORT).
Highlights of the SPORT Program:
SPORT Information on website:
http://www.nsa.gov/careers/opportunities_4_u/students/graduate/sport.shtml
Wednesday, 15 October 2014
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Wednesday, 1 October 2014
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Speaker: Kai Yang (GWU)
Title: Some Properties of a Nonlinear Schrödinger Equation
Wednesday, 24 September 2014
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Speaker: E. Arthur Robinson, Jr. (GWU)
Title: An Introduction to LaTeX
Wednesday, 17 September 2014
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Wednesday, 3 September 2014
2:30pm – 3:30pm. Monroe 267 (Seminar Room).
Speaker: Yanxiang Zhao (GWU)
Title: Periodic migration in a physical model of cells on micropatterns
Abstract: We extend a model for the morphology and dynamics of a crawling eukaryotic cell to describe cells on micropatterned substrates. This model couples cell morphology, adhesion, and cytoskeletal flow in response to active stresses induced by actin and myosin. We propose that protrusive stresses are only generated where the cell adheres, leading to the cell's effective confinement to the pattern. Consistent with experimental results, simulated cells exhibit a broad range of behaviors, including steady motion, turning, bipedal motion, and periodic migration, in which the cell crawls persistently in one direction before reversing periodically. We show that periodic motion emerges naturally from the coupling of cell polarization to cell shape by reducing the model to a simplified one-dimensional form that can be understood analytically. Additionally, we will discuss a turning instability arising from our model applying onto a free moving cell without interaction with the micropatterned substrates. Some attempts have made to test how the instability depends on the parameters in the model numerically. For a much simplified model, we do find that surface tension is a key factor to stabilize the cell turning.
Tuesday, 29 April 2014
3:30pm – 4:30pm. Monroe 250.
Speaker: Carl Hammarsten (GWU)
Title: Introduction to Spines of 3-manifolds
Abstract: In 1988 Matveev and Piergallini introduced the concept of branched spines as powerful and efficient descriptors of three-manifolds. In this talk, we will present the basic constructions needed to define spines for general manifolds, describe a few simple examples of spines for familiar manifolds, and give a couple nice theorems to indicate their usefulness.
Tuesday, 22 April 2014
2:00pm – 3:00pm. Monroe 267 (Seminar Room).
Speaker: Jing Wang (GWU)
Title: Introduction to Yang-Baxter Homology
Abstract: Yang-Baxter operators have been used to construct link invariants such as Jones Polynomial, HOMFLYPT Polynomial, etc. In this talk, I will introduce Yang-Baxter homology recently discovered by Jozef Przytycki and Victoria Lebed. In particular, the theory is motivated from distributive homology and set-theoretical Yang-Baxter homology.
Friday, 14 February 2014
12:15pm – 1:15pm. Monroe 267 (Seminar Room).
Speaker: Leah Marshall (GWU)
Title: What to LOVE About Computability Theory
Abstract: Happy Valentine's Day everyone! In this talk I will give an overview of computability theory. I will discuss the basic concepts and ideas of the field, the types of things we study, and give some fun examples of "computable" and "noncomputable" objects. This talk should be accessible to all math graduate students.
NB: Leah Marshall's talk was rescheduled for 4 March, 2014.
Thursday, 5 December 2013
4:00pm – 5:00pm. Monroe 267 (Seminar Room).
Speaker: David Shoup (GWU)
Title: Stable Solutions of Phase Separation Problems with the Inclusion of Boundary Droplets
Abstract: In the study of diblock copolymer morphology, a proper range of parameters from both a block composition term and a nonlocal interaction term leads to an equilibrium pattern in which many droplets exist in a planar domain. We determine the subrange of these parameters that allow for a stable solution, as well as map the location of these droplets, which take the form of round discs. Next we introduce the possibility of boundary droplets, and how they may affect the existence and location of interior droplets. Applications to chemistry and the biological sciences are also discussed.
Tuesday, 3 December 2013
5:00pm – 6:00pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Thursday, 14 November 2013
4:00pm – 5:00pm. Monroe 267 (Seminar Room).
