The following archive contains abstracts of lectures delivered at the Hunter College Mathematics Department during past years. You can find synopses of lectures by Professors Vincent Guirardel, Alina Vdovina, Catherine Pfaff, Ilya Kapovich, William F. Christensen, and others on topics as varied as germs of analytic diffeomorphisms, Wikipedia editing, algorithmic problems for quasiconvex subgroups of hyperbolic groups, statistics, and software development.

# Lectures

## Past Lectures

**Surface Groups in Germs of Analytic Diffeomorphisms in One Variable
**Wednesday, May 1, 2019 in Room 920 East Building, 1:10-2:00 pm (GRECS Seminar)

Presented by

**Vincent Guirardel**, University of Rennes, France

**Abstract:** Consider the group G of germs of analytic diffeomorphisms at the origin in the complex plane C, i.e. of power series in one variable with positive radius of convergence and with non-zero derivative at 0 (the group law being composition). For instance, given a codimension-one foliation of a complex manifold and a leaf L of this foliation, the holonomy along L gives morphism from the fundamental group of L to G. We prove that the group G contains subgroups isomorphic to the fundamental group of any closed orientable surface, thus answering a question by Ghys. This is a joint work with Cantat, Cerveau and Souto.

*Professor Vincent Guirardel is a leading expert in geometric group theory, geometric topology and dynamics. He has authored numerous papers published in the "Duke Mathematica Journal", "Commentarii Mathematici Helvetici", "Mathematische Annalen", "Geometry and Topology", "Journal of Topology", "Memoirs of the American Mathematical Society", "Asterisque", and other prestigious publication venues. He is a current editor of "The Annalen de la Faculte des Sciences de Toulouse" and of the "Annalen Henri Lebesque". Since 2016 he also serves as the Director of the Center Henri Lebesque in Rennes. He is also a member of the Institut Universitaire de France.*

**Higher-Dimensional Expanders with Applications to Clustering**

Wednesday, April 3, 2019 in Room 921 East Building, 1:10-2:00 pm (GRECS Seminar)

Presented by **Alina Vdovina**, Mathematics, Newcastle University, UK

**Abstract:** We will present explicit constructions of ramanujan graphs and ramanujan complexes, and discuss how extremal spectral properties can be used for optimal cuts of various data sets.

*Alina Vdovina was the Ada Peluso Visiting Professor of Mathematics at Hunter College for Fall 2017 and Spring 2018. She has published 40 papers in a broad range of fields: geometry and analysis on groups acting on buildings, graph theory, construction of new algebraic varieties, geometry of Riemann surfaces, knot theory, constructing C*- algebras and computing their K-theory, non-commutative geometry and operator theory, geometric and combinatorial group theory. Professor Vdovina was an invited speaker at over 20 international conferences and gave over 60 invited research seminar and colloquia talks, invitations for thematic programs at the Max-Planck-Institute, Bonn, Cambridge, Berkeley, ETH Zurich, IHES and Institute Henri Poincare Paris. She received the Lise Meitner award (Germany) in 2002. Some of her ongoing international collaborations include the "Harvard Picture Language Project". She is a trustee of the London Mathematical Society, a member of the LMS Research Grants Committee, and a Fellow of Higher Education Academy (UK).*

**Understanding outer automorphisms of free groups using geodesics in Culler-Vogtmann outer space**

Friday, November 9, 2018 in Room 921 East Building, 1:00-2:00 pm (GRECS Seminar)

Presented by **Catherine Pfaff**, Asst. Professor of Mathematics, Queen's University at Kingston, Ontario, Canada

**Abstract:** Outer space was defined by Culler and Vogtmann in 1986 as a simplicial complex (minus certain faces) on which the outer automorphism group of the free group would act nicely as a symmetry group. Through later developments, representatives of many of these outer automorphisms as geodesics were determined. In this talk I will introduce outer space, these geodesics, and several ways in which we've used them to understand outer automorphisms of free groups.

*About the Speaker: Catherine Pfaff is a tenure-track Assistant Professor of Mathematics at the Queen's University at Kingston in Ontario, Canada. She received a PhD in Mathematics from Rutgers University at New Brunswick in 2012, and has held postdoctoral and visiting positions at the Aix-Marseille University, at the University of Bielefeld, and at the University of California at Santa-Barbara. Catherine's research concentrates on the study of algebraic, probabilistic, dynamical and geometric properties of free group automorphisms.*

**Fibres of Failure: Diagnosing Predictive Models Using Mapper**

Thursday, October 18, 2018 in the Hemmerdinger Screening Room, 7th Fl Library, 5:30-6:30 pm (Department Colloquium)

Presented by **Prof.** **Mikael Veldemo-Johansson**, Department of Mathematics, College of Staten Island, CUNY

**Abstract:** The Mapper algorithm is able to produce intrinsic topological models of arbitrary data in high dimensions. Through a statistical adaptation of the Nerve lemma, the algorithm can be seen to reproduce the topology and parts of the geometry of the data source under assumptions of dense sampling and good parameter choices. In this talk, we will describe how by careful choice of the Mapper model parameters, the resulting topological model can be guaranteed to separate input values to the predictive process for prediction error, grouping high-error and low-error regions separately. This approach produces a diagnostic process where local failure modes can be classified, feeding into either a model development process or a local correction term to improve predictive performance. We have successfully applied this approach to temperature prediction in steel furnaces.

