Tuesday, April 27, 2010 in Room 714 West Building, 4:00-5:00 PM (First Distinguished Undergraduate RTG Lecture in Number Theory, a Joint Project of Columbia University, CUNY, and New York University)
The function n -> n!
Presented by Benedict Gross, Professor of Mathematics, Harvard University
I will first consider the size of n! when n is large,proving an estimatethat was obtained by de Moivre in the early 18th century. I will then define Euler's gamma function, which is a beautiful extension of the function n! to the real numbers, and will discuss some results on its values at rational numbers. Finally, I will introduce p-adic numbers, and study a p-adic analog of the gamma function. It's values at rational numbers bear a striking resemblance to the values in the real case.
Tuesday, October 27, 2009 in Room 920 East Building, 12 noon (Departmental
Supertropical Matrix Theory
Presented by Louis Rowen, Professor, Bar-Ilan University, Israel
In the previous talk, we discussed supertropical algebra as an algebraic framework for tropical geometry, focusing on roots of polynomials. In this talk (which is self-contained), we study matrices over supertropical algebras, and see how the theory parallels the standard theory of linear algebra (although there are a few surprises). Topics include versions of the determinant, the adjoint, the Hamilton-Cayley theorem, solutions of equations, and the rank of a matrix.
Wednesday, September 9, 2009 in Room 920 East Building, 12:10-1:00 pm (Departmental
Presented by Louis Rowen, Professor, Bar-Ilan University, Israel
Tropical geometry is a new area of mathematics which enables one to study properties of algebraic surfaces by taking logarithms and letting their bases approach zero. In this talk, we present an algebraic structure which supports this theory and describe its properties.
Wednesday, March 18, 2009 in Room 920 East Building, 1:10-2:00 pm (Departmental
The Discrete Charms of Topology
Presented by Murad Ozaydin, Professor of Mathematics, University of Oklahoma
There are theorems in discrete mathematics with con- tinuous proofs (sometimes with no other known proofs). Some examples are Lovasz’s proof of the Kneser Conjec- ture (on the chromatic number of certain graphs) and the prime power case of the Evasiveness Conjecture. These are consequences of classical theorems of topology such as the Borsuk-Ulam theorem or fixed point theorems of Lef- schetz and P. A. Smith. Another (which will be discussed in detail) is Alon and West’s solution (1986) of the Neck- lace Splitting problem: To split an open necklace with N types of gems (with an even number of identical gems of each type) fairly between two thieves N cuts suffice (no matter how many gems there are of each type, or how they are arranged on the necklace). Note that if we have the idiots necklace, i.e., all the rubies together, then all the emeralds, etc., we do need N cuts. The Borsuk-Ulam theorem, which is the key result, can and will be stated using only calculus. Only a little linear algebra may also be relevant in additional related material in convex geometry (if time permits).
Wednesday, February 25, 2009 in Room 920 East Building, 1:10-2:00 pm (Departmental
Computer Graphics and the Geometry of Complex Polynomials
Presented by Linda Keen, Professor of Mathematics, Lehman College and Graduate Center, CUNY
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 qa(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 sequence x0 = 1/2, x1 = qa(x0), x2= qa(x1),..., xn = qa(xn-1 ),... behave? What if we fix a and vary the starting point X0 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.
Wednesday, April 30, 2008 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)
Order or Chaos? Understanding Careers in Different Labor Markets via Clusters
for Nominal Longitudinal Data
Presented by Marc A. Scott, Visiting Associate Professor
at Hunter College and Associate Professor at Department of Humanities
and Social Sciences, School of Education, New York University
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.
Wednesday, April 9, 2008 in Room 920 East Building, 1:10 -2:00 PM (Departmental
One sided quantum groups and the boson-fermion correspondence
Presented by Earl Taft, Professor of Mathematics, Rutgers University
We will review the quantum groups, which are noncommutative Hopf algebra deformations of the rational functions on the general and special linear groups. Then we will indicate some recent one-sided versions of these constructed by A. Lauve, S. Rodriguez and myself. This in turn is related to a recent quantization of the boson-fermion correspondence of classical physics.
Thursday, December 6, 2007 in 1203 HE, 1:00-2:00 pm (Co-sponsored by the Hunter College Chapter of
Sigma Xi and the Thomas Hunter Honors Program)
Shahn's Art and Mid-twentieth Century Science
Presented by Ezra Shahn, Professor of Biological Sciences
at Hunter College
Four years ago, Professor Shahn embarked on a study of the ways in which
episodes in the history of science were reflected in contemporaneous works
of art. Among recent artists, several studies had already noted that images
of science played a significant role in a number of Ben Shahn’s
works. As these were examined, it became clear that they were not random
or artificial, but were actually based on advances in science that had
been made only scant years before the art was created. In fact, these
individual images had identifiable “sources” in the scientific
literature, and, surprisingly, they also jointly represented an illustrated
history of the development of the science of structural molecular biology
that took place in the middle third of the last century.
Wednesday, November 28, 2007 in 920 HE, 2:10-3:00 pm (Departmental Lecture Series)
Propagation of Ultra-short Optical Pulses in Nonlinear and Random Media
Presented by Tobias Schaefer at CUNY Graduate
Center and College of Staten Island of CUNY
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
Wednesday, November 14, 2007 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)
Mathematica as a Powerful Authoring Tool for the Classroom
Presented by John Kiehl, Adjunct Lecturer at Hunter
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.
Thursday, November 8, 2007 in 611 HN, 3:00 – 4:00
pm (Sigma Xi)
Mathematica in the CUBE
Presented by Mimi Tsuruga, student in Hunter's BA/MA
Program in Mathematics
Mathematica is a math application and a powerful visualization tool capable
of generating and rendering 2D and 3D objects with minimal lines of code.
The CUBE (a six-walled CAVE) is a 3D virtual environment at the Beckman
Institute at the University of Illinois at Urbana-Champaign. szgMathematica
is a project which interfaces the Mathematica Kernel with the CUBE Front
End. The CUBE has been used in psychology for experiments in spatial perception,
in biology for studying models of viruses and in medicine for 3D virtual
surgery. In this project a user can send a Graphics3D object using simple
Mathematica code, move the object with a wand, walk into the object or
fly through it on a user-defined curve. This program is ideal for people
who want a "true 3D" visual understanding of complicated 3D
Wednesday, October 10, 2007 in 920 HE, 1:10-2:00 pm (Departmental
with Kriging in the Design of a Product with Multiple Outcomes
Presented by Terrence Murphy at School
of Medicine,Yale University
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, October 3, 2007 in 920 HE, 1:10-2:00 pm (Departmental
A Buckling Problem for Graphene Sheets
Presented by Yevgeniy Milman, student in Hunter's BA/MA
Program in Mathematics
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.