Speaker: Thomas J. Savitsky (GWU)
Title: A Catalog of Small 2-polymatroids
Abstract: I will give a brief introduction to integer polymatroids and then discuss a theory of single-element extensions of integer polymatroids analogous to that of matroids. I will then discuss how I used a canonical deletion algorithm to generate a catalog of 2-polymatroids on at most 7 elements (up to isomorphism) with a computer. Note that this is the same technique that Dillon Mayhew and Gordon Royle used in 2007 to construct a catalog of matroids on 9 elements. Surprisingly, the number of 2-polymatroids on 7 elements fails to be unimodal in rank.
Tuesday, 3 November 2013
5:30pm – 6:30pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Thursday, 24 October 2013
3:00pm – 4:00pm. Monroe 267 (Seminar Room).
Speaker: Matthew Gerhart. (George Mason University)
Title: Contact Lenses and Tear Film Evolution.
Abstract: The tears that surround your eye are an integral part of proper eye function. Dry-eye is a condition when the tear film thins to a point where the tear film loses its ability function properly. The use of contact lenses in some patients can increase the likelihood of this condition. Through this talk, I will introduce the mechanics of the tear film (Navier-Stokes Equations) and the mechanics of the motion of the tears in the contact lens (Darcy's Equations), both of which are coupled together, in a thin film, lubrication theory setting. This coupled system is solved numerically and the results are then used to determine the influences certain boundary conditions and material properties of the contact lens have on the drying of the tear film.
Thursday, 10 October 2013
11:00am – 12:00pm. Monroe 267 (Seminar Room).
Speaker: Tim S. Long. (George Mason University)
Title: Ring Extensions Involving Amalgamated Duplication ("Bowtie") Rings.
Abstract: In the last few years interest has grown in commutative algebra in the study of a "forgotten" algebraic construction, now known as an amalgamated duplication of a ring along an ideal (or more simply, a bowtie ring). Most research has involved studying how a ring R sits inside a bowtie ring constructed from it. We will look more generally ring extensions of two bowtie rings on R, and describe topics involving the study of ring extensions, including integrality, going-down, and minimal extensions.
Tuesday, 8 October 2013
5:30pm – 6:30pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Monday, 30 September 2013
11:00am – 12:00pm. Monroe 267 (Seminar Room).
Speaker: Jason Suagee. (The George Washington University)
Title: Constructing Symmetric Cellular Decompositions of 3-manifolds.
Abstract: I will define what is meant by a cellular map on a closed surface with a given permutation-voltage assignment. These objects are useful for constructing cellular maps with high degrees of symmetry. I will then, by way of example, explain one possible direction for generalizing this construction to closed 3-manifolds. Briefly, every 3 manifold M can be viewed as an irregular branched cover over another 3-manifold, with branching set a link L. If one then takes a slightly modified spine of N, one can lift the resulting 2-complex according to the branching data. The result is a cellularly embedded 2-complex in M, with a high degree of symmetry. I will carry out this exact construction when N is S^3, L is a trefoil knot, and M is a certain 3-fold irregular branched cover of S^3 withbranch set L. This will be a slide talk, with pictures.
Tuesday, 24 September 2013
5:30pm – 6:30pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Thursday, 19 September 2013
11:00am – 12:00pm. Monroe 267 (Seminar Room).
Speaker: Steve Schluchter. (The George Washington University)
Title: Ordinary voltage graphs, pseudosurfaces, and derived graph embeddings: lifting cellular homology.
Abstract: Ordinary voltage graph embeddings algebraically and combinatorially encode highly-symmetric embeddings of highly-symmetric graphs in surfaces and pseudosurfaces. We will survey our recent results that partially develop a homological understanding of the encoded embedding that considers specific algebraic and topological properties of the encoding. We will also consider a few infinite families of graphs and and explain the way in which the symmetries of the graphs impact their embeddability in specific surfaces as embeddings encoded by ordinary voltage graph embeddings.
Thursday, 12 September 2013
11:00am – 12:00pm. Monroe 267 (Seminar Room).