**An Invitation to Wikipedia Editing**

Wednesday, October 17, 2018 in Room 920 East Building, 1:10-2:00 pm (Department Colloquium)

Presented by **Prof.** **Ilya Kapovich**, Department of Mathematics & Statistics, Hunter College, CUNY

**Abstract:** Wikipedia has become an indispensable resource that millions of people use every day as a source of knowledge and information. Yet surprisingly few academics, including scientists and mathematicians, regularly (or ever) edit Wikipedia. In this talk I will discuss the basics of becoming a Wikipedia editor, including the main rules, policies and differences in culture with the academic world. I will also show how to edit Wikipedia on mathematical/scientific topics, both in terms of modifying existing Wikipedia articles and creating new ones. We will conclude with a live demo of posting a brand new math article to Wikipedia. This talk is intended for a broad audience and no specific expertise in mathematics is required.

**Consensus Estimates of Precipitation from Diverse Data Sources in High Mountain Asia**

Wednesday, September 26, 2018 in Room 921 East Building, 2:00-2:30 pm

Presented by **William F. Christensen**, Chair of Statistics, Brigham Young University

Abstract: With the exception of the earth's polar regions, the High Mountain Asia region (including the Tibetan Plateau) contains more of the world's perennial glaciers than any other. Sometimes called the third pole because of its massive storage of ice, High Mountain Asia (HMA) provides water to one-fifth of the world's population. Due to changes in precipitation patterns and temperatures warming faster in HMA than the global average, the region faces increased risk of flooding, crop damage, mudslides, economic instability, and long-term water shortages for the communities down-river. In this talk, we discuss a large, interdisciplinary, multi-institutional research project for characterizing climate change in HMA. We illustrate the use of latent variable models for extracting consensus estimates of spatiotemporally-correlated climate processes from a suite of climate model outputs and remote-sensing observations, and we discuss the uncertainty quantification needed to inform probability-based decision making. We conclude with a discussion of decision making, uncertainty, and the important role of statisticians in framing the public debate about climate change abatement.

**Algorithmic problems for quasiconvex subgroups of hyperbolic groups**

Tuesday, April 24, 2018 in Room 920 East Building, 3:00-4:00 pm (GRECS Seminar)

Presented by **Eric Swenson**, Professor of Mathematics, Brigham Young University

**Abstract:** We discuss algorithms for determining whether a quasiconvex subgroup is almost malnormal and an algorithm for determining the numbers of ends of the pair for a quasiconvex subgroup.

**Methods and Software Development for Interval-Censored Time-to-Event Data**

Friday, March 9, 2018 in Room 920 East Building, 12 noon-1:00 pm

Presented by Chun Pan, Clinical Biostatistician, Novartis Oncology

**Abstract:** Interval-censored time-to-event data occur naturally in studies of diseases where the symptoms of interest are not directly observable, and periodic laboratory or clinical examinations are required for detection. Due to the lack of well- established procedures, interval-censored data have been conventionally treated as right-censored data; however, this introduces bias at the first place. This presentation gives an overview of my current research, which focuses on methodological research and software development for analyzing interval- censored data. Specifically, it will present the three research projects that have been completed. The first project is a Bayesian semiparametric proportional hazards model with spatial random effect for spatially correlated interval- censored data. In the second project, we developed a multiple frailty proportional hazards model with frailty selection for clustered interval-censored data, which is analogous to a mixed model in regression analysis. In the third project, we created an R package “ICBayes” for regression analysis and survival curve estimation of interval-censored data based on several published papers by our research team. At the end, this presentation will lay out some directions for future research.

