MATH 795 (Section 001)
Fall 2008

Mathematics Graduate Seminar

ABOUT THE COURSE

• Lectures: T (3:30 pm - 4:20 pm)
• Venue: Science and Tech I, Room 242
  

INSTRUCTOR

• Office:MATH 222B
• Office Hours: By Appointment
  
• E-mail: pseshaiy@gmu.edu

COURSE EXPECTATION

• Attendance at the presentations is compulsory for all registered students and will contribute to your final grade.
• Graduate Seminar Each week one graduate student will have the opportunity to present a talk on a mathematical research topic. Each talk will be given for a maximum of 20 minutes with a five minute question and answer session. These graduate topics may include ongoing research work or may include research topics from technical papers or advanced graduate texts. The student may use any presentation resources that they like. Other templates that the student may consider using for the presentation are Beamer and Prosper .
• Faculty Mentor and Student Interaction : In order to prepare for this presentation, each student much choose a faculty mentor (at least four weeks in advance), who should work very closely with the student. The mentor may help you to choose the material for your presentation. If you choose the material yourself, make sure that your mentor approves the material (at least three weeks in advance). Once a topic is agreed with the faculty mentor, it is important for the student to make arrangements with the faculty mentor to meet regularly and work on the research in the next three weeks before the presentation. Two weeks before the presentation, the student must meet with the mentor to discuss the outline of the talk. One week before the presentation, the student is encouraged to share the presentation with the mentor. This will give the mentor a chance to share comments and provide feedback that can help improve the talk and presentation skills. To assist the student (and that the student's mentor knows what to do), please fill out along with your mentor the mentor checklist . On Friday before the presentation, the student must email the title and abstract of their talk to the Chair of the seminar.
• Serving as the Chair One graduate student will serve as the Chair of the seminar each week. Chair's duties involves emailing the announcement of upcoming talks, with titles and abstracts to the rest of the class, monday before the talk. Also, the chair will have to prepare one question to ask the speaker.
• Research Seminar Requirement As part of learning about mathematical presentations, each student is required to attend five additional research seminars in math or a related field. The Math Colloquium is an excellent choice, as are the specialized math department seminars. By the last day of classes, a list of the titles and dates of five seminars that the student attended must be submitted to the instructor.
• Writing Requirement There will be one writing requirement that involves writing a short article (in a paper format) related to the talk presented. This paper will be due at the end of the semester.
• Seminar Grading Policy Each student will be graded on the timing and appropriateness of preparation listed in the timeline above, how well they communicate the material to the audience, and how well they understand the material they present and peer evaluations.

