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Dolciani Mathematics Learning Center


Riemann Hypothesis Seminar / Departmental Lecture Series / Knot Theory Seminar /
Case Seminar / Sigma Xi
2008 - 2009

Undergraduate Seminar on the Riemann Hypothesis - Spring 2009
Fridays, 920 HE
1:00-1:40pm Instructional Lecture
1:40-2:00pm Tea
2:00-2:50pm Main Lecture
The goal of the seminar is to enable participants to read Riemann’s seminal paper “On the Number of Prime Numbers less than a Given Quantity”. The instructional lecture is geared for students and will provide a primer on complex analysis. The main lecture is open to everyone. A copy of Riemann’s paper is available on Prof. Moreno’s website: http://www.baruch.cuny.edu/math/Riemann_Hypothesis/Riemann%27s_Paper(translation).pdf .

Main Lecture Schedule
February 6 - Prof. Dorian Goldfeld, Columbia University - Historical Introduction
February 13 - Prof. Cormac O’Sullivan, Bronx Community College/CUNY Graduate Center - Integral Representation/Analytic Continuation
February 20 - Prof. Marvin Knopp, Temple University - Functional Equation
February 27 - TBA - Explicit Formula
March 6 (Tea 2:20-2:30pm, Main Lecture 2:30- 3:20) - Prof. Stephen Miller, Rutgers University - Interpretation of Riemann’s Paper Using Distributions
March 13 - No Meeting
Thursday, March 19 (Tea 2:30-3:00 pm, Main Lecture 3:00-3:50pm) - Prof. Leon Ehrenpreis - Temple University - Where Are the Zeroes of Zeta of s? G. Bernhard Riemann Made a Good Guess.
March 27 - TBA - Asymptotic for N(T)
April 3 - TBA - Relation to Prime Number Theorem
April 10 and 17 - Spring break
April 24 - TBA
May 1 - Prof. Carlos Moreno, Baruch College/CUNY Graduate Center - Survey of Influence on Development of Mathematics
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Wednesday, February 25, 2009 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)
Computer Graphics and the Geometry of Complex Polynomials
Presented by: Linda Keen, Professor of Mathematics, Lehman College and Graduate Center, CUNY
Abstract:
The last thirty years have seen incredible developments in understanding the field of dynamical systems and there is every indication that it will continue to be a gold mine for mathematics for many more years to come. One way into the theory is to take a family of functions, like the family q_a(x) = ax(1 - x) of quadratic polynomials, and to apply them repeatedly to a particular value of x. For example, as a varies, is there any difference in how the sequences x_0 = 1/2, x_1 = q_a(x_0), x_2 = q_a(x_1), ... , x_n = q_a(x_n-1), ... behave? What if we fix a and vary the starting point x_0 away from 1/2? Already in these simple cases, we will see there are interesting things to say, and if we allow complex numbers as the values for a and x, rather than just real values, some truly fascinating and beautiful geometry emerges. The famous Mandelbrot set arises from this example. We will see why, and we will see how computer-generated patterns can get our intuition primed to create new mathematics.

Tuesday, December 9, 2008 in 611 HN, 3:30-4:30 pm with refreshments at 3:00 pm (Sigma Xi)
The Earth in Crisis: Pollution of Water in the Biosphere – Current Status and Steps Toward Renewal
Presented by: Spiro D. Alexandratos, Professor of Chemistry, Hunter College
Abstract:
Groundwater is an essential resource yet it is being contaminated with metals and molecules that are highly toxic to plant and animal life. Metals (nickel, cobalt, chromium, copper, lead, cadmium, etc.) may be present at a level of 1 part per million – a level that can be toxic. Compounds that can contaminate groundwater include fuel components, pesticides, and steroids; this is especially serious because some alter the reproductive and endocrine systems of wildlife and humans by acting with estrogen, androgen, and thyroid hormone receptors. Current approaches to the removal of toxic metals from groundwater will be described, including contributions from our laboratory that have led to the development of three polymer-supported reagents: one for the removal of arsenic, one for the removal of radioactive metals, and one for the removal of perchlorate.

Wednesday, December 3, 2008 in 920 HE, 1:10 - 2:00 pm (Departmental Lecture Series)
Eisenstein Series Formed with Eta Multiplier
Presented by Karen Taylor, Visiting Assistant Professor, Hunter College
Abstract:
In 1937 Maass calculated the Fourier coefficients of half-integer weight Eisenstein series with theta multiplier. Dirichlet L-functions appear as factors of these coefficients. In 1985 Goldfeld and Hoffstein exploited this relation to prove asymptotic estimates for the mean value of Dirichlet L-functions. The talk will discuss and define the objects needed to state Goldfeld and Hoffstein's result and attempt to pose a similar problem for an Eisenstein series formed with eta multiplier.

Thursday, November 20, 2008 in 920 HE, 7:40-8:15 pm (Case Seminar)
Method of Lines, a Comprehensive Approach to the Solution of Time Dependent PDE Problems
Presented by Yevgeniy Milman, a student in Hunter's BA/MA Program in Mathematics
Abstract:
The Method of Lines (MOL) is a numerical procedure for solving partial differential equations. The method proceeds in two steps. First, spatial derivatives are approximated using finite differences, finite elements or collocation. This results in an initial value problem (IVP) for a system of ordinary differential equations (ODEs). Second, the system is integrated using well known techniques for solving an IVP. I will outline the techniques for solving IVPs, present the Method of Lines with several examples taken from the physical sciences, and then apply the method to solve a PDE derived from a financial model based on optimum control theory.
This work was supported by the NSF via a Summer 2008 REU program at Hong Kong Polytechnic University.

