Wednesday, April 19, 2017 in Room 920 East Building, 1:10-2:10 pm  (GRECS Seminar)
Growth of finitely presented Rees quotients of free inverse semigroups
Presented by Professor David Easdown, School of Mathematics and Statistics at the University of Sydney, Australia
Inverse semigroups are an abstraction of collections of partial one-one mappings of a set closed under composition and inversion.  Free inverse semigroups exist, and resemble free groups, except that in the usual reduction of words, one "remembers" detail about the cancellations that have taken place, captured precisely using concatenation and reduction of Munn trees.   Free inverse semigroups possess ideals, factoring out by which yields Rees quotients, which are also inverse semigroups, now with zero.  When everything is finitely generated, we have usual notions of growth.  Idempotents proliferate when working with inverse semigroup presentations with zero, introducing subtleties and requiring new techniques compared with group or semigroup presentations.  Growth of finitely presented Rees quotients of free inverse semigroups turns out to be polynomial or exponential, and algorithmically recognizable, using modifications of graphical constructions due to De Bruijn, Ufnarovsky, Gilman, and can also be understood with respect to criteria involving height, in the sense of Shirshov.  Polynomial growth is coincidental with satisfiability of semigroup identities, in particular related to Adjan's identity for the bicyclic semigroup.  The boundary between polynomial and exponential growth is also interesting with regard to the notion of deficiency of the presentation, yielding concise sharp lower bounds for polynomial growth, and classifications of classes of semigroups where the lower bounds are achieved.

This is joint work with Lev Shneerson, Hunter College of CUNY.

Wednesday, March 29, 2017 in Room 922 East Building, 1:15-2:25 pm  (CUNY Applied Probability & Statistics Seminar)
Interpreting variation across trials in neurophysiology
Presented by Asohan Amarasingham, Associate Professor, Department of Mathematics, City College of  New York
How do neurons code information, and communicate with one another via synapses?  Experimental approaches to these questions are challenging because the spike outputs of a neuronal population are influenced by a vast array of factors.  Such factors span all levels of description, but only a small fraction of these can be measured, or are even understood.  As a consequence, it is not clear to what degree variations in unknown and uncontrolled variables alternately reveal or confound the underlying signals that observed spikes are presumed to encode.  A related consequence is that these uncertainties also disturb our comfort with common models of statistical repeatability in neurophysiological signal analysis.  I will describe these issues to contextualize tools developed to interpret large-scale electrophysiology recordings in behaving animals, focusing on conceptual issues.  Applications will be suggested to the problems of synaptic and network identification in behavioral conditions as well as neural coding studies.?

Wednesday, March 22, 2017 in Room 922 East Building, 12:15-1:05 pm  (CUNY Applied Probability & Statistics Seminar)
Semi-parametric dynamic factor models for non-stationary time series
Presented by Giovanni Motta, Pontificia Universidad Catolica de Chile
A novel dynamic factor model is introduced for multivariate non-stationary time series. In a previous work, we have developed asymptotic theory for a fully non-parametric approach based on the principal components of the estimated time-varying covariance and spectral matrices. This approach allows both common and idiosyncratic components to be non-stationary in time. However, a fully non-parametric specification of covariances and spectra requires the estimation of high-dimensional time-changing matrices. In particular when the factors are loaded dynamically, the non-parametric approach delivers time-varying filters that are two-sided and high-dimensional. Moreover, the estimation of the time-varying spectral matrix strongly depends on the chosen bandwidths for smoothing over frequency and time. As an alternative, we propose a new approach in which the non-stationarity in the model is due to the low-dimensional latent factors. We distinguish between the (double asymptotic) framework where the dimension of the panel is large, and the case where the cross-section dimension is finite. For both scenarios we provide identification conditions, estimation theory, simulation results and applications to real data.

Wednesday, March 15, 2017 in Room 921 East Building, 12:15-1:05 pm  (GRECS Seminar)
Groups as geometric objects
Presented by Ilya Kapovich, the Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, University of Illinois at Urbana-Champaign
We will give a broad survey of geometric group theory, an active area of mathematics which emerged as a distinct subject in early 1990s and which is located at the juncture of group theory, differential geometry, and geometric topology.  We will discuss the various questions, tools and ideas from geometric group theory, as well as some open problems.  The talk does not assume any prior knowledge of the subject and should be accessible to general audience.