Speaker: E. Arthur Robinson, Jr. (The George Washington University)
Title: An Introduction to LaTeX for math students (graduate and undergraduate).
Abstract: LaTeX is the standard software for producing documents with mathematical content. As such, every student of math (physics, statistics, engineering, economics…) should know at least the basics of LaTeX. Despite its prickly reputation, getting started started in LaTeX is easy, and within minutes you can achieve beautiful results. In this lecture, I'll show you how to install and run LaTeX on your computer (Windows, Mac or Linux), type text and type basic math. I'll show you how to produce homework solution sets, research papers (including thesises and dissertations) and lecture slides.
Tuesday, 10 September 2013
5:30pm – 6:30pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Thursday, 29 August 2013
11:00am – 12:00pm. Monroe 267 (Seminar Room).
Graduate Teaching Seminar
Wednesday, 1 May 2013
12:00 – 1:00pm. Monroe 267 (Seminar Room).
Speaker: Jason Suagee (The George Washington University)
Title: Highly symmetric pseudo-cellular decompositions of 3-manifolds.
Abstract: For the purposes of my talk a cellular decomposition of a compact closed 3-manifold M is an embedding of a 2-cell complex K --> M such that the complement M - K is homeomorphic to a disjoint union of 3-Cells. If we loosen the previous condition and allow M - K to include sets of solid g-holed tori we get the notion of a pseudo-cellular decomposition of M. As in the case of cellular decompositions of surfaces, it is worthwhile to have methods available of constructing such decompositions that exhibit high degrees of symmetry. Here, symmetry is interpreted to mean vertex transitivity under an associated automorphism group. In this talk I will present one of several methods of constructing highly symmetric pseudo-cellular decompositions of 3-manifolds using voltage graph techniques. I will also highlight the obvious question of which compact closed 3-manifolds support such highly symmetric decompositions.
Wednesday, 1 May 2013
10:30 – 11:30am. Monroe 267 (Seminar Room).
Speaker: Carl Hammarsten (The George Washington University)
Title: Heegard Floer Homology & Strip Diagrams.
Abstract: Heegaard Floer homology is a collection of invariants for closed oriented three-manifolds, introduced by Ozsvath and Szabo (2004). More recently, Sarkar and Wang (2008) and Ozsvath, Stipsicz, and Szabo (2010/2013) have determined combinatorial methods for computing the simplest version. Both methods rely on the construction of very specific Heegaard diagrams, which are generally very complicated. Matveev and Piergallini (1988) introduced the concept of (branched) spines as efficient and powerful descriptors of three-manifolds. We show that a branched spine gives rise to a natural Heegaard diagram. By comparing our construction with the one by S-W we find a more streamlined combinatorial description for certain manifolds. Our construction's main advantage is a very large "marked region,'' which restricts the total number of generators in the complex. Furthermore, because the "marked region'' does not contribute to the differential maps, the combinatorial complexity of counting differentials is greatly simplified as well. Another advantage of branched spines is that they give rise to a convenient presentation of the Heegaard diagram by a Strip Diagram.
Wednesday, 10 April 2013
12:00 – 1:00pm. Monroe 267 (Seminar Room).
Speaker: Jing Wang (The George Washington University)
Title: An introduction to homology of a small category with functor coefficients and Khovanov type homology.
Abstract: I will start by defining homology of a small category with functor coefficients. As an example, we can realize Khovanov homology in this "category" language. I will also introduce J.Przytycki's idea of relating Hochschild homology with Khovanov homology via the tool of graph cohomology.
Wednesday, 27 March 2013
12:00 – 1:00pm. Monroe 267 (Seminar Room).
Speaker: Jonathan Beagley (George Mason University)
Title: Convex Geometries and The Copoint Graph.
Abstract: We introduce abstract convex geometries. Much as matroids can be thought of as ``discrete vector spaces", convex geometries are ``discrete convex hulls". There are specific convex sets of particular importance, called copoints. In 2006, Morris introduced a graph on the copoints where the cliques in this graph correspond to convexly independent sets in the convex geometry. We discuss results related to the chromatic number of this graph, both generally, and for planar point sets in general position.