GRADING

SCHEDULE OF TALKS

• Speaker: Mr. Robert I. Reznik
  Date: September 16, 2008
  Title: Modeling the Effects of the Electrical Conductivity of Neural Tissue On Spike Propagation
  Abstract : Do the ionic currents flowing in and out of neural cells and into the surrounding tissue influence the behavior of neighboring neurons? How much do these trans-cellular currents (commonly referred to as being an ephaptic effect) modify the state of a quiescent neuron relative to common synaptic processes? How is the propagation of synaptically coupled neurons embedded in their conductive tissue modified by applied electric fields? To answer these questions computational experiments consisting of the numerical integration of 10 x N simultaneous nonlinear ODE's and a large sparse array to solve for the extra-cellular currents were performed. A bifurcation diagram of a single embedded and polarized model neuron is calculated to further our understanding. Finally, results of spike propagation in an embedded chain are presented. This work will be presented at a graduate level although some time will be taken to explain some basic concepts in neuroscience.
• Speaker: Mr. Robert Allen
  Date: September 23, 2008
  Title: Multiplication Operators on the Bloch Space of the Unit Disk
  Abstract : In this talk, we will discuss the multiplication operators on the Bloch space of the unit disk. We will discuss the conditions on which the multiplication operators are bounded and compact. We then discuss new research which include norm estimates, characterization of isometries amongst the multiplication operators, and the computation of the spectrum.
• Speaker: David Johannssen
  Date: September 30, 2008
  Title: What is a Kaehler manifold?
  Abstract : A Kaehler manifold is a manifold equipped with ?compatible? Riemannian metric, complex structure, and symplectic form. In recent years, Kaehler manifolds have found wide applicability in theoretical physics (string theory and supersymmetry theory) and in mathematics (Ricci flat manifolds and Hodge theory and the hard Lefschetz theorem). We hope to give a general understanding of what a Kaehler manifold is and to indicate some of the open problems in Kaehler geometry. We will not presume prior acquaintance with manifold theory.
• Speaker: Tim Long
  Date: October 7, 2008
  Title: Mixed Matrices and Binomial Ideals
  Abstract : For a given vectors u in R^n, we associate the binomial f_u = X^u+ - X^u- where u+ and u- are the positive and negative supports of the vector u, respectively. Then given a finite set of vectors u_1, ..., u_r, we will consider the finitely generated ideal in Z[x] = Z[x_1, ..., x_n]. We will construct a matrix M with these vectors as its rows and then describe some conclusions that can be made about the above ideal, noting only the sign pattern of the entries of M.
• Speaker: Andrew Samuelson
  Date: October 7, 2008
  Title: Effect of Viscoelasticity on the Elastodynamics of Intracranial Aneurysms
  Abstract : In this talk, we will discuss the effect of viscoelasticity in the wall of a cerebral aneursym. An elastodynamic model for a subclass of intracranial saccular aneurysms is presented and analyzed. While no one has fully characterized the conditions under which such aneurysms are dynamically stable, we dis- cuss certain conditions under which they seem to be, and the ways in which viscoelasticity affects stability.
• Speaker: Greg Scott Cochran
  Date: October 21, 2008
  Title: Eigenvalue Expansion of Covariance Matrices using the Newton Polygon
  Abstract : For random fields, there are many questions that seem simple to answer. For an interval (a,b), one of the simplest questions is what is the probability of having a sign change? Although, a simple question, many questions must be answered. Specifically, we must gather information about the asymptotic behavior of the eigenvalues for the covariance matrix. The Newton Polygon is a tool to get the needed asymptotic information.
• Speaker: Javed Siddique
  Date: October 21, 2008
  Title: Capillary rise of liquid into deformable porous materials: theory and experiments
  Abstract : We examine a mathematical model for capillary rise of a fluid into an initially dry and deformable porous material. We use mixture theory to formulate the model. We obtain analytic results for steady state positions of the wet porous material--dry porous material interface as well as liquid--wet material interface. The time-dependent free-boundary problem is solved numerically and the results compared to the steady state predictions. In the absence of gravity, the liquid rises to an infinite height and the porous material deforms to an infinite depth, following square-root in time scaling. In contrast, in the presence of gravity, the liquid rises to a finite height and porous material deforms to a finite depth. We also show results of basic experiments on capillary rise of water into a deformable sponge. Here we measured the capillary rise height and sponge deformation and compared with our theoretical predictions. For early times, the experimental data and theoretical predictions for these interface dynamics are in general agreement but for long time, the long time equilibrium predicted theoretical is not observed in our experimental data. Finally, we also examine the capillary rise of non--Newtonian liquid into deformable porous material. The results are then compared with Newtonian case.