Wednesday, March 1, 2017 in Room 920 East Building, 1:10-2:10 pm  (GRECS Seminar)
Groups and Semigroups with Applications to Computer Science
Algebraic Rigidity and Randomness in Geometric Group Theory
Presented by Ilya Kapovich, the Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, University of Illinois at Urbana-Champaign
Counting particular mathematical structures up to an isomorphism is an important basic mathematical problem.   In many instances, e.g. for counting graphs and finite groups (with various restrictions), good precise or asymptotic counting results are known.   However, until recently very little has been known about counting isomorphism types of finitely presented groups, with various restrictions on the size and the type of a group presentation.   The reason is that, by a classic result of Novikov and Boone, the isomorphism problem for finitely presented groups is algorithmically undecidable.   Even for those classes of groups where the isomorphism problem is decidable, the known algorithms are usually too complicated to help with counting problems.

In this talk we will survey recent progress in this direction, based on joint work with Paul Schupp.  The key results, allowing for asymptotic counting of isomorphism types, involve establishing several kinds of algebraic rigidity properties for groups given by "generic" presentations.  A representative result here is an isomorphism rigidity theorem for generic one-relator groups.  As an application, we compute the precise aymptotics of the number of isomorphism classes of one-relator groups as the length of the defining relator tends to infinity.

Wednesday, February 22, 2017 in Room 920 East Building, 1:10-2:10 pm  (GRECS Seminar)
The primitivity index function for a free group, and untangling closed geodesics on hyperbolic surfaces
Presented by Ilya Kapovich, the Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, University of Illinois at Urbana-Champaign
An important result of Scott from 1980s shows that every closed geodesic on a compact hyperbolic surface can be lifted (or ``untangled") to a simple closed geodesic in some finite cover of that surface.  Recent work of Patel and others initiated quantitative study of Scott's result, which involves understanding the smallest degree of a cover where a closed geodesic ``untangles", compared with the length of the curve.

Motivated by these results of Scott and Patel, we introduce several ``untangling'' indexes for nontrivial elements of a finite rank free group F, such as the ``primitivity index'', the ``simplicity index'' and the ``non-filling index".  We obtain several results about the worst-case behavior of the corresponding index functions and about the probabilistic behavior of the indexes on ``random'' elements of F.

We also discuss applications of these results to the original setting of Scott and Patel of untangling closed geodesics on hyperbolic surfaces.

The talk is based on a joint paper with Neha Gupta, with an appendix by Khalid Bou-Rabee.

Wednesday, November 16, 2016 in Room 920 East Building, 1:10-2:10 pm  (GRECS Seminar)
First-Order Definable Languages and Counter-Free Automata
Presented by Pascal Weil, the Ada Peluso Visiting Professor, Hunter College; Research Professor, National Centre for Scientific Research, Université Bordeaux, France
We will discuss the deep connections between automata theory, formal language theory and logic.  Regular languages (those that are accepted by finite state automata) are known to be exactly those specified by monadic second order logic (MSO).  First-order logic is a very natural fragment of MSO: it is natural to ask whether that fragment is sufficient to specify regular languages (it isn’t!), and to characterize first-order definable languages.  The theorems of Schützenberger and McNaughton-Papert give a nice solution to this problem, with characterizations in terms of automata theory and in terms of regular expressions.  It is however a third characterization, of an algebraic nature (it uses the notion of the syntactic monoid of a language: a finite, effectively computable monoid attached to a regular language), which provides the tools to effectively decide first-order definability.

Quantifier alternation defines a natural hierarchy within first order logic, which yields an infinite hierarchy of within the class of first-order definable languages.  Investigating the decidability of this hierarchy is a challenging and active research area.  Only a few of the lower levels of this hierarchy are known to be decidable.

Pascal Weil is a Research Professor of the highest rank in the National Centre for Scientific Research.  Professor Weil received a Doctorate degree in Informatics from the University of Paris-7 in 1985, a PhD in Mathematics from the University of Nebraska- Lincoln in 1988, and a Habilitation Degree in Informatics from the University of Paris-6 in 1989.  He was director of LaBRI (Bordeaux Research Lab in Computer Science) from 2011 to 2015, as well as the Chair of the Scientific Council for Information Sciences (a national council within CNRS) from 2010 to 2014.  Professor Weil has over 80 publications (including over 50 journal articles) focused on algebraic methods in computer science, notably in the field of automata and formal language theory and algorithmic and combinatorial problems in group theory.