Thursday, November 13, 2008 in 920 HE, 2:30 – 3:30 pm (Knot Theory Seminar)
Robot Paths: A Configuration Space Approach to Cylindrical Braids
Presented by Michael Vitz, a Mathematics and Physics Major at Hunter College
This work was supported by the NSF via a Summer 2008 REU program in Geometric Group Theory at the University of Illinois at Urbana – Champaign.

Thursday, November 13, 2008 in 920 HE, 7:40 – 8:15 pm (Case Seminar)
The Meaning of Numerical Methods, the Universe and Everything Else
Presented by John Loustau, Professor of Mathematics, Hunter College
Abstract:
In 1953, R. B. Braithwaite gave a metaphor to describe how mathematics interfaces with science. Over the years, this work provided me with an understanding of what I do. Recently, I have found it inadequate and the cause of confusion as I interact with colleagues. Through an example I will identify the problem and propose an extension to the basic paradigm.

 

Departmental Lecture Series
2007-2008


Wednesday, October 3, 2007 in 920 HE, 1:10-2:00 pm
A Buckling Problem for Graphene Sheets
Presented by Yevgeniy Milman, a student in Hunter's BA/MA Program in Mathematics
Abstract:
The speaker develops a continuum model that describes the elastic bending of a graphene sheet interacting with a rigid substrate by van der Waals forces. Using this model, he studies a buckling problem for a graphene sheet perpendicular to a substrate. After identifying a trivial branch, he combines analysis and computation to determine the stability and bifurcations of solutions along this branch. Also presented are the results of atomistic simulations. The simulations agree qualitatively with the predictions of the continuum model but also suggest the importance, for some problems, of developing a continuum description of the van der Waals interaction that incorporates information on atomic positions. This research is based on Mr. Milman’s participation in the Research Experience for Undergraduates (REU) program at the University of Akron in Summer 2007.

Wednesday, October 10, 2007 in 920 HE, 1:10-2:00 pm
Meta-Modeling with Kriging in the Design of a Product with Multiple Outcomes
Presented by Terrence Murphy, PhD, School of Medicine,Yale University
Abstract:
Engineers designing complex products routinely consider a number of outcomes whose desired performance characteristics place contradictory demands on the explanatory variables. In early design stages meta-models, i.e., statistically based models constructed from deterministic data, are used to emulate more sophisticated and computationally intensive simulations that are very accurate. We compare the performance of meta-models based on simple linear regression, Kriging, and splines to the very accurate design solutions yielded by finite element analysis (FEA) in the modeling of multivariate mechanical engineering data in the design of an auto-chassis. We find in our example that the Kriging models most closely reproduce the “true” solution yielded by the FEA simulations in a full information scenario and in some less than full information scenarios based on subsets of principal components.

Wednesday, November 14, 2007 in 920 HE, 1:10-2:00 pm
Mathematica as a Powerful Authoring Tool for the Classroom
Presented by John Kiehl, Adjunct Lecturer, Hunter College
Abstract:
The newest release of the software package Mathematica trivializes the creation of animated and interactive charts, plots, and other graphics. The speaker will create stunning demonstrations within minutes that could be used in a lecture as self-discovery tools for students.

Wednesday, November 28, 2007 in 920 HE, 2:10-3:00 pm
Propagation of Ultra-short Optical Pulses in Nonlinear and Random Media
Presented by Tobias Schaefer, PhD, CUNY Graduate Center and College of Staten Island of CUNY
Abstract:
The basic model for pulse propagation in optical media is the cubic nonlinear Schroedinger equation (NLSE). In the regime of ultra-short pulses, however, the basic assumption made in the derivation of the NLSE from Maxwell’s equations as a slowly varying amplitude approximation is not valid anymore. The speaker will give first a sketch of the derivation of the NLSE from Maxwell’s equations and then discuss applications of the basic model in the context of fiber optics. Then he will present a different approximation, the short-pulse equation and discuss its validity as well as its mathematical properties.

Wednesday, April 9, 2008 in 920 HE, 1:10-2:00 pm
One-sided Quantum Groups and the Boson-fermion Correspondence
Presented by Earl Taft, Professor of Mathematics, Rutgers University
Abstract:
The lecturer will review the quantum groups, which are noncommutative Hopf algebra deformations of the rational functions on the general and special linear groups. Then he will indicate some recent one-sided versions of these constructed by A. Lauve, S. Rodriguez and himself. This in turn is related to a recent quantization of the boson-fermion correspondence of classical physics.

Wednesday, April 30, 2008 in 920 HE, 1:10-2:00 pm
Order or Chaos? Understanding Careers in Different Labor Markets via Clusters for Nominal Longitudinal Data
Presented by Marc A. Scott, Visiting Associate Professor, Hunter College, and Associate Professor, Department of Humanities and Social Sciences, School of Education, New York University
Abstract:
The speaker customizes techniques used in biological sequence analysis to generate homogeneous clusters for nominal longitudinal data in which the number of states is large. The outcomes are career trajectories through a space of “job types,” stratified by long-term economic mobility. He then uses information-theoretic measures to quantify the degree of order or chaos present in these trajectories over time. The clusters and information-theoretic techniques help refine our understanding of certain “stylized facts” about careers with different levels of mobility.
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Department of Mathematics and Statistics


last updated 2/18/09
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Hunter College Department of Mathematics and Statistics
Room 919/944 East
695 Park Avenue
New York, NY 10065
Phone: 212-772-5300
http://math.hunter.cuny.edu