• Speaker: Jill Bigley-Dunham
  Date: October 28, 2008
  Title: Rational Representation of Flowers
  Abstract :A flower is an embedding of the wheel graph in the Euclidean plane as a coin graph. In a given flower with n petals, the radii of the petals satisfy an algebraic equation, that we show is equivalent to a polynomial equation P_n = 0 where P_n belongs to Q[x1, . . . , xn] is irreducible. We will explore the properties of these polynomials and what they can tell us about the underlying graphs. In particular one might ask: when can we realize these flowers, using all rational radii? The case where the number of petals of the flower is 3 has a nice solution. In the case where n is greater than equal to 4, only partial answers are known.
• Speaker: Trey Andreani
  Date: October 28, 2008
  Title: Ehrhart polynomials of cyclic polytopes?
  Abstract : For an integral convex polytope, the Ehrhart polynomial counts the lattice points in dilates of the polytope. I will give a brief introduction to Ehrhart polynomials and what information is encoded in the coefficients when the polytope is cyclic, as is described in the paper ?Ehhart polynomials of cyclic polytope ?by Fu Li
• Speaker: Samah Mahmoud
  Date: November 4, 2008
  Title: Linear Transformations
  Abstract: The goal of this talk is to discuss the different properties of linear transformation and the space they form. It will also discuss the topological properties of this space such as convergence and how it relates to the space of matrices. Finally it will present some results and observations of this space.
• Speaker: Keith Fox
  Date: November 4, 2008
  Title: Remote points and constructions of remote points
  Abstract: This talk will familiarize the audience with remote points and techniques for constructing remote points.
• Speaker: Mike Coleson
  Date: November 11, 2008
  Title: Topological Classifications of Infinite Dimensional Spaces
  Abstract: Infinite dimensional spaces where first classified by Hurewicz(1928) and Alexandroff(1948). However, this area remained underdeveloped until the 1960's, [Engelking 1995]. These classifications are heavily based on two theorems in finite dimensional theory. This talk will review finite dimensional spaces and these two theorems. Then show how they extend to infinite dimension and introduce some dimensional properties of the Hilbert cube and an example by Pol(1981).
• Speaker: Lars Aiken
  Date: November 11, 2008
  Title: The Stone-Cech Compactification of N
  Abstract: Discovered independently by Marshall Stone and Eduard Cech in 1937, the Stone-Cech Compactification of a topological space is the largest compact Hausdorff space in which that space can be densely embedded. We will look at a construction of the Stone-Cech compactification of N and some basic properties of the space obtained.
• Speaker: Andrew Corrigan
  Date: November 18, 2008
  Title: Kernel-Based Meshless Interpolation Using Stationary Refinement
  Abstract: Kernel-based meshless interpolation and a technique for obtaining error estimates in Sobolev spaces due to [Narcowich et al., Math. Comp., 2005] is reviewed. The reason why this technique only applies in the case of nonstationary refinement is then explained. To circumvent this problem, a generalized notion of stationary refinement is proposed and it is then conjectured that there exists a scale of kernels satisfying its requirements which also leads to a convergent kernel-based meshless interpolation scheme.
• Speaker: Jeannie Genoese-Zerbi
  Date: November 18, 2008
  Title: Edge-Magic Graph Labeling
  Abstract: The edge-magic graph is one of many generalizations and extensions of the magic square into the graph theoretic realm. Beginning with a classical problem involving Latin squares, we will discuss the construction of a magic square, and then the edge-magic total labeling of several classes of graphs. We will touch briefly on other types of graph magic labeling, including vertex-magic and antimagic labeling.
• Speaker: Cindy Merrick
  Date: December 2, 2008
  Title: Choquet Simplices in R^n
  Abstract: In the 1950s, the work of Choquet, Rogers, Shephard, and others resulted in the establishment of several fundamental properties and basic theorems about convex sets known as simplices. I'll give a short survey of these properties and theorems.