Wednesday, October 19, 2016 in Room 922 East Building, 1:15-2:05 pm 
The 2016 Nobel for the Economics of Contracts:
A Primer on Contract Design Modeling as a Problem of Statistical Inference with Applications in Financial Contracting

Presented by Jonathan Conning, Associate Professor, Department of Economics, Hunter College and the CUNY Graduate Center
The 2016 Nobel Prize in Economics has just been awarded to Oliver Hart and Bengt Holmstrom "for their contributions to contract theory."  This talk will provide a short primer on some of the main modeling ideas in the field of field contract design under asymmetric information, with an emphasis on financial contracting under moral hazard.  Holmstrom's (1979) paper on Moral Hazard and Observability and Grossman and Hart's (1983) paper An Analysis of the Principal-Agent Problem established the modern "state space" approach to the problem which allowed the field to flourish and explode.  In the canonical single-task moral hazard contracting problem a Principal (e.g. landowner, firm owner, investor) wishes to enter into a contract with an Agent (e.g. worker-cum-tenant, employee, entreprenneur/borrower) to carry out a task or project whose stochastic outcome can be described by a statistical distribution which that can be shifted by the agent's choice of action (e.g. the agent's diligence or effort).  When both the project's outcomes and the agent's action choices are both observable and contractible this is just a standard neo-classical problem (e.g. financial contracts with Arrow-Debreu state-contingent commodities and standard asset pricing formulas).  When the agent's actions are not observable the contract design problem becomes a statistical inference and constrained optimization problem: how to design a contract that ties the agent's renumeration to observable outcomes that strikes a balance between providing incentives for the agent to choose a right level of unobserved diligence/effort without imposing too much costly risk.  After establishing a few key results of the canonical case the presentation moves on to study more challenging and interesting contracting situations from Holmstrom's work (and this author's own work) to study multi-task and multi-agent principal agent problems.  I discuss questions such as the possible uses of relative-performance evaluation (tournaments), whether to organize contracting directly through bilateral contracts or via specialized intermediaries of joint-liability structures and other topics and show how the framework is helpful for analyzing key questions in modern corporate finance such as how firms borrow (via bonds, bank debt or equity), the design of microfinance contracts for the (collateral) poor, questions of regulation, the optimal size of banks and ownership structure of banks and much else.

Wednesday, September 28, 2016 in Room 920 East Building, 1:15 pm  (GRECS Seminar)
Algebra in Automata Theory
Presented by Pascal Weil, the Ada Peluso Visiting Professor, Hunter College; Research Professor, National Centre for Scientific Research, Université Bordeaux, France
Automata and formal language theory are cornerstones of theoretical computer science with a strong mathematical flavor.  The basic concepts include finite state automata and regular languages.  Automata are a natural tool to represent and work on regular languages.  Another important tool for specifying regular languages is provided by logic (first order and monadic second order).  Logic is a great specification tool, but it does not have good algorithmic properties, and this is where algebra comes into play.  With every finite state automaton, we can associate a finite algebraic structure, namely a monoid whose algebraic properties reflect the combinatorial or logical properties of the language accepted by the automaton.  The fact that this so-called syntactic monoid is finite and effectively constructible gives us an elegant tool to effectively decide certain properties of regular languages.

Pascal Weil is a Research Professor of the highest rank in the National Centre for Scientific Research.  Professor Weil received a Doctorate degree in Informatics from the University of Paris-7 in 1985, a PhD in Mathematics from the University of Nebraska- Lincoln in 1988, and a Habilitation Degree in Informatics from the University of Paris-6 in 1989.  He was director of LaBRI (Bordeaux Research Lab in Computer Science) from 2011 to 2015, as well as the Chair of the Scientific Council for Information Sciences (a national council within CNRS) from 2010 to 2014.  Professor Weil has over 80 publications (including over 50 journal articles) focused on algebraic methods in computer science, notably in the field of automata and formal language theory and algorithmic and combinatorial problems in group theory.