**Robust Nonparametric Functional Data Analysis Based on Depth**

Friday, March 2, 2018 in Room 920 East Building, 12 noon-1:00 pm

Presented by **Sara Lopez-Pintado**, Professor of Statistics, Columbia University

**Abstract:** Technological development in many emerging research fields has led to the acquisition of large collections of data of extraordinary complexity. In neuroscience for example, brain-imaging technology has provided us with complex collections of signals from individuals in different neurophysiological states in healthy and diseased populations. These signals can be collected and represented as functions. The development of statistical tools to analyze this type of high-dimensional data set is very much needed. I will present new robust methodologies for analyzing functional and imaging data based on the concept of depth. Functional depth provides a rigorous way of ranking a sample of functions from center-outward. This ordering allows us to define robust descriptive statistics such as medians, trimmed means and central regions for functional data. Moreover, data depth is often used as a building block for developing robust statistical methods and outlier-detection techniques. Permutation and global envelope depth-based tests for comparing the locations of two groups of functions or images are proposed and calibrated. The performances of these methods are illustrated in simulated and real data sets. In particular, we tested differences between PET (Positron Emission Tomography) brain images of healthy controls and patients with severe depression. We also used these methods to test differences between the growth pattern of normal and low birth weight children.

**Constrained Factor Models for High-Dimensional Matrix-Variate Time Series**

Friday, February 23, 2018 in Room 920 East Building, 12 noon-1:00 pm

Presented by **Elynn Chen**, Statistics PhD Candidate, Rutgers University

**Abstract:** High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang et al. 2017 proposed a matrix factor model that is shown to provide effective analysis. In this paper, we establish a general framework for incorporating domain or prior knowledge in the matrix factor model through linear constraints. The proposed framework is shown to be useful in achieving parsimonious parameterization, facilitating interpretation of the latent matrix factor, and identifying specific factors of interest. Fully utilizing the prior-knowledge-induced constraints results in more efficient and accurate modeling, inference, dimension reduction as well as a clear and better interpretation of the results. In this paper, constrained, multi-term, and partially constrained factor models for matrix-variate time series are developed, with efficient estimation procedures and their asymptotic properties. We show that the convergence rates of the constrained factor loading matrices are much faster than those of the conventional matrix factor analysis under many situations. Simulation studies are carried out to demonstrate the finite-sample performance of the proposed method and its associated asymptotic properties. We illustrate the proposed model with three applications, where the constrained matrix-factor models outperform their unconstrained counterparts in the power of variance explanation under the out-of-sample 10-fold cross-validation setting.

**Infinite Periodic Groups and Burnside Problems**

Wednesday, December 13, 2017 in Room 921 East Building, 3:00-4:00 pm (GRECS Seminar)

Presented by **Diljit Singh**, Mathematics Major at Hunter College

**Abstract:** We will talk about different formulations of Burnside's problems and list major milestones towards the 1994 result by Zelmanov. We will sketch a short proof of the Golod and Shafarevich theorem and the construction of a counterexample to the General Burnside Problem.

**Analysis of Error Control in Large Scale Two-Stage Multiple Hypothesis Testing**

Wednesday, November 29, 2017 in Room 921 East Building, 1:15-2:15 pm (CUNY Applied Probability and Statistics Seminar)

Presented by **Wenge Guo**, Associate Professor of Statistics, New Jersey Institute of Technology

**Abstract:** When dealing with the problem of simultaneously testing a large number of null hypotheses, a natural testing strategy is to first reduce the number of tested hypotheses by doing screening or selection, and then to simultaneously test selected hypotheses. The main advantage of this strategy is to greatly reduce the severe effect of high dimensions. However, the first screening or selection stage must be properly accounted for in order to maintain some type of error control. In this talk, we will introduce a selection rule based on the selection statistic which is independent of the test statistic when the tested hypothesis is true. Combining this selection rule and the conventional Bonferroni procedure, we can develop a powerful and valid two-stage procedure. The suggested procedure has several nice properties: (i) completely remove the selection effect; (ii) reduce the multiplicity effect; (iii) do not waste any samples while carrying out both selection and testing. Asymptotic power analysis and simulation studies illustrate that this proposed method provides higher power compared to usual multiple testing methods while controlling the type 1 error rate. Optimal selection thresholds are also derived based on our asymptotic analysis. This is a joint work with Joseph Romano from Stanford University.

**Wicks forms and normal forms for the mapping class group of a once punctured surfaces**

Friday, November 17, 2017 in Room 5417 CUNY Graduate Center, 4:00-5:00 pm (NY Group Seminar and GRECS Seminar)

Presented jointly by **Eric Swenson**, Professor of Mathematics, Brigham Young University, and **Alina Vdovina**, the Ada Peluso Visiting Professor, Hunter College

**Abstract:** Mosher obtains a automatic structure on the mapping class group of a once punctured surface of genus $g$ using ideal "triangulations" of the surface. We translate this into the setting of wicks forms of genus $g$ of maximal length, which I think of as a connected cubic graph $\Gamma$ on 4g-2 vertices with specified orientable circuit. Let $v$ be the vertex corresponding to $\Gamma$ in the Mosher complex $Y$. Any other vertex $w$ of $Y$ is uniquely represented as a finite sequence of paths (without backtracking) in $\Gamma$. Any edge path in $Y$ from $v$ to $w$ is realized as a sequence of elementary moves on $Y$ (each of which takes a path without backtracking to a path without backtracking). These moves will change each of the given paths into an empty path.