OPPORTUNITIES

• NSF Graduate Research Fellowship Program(GRFP) : The National Science Foundation aims to ensure the vitality of the human resource base of science, technology, engineering, and mathematics in the United States and to reinforce its diversity by offering approximately 900-1,600 graduate fellowships in this competition pending availability of funds. The Graduate Research Fellowship provides three years of support for graduate study leading to research-based master?s or doctoral degrees and is intended for students who are in the early stages of their graduate study. The Graduate Research Fellowship Program (GRFP) invests in graduate education for a cadre of diverse individuals who demonstrate their potential to successfully complete graduate degree programs in disciplines relevant to the mission of the National Science Foundation. For U.S. citizens, nationals, or permanent resident aliens at or near the beginning of their graduate studies, this program offers a stipend of $30,000 a year for three years and a $10,500 cost of education allowance and a one-time $1,000 travel allowance. For application and deadline information, go to: FASTLANE . For additional program information, go to: NSF-GRFP website for more details. Application open and closes early November.
• Project NExT/Young Mathematician's Network Poster Session : Project NExT and the Young Mathematician's Network invite submissions of abstracts for a poster session to be held on Tuesday, January 6, 2009 from 2:15 to 4:15 p.m. (room TBA) at the Joint Mathematics Meetings in Washington DC. The poster size will be 48" by 36"; it is best to have the posters 36 inch high. Posters and materials for posting pages on the posters will be provided on-site. We expect to accept about thirty posters from different areas within the mathematical sciences. This poster session is intended to highlight the research activities, both mathematical and pedagogical, of recent or future PhD's in mathematics and related fields. The organizers seek to provide an open venue for people who are near completion, or have finished their graduate studies in the last 5 years to present their work and make connections with other same-stage professionals, in much the same spirit as the YMN and Project NExT. Should you have a special requirement involving a computer hook-up, please let us know and we will check to see if it may be accommodated. If you are interested in participating, submit copies of your abstract to: Prof. Mike Axtell Department of Mathematics, OSS 201, 2115 Summit Avenue, University of St. Thomas, St. Paul, MN 55105. Phone: (651) 962-5495 e-mail: AND Prof. Kevin Charlwood, Dept. of Math & Statistics, Morgan Hall 275 I, Washburn University, Topeka, KS 66621. Phone: (785) 670-1499 e-mail: Our poster sessions the past twelve years were a great success. Visitors to the session each year were numerous, and included many prospective employers. This session provides an excellent way to showcase one's work in a relaxed, informal environment. The deadline for final consideration is December 17, 2008. Preference will be given to those who did not earn a Ph.D. prior to 2003; please include with your submission when and where you received your Ph.D., or indicate when you expect to receive it. Please submit your abstract via e-mail, not an attachment. If it includes mathematical formulas, please submit it in basic LaTeX or TeX format. Submissions will be acknowledged quickly by e-mail. Accepted abstracts will be posted here before the Joint Meetings.
• NSA Graduate Mathematics Program : The Graduate Mathematics Program (GMP) is a highly competitive program for exceptional graduate mathematics students. It is a 12-week paid work assignment that runs from the end of May through the middle of August. This program provides students with the opportunity to work directly with NSA mathematicians on missions-critical problems and experience the excitement of the NSA mathematics community first hand. Applicants must be currently enrolled in a mathematical graduate program where he or she has demonstrated superior mathematical aptitude and problem-solving skills. Evidence of successful work on an independent project in pure or applied mathematics or computer science is desirable. Applicants may be at any stage in their graduate careers and working, or intending to work, in any area of mathematics. Computer programming experience, especially C or C++, is desirable. State-of-the-art computing resources are available to GMP participants, as well as computational software packages, such as MATHEMATICA, MATHLAB, MAGMA, MAPLE, and SPLUS. Applications must be received by October 15th. Applications received after the deadline, as well as incomplete packets, will not be considered. To submit a resume online during open season, click any "Apply Online" link and select "View Job Posting/Apply for Job". Under "Student Programs" select "College Summer Programs" and click on the "Search" button. Add "Graduate Mathematics Program" to your "Job Basket" and click on "Apply for Jobs in Basket". Follow directions as prompted. To be considered for any of the summer math programs, you must submit a complete application packet that includes: (a) A resume; (b) At LEAST two teacher recommendations from faculty members familiar with your technical work and; (c)ALL official college transcripts through current academic year. Submit your application package to:
  National Security Agency
  Attn: R1 (DSP/MSEP/GMP)
  9800 Savage Road, Suite 6515
  Ft. George G. Meade, MD 20755-6515
  You may also fax your application materials to (301) 688-0689 or e-mail them to math@NSA.gov. For additional information about our summer math programs, call (301) 688-0983.
• Science, Mathematics and Research for Transformation (SMART) Scholarship for Service Program : The purpose is to promote the education, recruitment and retention of outstanding undergraduate and graduate students in science, mathematics, and engineering studies; the DoD is also interested in supporting the education of future scientists and engineers in a number of interdisciplinary areas. Scholarships awarded include a cash award, full tuition, required fees, and a book allowance. The SMART Program will allow individuals to acquire an education in exchange for a period of employment with the Department of Defense. The program is intended for citizens of the United States; students must be at least 18 years of age to be eligible for an award. Application open and the deadline is December 15, 2008. For information and to apply online, go to SMART .
• The National Defense Science and Engineering Graduate Fellowship Program (NDSEG) The fellowship program is sponsored by the Army Research Office, Office of Naval Research, Air Force Office of Scientific Research and the DoD High Performance Computing Modernization Program. This program is intended for U.S. citizens at or near the beginning of their doctoral studies in science or engineering programs. The fellowships are for three year tenures and include full tuition and fees, a competitive stipend, and a health insurance allowance. The application deadline is January 5, 2009. Go to: NDSEG for applications and detailed program information.
• The National Science Foundation East Asia and Pacific Summer Institutes (NSF-EAPSI) Program : The East Asia and Pacific Summer Institutes provide U.S. graduate students in science and engineering first-hand research experience in Australia, China, Japan, Korea, New Zealand, Singapore orTaiwan. Students receive a $5000.00 stipend and international roundtrip airfare. The primary goals of EAPSI are to introduce students to East Asia and Pacific science and engineering in the context of a research setting, and to help students initiate scientific relationships that will better enable future collaboration with foreign counterparts. The institutes last approximately eight weeks from June to August. Application open and closes December 9, 2008. For additional program information, go to EAPSI .
• The Naval Research Enterprise Intern Program (NREIP) NREIP is a ten week summer research opportunity for undergraduate Juniors & Seniors, and Graduate students, under the guidance of a mentor, at a participating Navy Laboratory. The stipend amounts for the program are $5,500 for undergraduate students and $6,500 for graduate students. U.S. citizenship required; Permanent residents accepted at certain labs (Please see website for details.) The application opens October 15, 2008 and must be completed by January 12, 2009. Go to: NREIP .
• NASA Aeronautics Scholarship Program The purpose of this NASA program is to help advance the nation?s aeronautics enterprise by investing in the educational development of the future aeronautics workforce and to provide opportunities to attract highly motivated undergraduate and graduate students to aeronautics and related fields. Scholarships awarded include competitive stipend payments anticipated amount for undergrad up to $15,000 and up to $35,000 for graduate. There is an option to attend a summer internship (up to $10,000 per summer) at a participating NASA Research Center. The undergraduate program is open to U.S. citizens, and applicants should have completed their sophomore year of college by fall of 2009, and should be in good standing at an accredited college or university. The graduate program is open to U.S. citizens, the applicants should be accepted or enrolled in an accredited program, and remain in good academic standing at their respected college or university. Application is now open and closes January 2009. For more information, send emails to: nasa.asp@asee.org .

ACADEMIC INTEGRITY

DISABILITY ACCOMODATION