Wednesday, April 20, 2016 in Room 920 East Building, 1:30-2:30 pm  (GRECS Seminar)
Matrix Identities Involving Multiplication And Transposition
Presented by Mikhail Volkov, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia
Matrices and matrix operations constitute basic tools for algebra, analysis and many other parts of mathematics.  Important properties of matrix operations are often expressed in form of laws or identities such as the associative law for multiplication of matrices.  Studying matrix identities that involve multiplication and addition is a classic research direction motivated by several important problems in geometry and algebra.  Matrix identities involving along with multiplication and addition also certain involution operations (such as taking the usual or symplectic transpose of a matrix) have attracted much attention as well.

If one aims to classify matrix identities of a certain type, then a natural approach is to look for a collection of "basic" identities such that all other identities would follow from these basic identities.  Such a collection is usually referred to as a basis.  For instance, all identities of matrices over an infinite field involving multiplication only are known to follow from the associative law.  Thus, the associative law forms a basis of such "multiplicative" identities.  For identities of matrices over a finite field or a field of characteristic 0 involving both multiplication and addition, the powerful results by Kruse–L'vov and Kemer ensure the existence of a finite basis.  In contrast, multiplicative identities of matrices over a finite field admit no finite basis.

Here we consider matrix identities involving multiplication and one or two natural one-place operations such as taking various transposes or Moore–Penrose inversion.  Our results may be summarized as follows.

None of the following sets of matrix identities admits a finite basis:
• the identities of n×n-matrices over a finite field involving multiplication and usual transposition;
• the identities of 2n×2n-matrices over a finite field involving multiplication and symplectic transposition;
• the identities of 2×2-matrices over the field of complex numbers involving either multiplication and Moore–Penrose inversion or multiplication, Moore–Penrose inversion and Hermitian conjugation;


Wednesday, February 24, 2016 in Room 920 East Building, 1:00-2:00 pm  (GRECS Seminar)
Road Coloring Theorem
Presented by Mikhail Volkov, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia
I shall present a recent advance in the theory of finite automata: Avraam Trahtman's proof of the so-called Road Coloring Conjecture by Adler, Goodwyn, and Weiss; the conjecture that admits a formulation in terms of recreational mathematics arose in symbolic dynamics and has important implications in coding theory.  The proof is elementary in its essence but clever and enjoyable.

Wednesday, February 17, 2016 in Room 920 East Building, 1:00-2:00 pm  (Departmental Lecture Series)
Synchronizing finite automata: a problem everyone can understand but nobody can solve (so far)
Presented by Mikhail Volkov, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia
Most current mathematical research, since the 60s, is devoted to fancy situations: it brings solutions which nobody understands to questions nobody asked” (quoted from Bernard Beauzamy, "Real Life Mathematics", Irish Math. Soc. Bull. 48 (2002), 43-46).  This provocative claim is certainly exaggerated but it does reflect a really serious problem: a communication barrier between mathematics (and exact science in general) and human common sense.  The barrier results in a paradox: while the achievements of modern mathematics are widely used in many crucial aspects of everyday life, people tend to believe that today mathematicians do "abstract nonsense" of no use at all.  In most cases it is indeed very difficult to explain to a non-mathematician what mathematicians work with and how their results can be applied in practice.  Fortunately, there are some lucky exceptions, and one of them has been chosen as the present talk's topic.  It is devoted to a mathematical problem that was frequently asked by both theoreticians and practitioners in many areas of science and engineering.  The problem, usually referred to as the synchronization problem, can be roughly described as the task of determining the simplest way to restore control over a device whose current state is not known:– think of a satellite which loops around the Moon and cannot be controlled from the Earth while "behind" the Moon.  While easy to understand and practically important, the synchronization problem turns out to be surprisingly hard to solve even for finite automata that constitute the simplest mathematical model of real-world devices.  This combination of transparency, usefulness and unexpected hardness should, hopefully, make the talk interesting for a wide audience.

Professor Volkov will also give a semester course on synchronizing automata (Synchronizing Finite Automata: Math 795.64. Th, 7:35-9:25 pm, Room 921 East). The course is basically self-contained as it requires almost no prerequisites; in particular, no prior knowledge of automata theory is assumed. The course contains a detailed overview of the current state-of-the-art in the theory of synchronizing automata and quickly leads to some recent advances of the theory and a number of tantalizing open problems.

Special Year in Hyperbolic Geometry

Hunter College, City University of New York, Room 920 East Building, Fall 2014-Spring 2015

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
Room 919/944 East
695 Park Avenue
New York, NY 10065
Phone: 212-772-5300