Special Year in Hyperbolic Geometry
Hunter College, City University of New York, Room 921 East Building, Wednesdays, 3:30 pm

The research theme for the academic year 2014-2015 will be the subject of hyperbolic geometry and its many related areas.  The year will feature a series of lectures, an ongoing seminar, and several visitors. During this period the Ada Peluso Visiting Professors will be
Athanase Papadopoulos of the Universite de Strasbourg (Fall 2014).
Hugo Parlier of the University of Fribourg, Switzerland (Spring 2015).

The first two seminars will be given by Ara Basmajian and the next four by Athanase Papadopoulos.  For the latest information about the seminar and abstracts for the talks go to the website: http://wfs.gc.cuny.edu/CArettines/hypgeo/index.html

The Schedule 

October 1, 2014      A Crash Course on Hyperbolic Surfaces I                         

October               A Crash Course on Hyperbolic Surfaces II                       

October 15             On Funk Geometry                                                             

October 22             Hilbert Problem No. IV                                                      

October 29             Spherical and Hyperbolic Geometry                                  

November 5            Spherical and Hyperbolic Trigonometry                           

November 12         Filling Curves on Hyperbolic Surfaces                             

November 19        Angles of Intersection on the Punctured Torus                 

November 26        The Work of Maryam Mirzahani                                          

February 4, 2015   Pants and Infinite Type Surfaces                                             

February 11           Combinatorial Moduli Spaces                                               

February 18          no meeting                                                                              

February 25          Systolic Inequalities and Kissing Numbers for Surfaces     

March 4               presenter, Federica Fanoni (University of Fribourg)             

March 11             Chromatic Numbers for Hyperbolic Surfaces                         

March 18             presenter, Julien Paupert (Arizona State University)           

March 25             presenter, Bram Petri (University of Fribourg)                      

April 1                 Curve Graphs, Pants Graphs and Flip Graphs of Surfaces  

April 8                 no meeting, Spring Break                                                        

April 15               no meeting, MSRI Workshop                                                 

April 22               no meeting, Identities Workshop                                            

April 29               Puzzles, Triangulations and Moduli Spaces -- by Hugo Parlier,                       
      Ada Peluso Visiting Professor, Hunter College;   Professor, University of Fribourg         

CONTACT:  Contact Ara Basmajian (abasmajian@gc.cuny.edu) for further information or questions regarding this special year.

VISITORS:  Enter by way of the Hunter West building, located on the southwest corner of Lexington Avenue and 68th Street.  After going through security, go up to the 3rd floor and walk across the bridge to the East Building. Take the elevator to the 9th floor, Room 921.


Tuesday, March 12, 2013 in Room 714 West Building, 5:30 pm. (Fourth Distinguished Undergraduate RTG Lecture in Number Theory, a Joint Project of Columbia University, CUNY, and New York University)
Taxicabs and the Sum of Two Cubes
Presented by Joseph H. Silverman
Some numbers, such as 9=13+23 and 370=33+73, can be written as the sum of two cubes.  Are there numbers that can be written as the sum of cubes in two (or more) essentially different ways?  This elementary question will lead us into beautiful areas of mathematics where number theory, geometry, algebra, calculus, and even internet security interact in surprising ways.


Wednesday, November 7, 2012 in Room 920 East Building, 1:10-3:00 pm.  Lunch and refreshments served following the talk.  (Soup and Science Series)
A Knot's Tale For Halloween
Presented by Tatyana Khodorovskiy, Assistant Professor of Mathematics, Hunter College of the City University of New York.
Knots have appeared many times in human history, from marine knots to Celtic knots to our own knotted up DNA!  As a mathematical subject, knot theory began in 1867, when Lord Kelvin was working on creating the periodic table of elements.  He proposed that the different chemical properties of atoms can be described by the different ways their tubes of ether are knotted up.  He and physicist Peter Tait went on to compose the first table of knots.  Well, this particular connection didn’t really pan out so well...  Today, however, knot theory is an indispensable part of a field of math called topology.  In this talk, I will define what knots are and discuss their role in life and math.

Wednesday, October 24, 2012 in Room 920 East Building, 1:30-2:30 pm, preceded by a Tea at 1:00 pm (Departmental Lecture Series)
Overgroup Lattices in Finite Groups

Presented by Levi Biock, BA/MA student in Mathematics, Hunter College of the City University of New York.
To answer the Palfy-Pudlak Question, John Shareshian conjectured that a certain class, Dd, of lattices are not overgroup lattices in any finite group.  To prove this conjecture one needs to know the structure of a group G and the embedding of a subgroup H in G, such that there are only two maximal overgroups of H in G and H is maximal in both.  Towards a proof of this conjecture, we consider the minimal normal subgroups of G and use these minimal normal subgroups to determine the structure of G and determine the embedding of H in G.
This work was carried out at SURF 2012, California Institute of Technology, mentor: Michael Aschbacher.


Wednesday, March 7, 2012 in 224 East Building, 1:10-2:30 pm (Soup and Science Series)
Using Geometry To Classify Surfaces

Presented by Ara Basmajian, Professor of Mathematics, Hunter College and the Graduate Center of the City University of New York.
We will begin with the question: What properties do the surface of a basketball and the surface of a football share? In what sense are they the same? In what sense are they different? This discussion will lead naturally to the notion of a surface (a two dimensional space). Next, we introduce the three basic geometries (euclidean, spherical, hyperbolic) and their properties. Hyperbolic geometry, though the least known of the three, plays a prominent, fundamental role in our understanding of surfaces and the geometries they admit. In fact, we will see thet most surfaces admit a hyperbolic geometry. We will finish by mentioning some recent work on three dimensional spaces.

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 Lecture Series)
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 Lecture Series)
Supertropical Algebras
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 Lecture Series)
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 Lecture Series)
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 Lecture Series)
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)
Ben 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 properties.

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 College
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)
3D 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 surfaces.

Wednesday, October 10, 2007 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)
Meta-Modeling 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 Lecture Series)
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.

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Hunter College
Department of Mathematics and Statistics
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New York, NY 10065
Phone: 212-772-5300