Wednesday, 20 February 2013
12:00 – 1:00pm. Monroe 267 (Seminar Room).
Speaker: Tanner Crowder (NRL/Howard University)
Title: Representations of quantum channels.
Abstract: Every qubit channel can be realized as an affine map on the unit ball; the map is called the Bloch representation of the qubit channel. This representation has proven extremely useful in calculating information theoretic quantities associated with the channel. We consider the Bloch representation for n-qubit systems and discuss the applications and challenges with the higher dimensional extension. We will conclude with some open problems in quantum information.
Wednesday, 13 February 2013
12:00 – 1:00pm. Monroe 267 (Seminar Room).
Speaker: Lowell Abrams (The George Washington University)
Title: Cellular Automorphisms of Surfaces.
Abstract: I will outline a precise multi-step process for constructing automorphisms of cellular structures on topological surfaces. As applications, I will then describe two kinds of catalogs of such automorphisms. The first focuses on specific surfaces, and the second (which is under development) focuses on automorphisms that "work" on [nearly] all orientable surfaces.
Wednesday, 6 February 2013
12:00 – 1:00pm. Monroe 267 (Seminar Room).
Speaker: Kai Maeda (The George Washington University)
Title: Representability of the Regular Language by the corresponding Nerve Nets.
Abstract: The Regular Language is a concept in mathematical logic. Each word in the regular language including all formulas in the associated predicate calculus, can be represented as a corresponding element in a partially ordered set. This is the main result by McCulloch and Pitts in their 1943 paper “Logical Calculus of the Ideas Immanent in the Neural Activity". The namesake MCP model of the neural network in human brains employs some simple but accurate assumptions describing anatomical facts about the neural network. This model became the foundation of a field called computational neurology. Some variants of this model have been developed. In this talk, I will introduce some basic facts about the human neural network and its associated mathematical model, a nerve net. I will present a mathematical proof showing the representability of the regular language by this model.
Wednesday, 30 January 2013
12:00 – 1:00pm. Monroe 267 (Seminar Room).
Speaker: Erblin Mehmetaj (The George Washington University)
Title: Generalized Continued Fractions
Abstract: In this talk, I will consider the generalized continued fraction operator $T: [0,1) \to [0,1)$ defined by $T(x) = \frac{r}{x}-\left\lfloor\frac{r}{x}\right\rfloor,$ where r is any real number greater than zero. When r is an integer, I will show explicitly that there is an absolutely continuous T-invariant measure. Additionally, I will show how we can use ergodic theory to study the behavior of the map.
Wednesday, 23 January 2013
12:00 – 1:00pm. Monroe 267 (Seminar Room).
Speaker: Joseph Herning (The George Washington University)
Title: Inconsistent Factors of Substitutions
Abstract: In this talk I will explain the basics of substitution dynamical systems, then I will consider the nature of topological factor systems. Specifically, I will address the question of when we can be sure that a factor of a substitution system is isomorphic to a substitution system. The talk will contain the construction of an isomorphism for a certain case and explain the difficulties of the problem.
Monday, 3 December 2012
1:00 – 2:00pm. Monroe 267 (Seminar Room).
Speaker: Dave Shoup (GWU)
Title: The Mountain Pass Theorem and Its Dependence on the Palais-Smale Compactness Condition
Abstract: Much of PDE theory is devoted to locating minimizers of various energy functionals subject to given constraints. But few theorems deal with the existence of critical points that will not in general be minimizers, but rather saddle points. The Mountain Pass Theorem applies to functionals in which a 'valley' is surrounded by a ring of 'mountains' and under which conditions we are able to find an appropriate 'mountain pass', or saddle point. Without specific compactness conditions this can be quite hard, or even impossible. I will outline this theorem with the aid of visuals, and provide real world applications.
Monday, 19 November 2012
1:00 – 2:00pm. Monroe 267 (Seminar Room).
Speaker: Eric Taylor (Cal. State San Bernardino)
Title: A Few Comments On Whitney's Theorem
Abstract: Whitney's 2-Isomorphism Theorem for graphs is a cornerstone of graph theory. It characterizes when two graphs have isomorphic cycle matroids. We will discuss generalizing Whitney's 2-Isomorphism Theorem to hypergraphs by characterizing when two hypergraphs have isomorphic associated polymatroids.
Monday, 12 November 2012
1:00 – 2:00pm. Monroe 267 (Seminar Room).
Speaker: Chubo Deng (GWU)
Title: Some Analyses of Divergent Series Using Software
Abstract: We will compare the divergence of the sequence of partial sums of the harmonic series with the divergence of the sequence of partial sums of the series $\sum_{primes p} 1/p$. This comparison will be drawn using MATLAB, and the statistical program R. We will also survey a few interesting results about series including primes numbers.
Monday, 5 November 2012
1:00 – 2:00pm. Monroe 267 (Seminar Room).
Speaker: Jason Suagee (GWU)
Title: Group extensions constructed using ordinary voltage graphs
Abstract: A cayley graph for a group G is a directed graph C(G,X) that encodes the multiplicative structure of G, relative to a chosen set of generators X. A group extension of a group G by another group K produces another group E and an epimorphism f: E --> G, such that the kernel of f is isomorphic to K. If K is assumed to be an abelian group, there is a well developed theory of group extensions using some cohomology theory. I will show how a large class of group extensions of G can be constructed from an associated cayley graph C(G,X) by using ordinary voltage graph theory. Using appropriate "voltage assignments" to directed edges, we can produce a graph which covers C(G,X), and also happens to be a cayley graph. This new cayley graph and graph covering map corresponds to a group E and group epimorphism f:E --> G, with kernel K.
Monday, 15 October 2012
1:00 – 2:00pm. Monroe 267 (Seminar Room).
Speaker: Steve Schluchter (GWU)
Title: Ordinary Voltage Graphs and Derived Cellular Homology
Abstract: Ordinary voltage graph imbeddings provide a way to combinatorially encode branched coverings of surfaces. In this short talk, we will introduce ordinary voltage graphs, and present a result concerning the homology of the covering space.
Friday, 2 December 2011
3:35 – 4:30pm. Monroe 353. (Note special time and location).
Speaker: Callie Freitag (GWU)
Title: Modeling the cholera outbreak in post-earthquake Haiti
Abstract: Ten months after a 7.0 magnitude earthquake devastated Haiti, a cholera outbreak began to further ravage the population. Cholera is expected to have affected 500,000 and claimed the lives of over 6,000 Haitians by the end of 2011. Will cholera become endemic to Haiti? What interventions would be most effective at preventing the spread of disease? Mathematical models using ordinary differential equations allow us to predict the extent of the epidemic and simulation the effects of different intervention strategies, like vaccinations. This talk will cover not only the basics of epidemiological modeling, but address the challenges and potential future of cholera prevention in Haiti.
17 November 2011
11:00am. Monroe 267 (Seminar Room).
Speaker: Yongwu Rong (GWU)
Title: Topology and Dynamics of Biological Networks
Abstract: In recent years, networks have been of great interests in many disciplines including mathematics, computer science, biology, and social studies. Such a network often consists of units with various levels of activities that evolve over time, mathematically represented by the dynamics of the network. The interaction between units is represented by the topology of a graph. An interesting problem is to study the connection between topology and dynamics of such networks. In particular, the so called reverse engineering problem asks for the topology of the network given information on its dynamics.
In this talk, we focus on a specific Boolean network model for biological networks. Under this model, the reverse engineering problem is naturally related to the Satisfiability Problem. We show the following results.
(1) The decision problem for network solution can be solved in polynomial time. That is, given information on dynamics, there is a polynomial time algorithm that determines either (a) there is no network which yields the given dynamics or (b) there is such a network. In the case of (b), the algorithm provides a specific network solution.
(2). The problem of finding a "minimal network" with the given property of dynamics is NP-hard.
3 November 2011
11:00am. Monroe 267 (Seminar Room).
Speaker: Erblin Mehmetaj (GWU)
Title: Rohlin's Entropy Formula.
27 October 2011
11:00am. Monroe 267 (Seminar Room).
Speaker: Kai Maeda (GWU)
Title: Turing Degrees of the Isomorphism Types of Structures
Abstract: Richter's degree of a countable algebraic structure is a computability theoretic measure of complexity of its isomorphism class. It has been shown that some classes, such as abelian groups or partially ordered sets, have arbitrary degrees, while other structures, such as linear orderings or trees, have degree 0. In this presentation, I will explain how we measure this degree of complexity of isomorphism types and will survey some known results. Finally, I will further extend these results to structures not previously studied in logic.
20 October 2011
11:00am. Monroe 267 (Seminar Room).
Speaker: Joseph Herning (GWU)
Title: Spectra and topological factors of substitution subshifts
Abstract: The dynamical and diffraction spectra associated with a substitution dynamical system are of interest in many fields including the physics of quasicrystals. I will define these spectra for one-dimensional substitutions and show how to create factors of certain substitutions having interesting spectral properties. This talk includes some new work, and should be accessible to all graduate students.
6 October 2011
11:00am. Monroe 267 (Seminar Room).
Speaker: Tyler White (GWU)
Title: Tilings of the plane via generalized substitutions
29 September 2011
11:00am. Monroe 267 (Seminar Room).
Speaker: Thomas Savitsky (GWU)
Title: A proof of the Tutte-Berge formula via matroids
18 April 2011
4:00pm. Monroe 267 (Seminar Room).
Speaker: Steven Schlucter (GWU)
Title: Algebraic criteria for imbeddability of graphs in surfaces and pseudosurfaces
Abstract: We approach the question of (cellular) graph imbeddability of a graph G in a (pseudo)surface S by attempting to realize S as a 2-complex with 1-skeleton G. We will begin with the well-known results of Whitney and MacLane, and progress to more recent generalizations. We will examine these results in a unified algebraic framework, which treats the edge set of G as a vector space over Z_2.
4 April 2011
4:00pm. Monroe 267 (Seminar Room).
Speaker: Xiaofeng Ren (GWU)
Title: Self-organization phenomena in physical and biological systems
Abstract: Pattern formation problems arise in many physical and biological systems as orderly outcomes of self-organization principles. Examples include animal coats, skin pigmentation, and morphological phases in block copolymers. Recent advances in singular perturbation theory and asymptotic analysis have made it possible to study these problems rigorously. In this talk I will discuss a central theme in the construction of various patterns as solutions to some well known PDE and geometric problems: how a single piece of structure built on the entire space can be used as an ansatz to produce a near periodic pattern on a bounded domain. We start with the simple disc and show how the spot pattern in morphogenesis and the cylindrical phase in diblock copolymers can be mathematically explained. More complex are the ring structure and the oval structure which can also be used to construct solutions on bounded domains. Finally we discuss the newly discovered smoke-ring structure and the toroidal tube structure in space.
21 March 2011
4:00pm. Monroe 267 (Seminar Room).
Speaker: Frank Baginski (GWU)
Title: The Mathematics of Balloons
Abstract: One hundred twenty meter diameter balloons are used by NASA to lift scientific instruments to an altitude of 40 kilometers to carry out science experiments. During ascent, the volume of helium enclosed by the balloon expands by a factor of 300 and the balloon undergoes dramatic shape change. The study of these configurations leads to some challenging mathematical problems in modeling, analysis and computation. In this talk, I will given an introduction to the subject of balloons, discuss recent research, and outline some future projects on balloons and related structures.
7 March 2011
4:00pm. Monroe 267 (Seminar Room).
Speaker: John Conway (GWU)
Title: The Functional Calculus for Operators; Operators Having a Square Root
Abstract: PDF
28 February 2011
4:00pm. Monroe 267 (Seminar Room).
Speaker: Daniel Ullman (GWU)
Title: Multicolorings of graphs
Abstract: In 1995, Saul Stahl published a paper in which he showed that the Groetzsch graph can be colored with 32 colors, placing 11 colors on each vertex, in such a way that adjacent vertices get disjoint color sets. In this talk, I will answer the obvious question about this: Who cares?
Older talks can be found on the old website.