**Classifying Amalgams**

Wednesday, November 1, 2017 in Room 921 East Building, 1:10-2:14 pm (GRECS Seminar)

Presented by Corneliu Hoffman, University of Birmingham, UK

**Abstract:** We discuss the problem of classifying amalgams that look like the amalgam of small rank Levi subgroups in groups of Kac-Moody type (and some interesting subgroups). It turns out that, under very mild assumptions, these either collapse or are isomorphic to a standard amalgam of a twisted form of the corresponding group of Kac-Moody type. This is a result that is needed in the second generation proof of the Classification of Finite Simple Groups.

*About the Speaker: Corneliu Hoffman obtained his PhD in 1998 from the University of Southern California. Prior to moving to Birmingham held academic positions at the University of California Irvine, and The Mathematical Research Institute in Berkeley and Bowling Green State University in the US. His research interests include various kinds of Group Theory as well as some topics in Computer Assisted Proofs.*

**Ring Theoretic Analogues of C*-Algebras**

Wednesday, October 25, 2017 in Room 921 East Building, 1:10-2:10 pm (GRECS Seminar)

Presented by **Ben Steinberg**, Professor of Mathematics, City College of New York, CUNY

**Abstract:** Many C*-algebras have purely algebraic analogues over an arbitrary base commutative ring. For example, group C*-algebras correspond to group rings. Over the past decade there has been a lot of work on the ring theoretic analogue of Cuntz-Krieger (or graph) C*-algebras, called Leavitt path algebras. There are a number of interesting commonalities between graph C*-algebras and Leavitt path algebras, such as they both have the same criteria for simplicity, primitivity and they both have the same K_0-groups. The proofs however have been entirely different in the analytic and algebraic contexts.

Most of the C*-algebras are examples of groupoid algebras. I recently introduced a ring theoretic analogue of groupoid C*-algebras. The close relations between the C*-algebras and their algebraic counterparts are usually explained by the groupoid. Many other interesting C*-algebras now have purely algebraic versions that are quite natural. Nekrashevych has use groupoid algebras to construct simple algebras of quadratic growth over fields of any characteristic, answering a question of Jason Bell.

In this talk we’ll survey some examples, results and open questions.

**Expander Graphs From Buildings**

Wednesday, October 11, 2017 in Room 920 East Building, 1:15 pm (Department Colloquium)

Presented by **Alina Vdovina**, the Ada Peluso Visiting Professor, Hunter College; Lecturer Pure Mathematics, Newcastle University, United Kingdom

**Abstract:** Expander graphs are one of the deepest tools of several branches of mathematics and theoretical computer science, appearing in all sorts of contexts since their introduction in the 1970s. Expander graphs are graphs which are sparse and highly connected in the same time. We will cover our construction of the first examples of Cayley graph expanders of groups defined explicitly by generators and relations.

*Alina Vdovina (Newcastle University, UK) is the Ada Peluso Visiting Professor of Mathematics at Hunter College for Fall 2017 and Spring 2018. She has published 35 research articles in a broad range of fields: geometry and analysis on groups acting on buildings, graph theory, construction of new algebraic varieties, geometry of Riemann surfaces, knot theory, constructing C*- algebras and computing their K-theory, non-commutative geometry and operator theory, geometric and combinatorial group theory, cryptography. Professor Vdovina was an invited speaker at over 20 International conferences and gave over 60 invited research seminar and colloquia talks, including lectures for thematic programs at the Max-Planck-Institute (Bonn), Cambridge, Berkeley, ETH (Zurich), IHES and Institute Henri Poincare (Paris). She received the Lise Meitner award (Germany) in 2002. Some of her ongoing international collaborations include the "Harvard Picture Language Project". She is a trustee of the London Mathematical Society, a member of the LMS Research Grants Committee, and a Fellow of Higher Education Academy (UK).*

**Growth of finitely presented Rees quotients of free inverse semigroups**

Wednesday, April 19, 2017 in Room 920 East Building, 1:10-2:10 pm (GRECS Seminar)

Presented by Professor David Easdown, School of Mathematics and Statistics at the University of Sydney, Australia

**Abstract:** 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.

**Interpreting variation across trials in neurophysiology**

Wednesday, March 29, 2017 in Room 922 East Building, 1:15-2:25 pm (CUNY Applied Probability & Statistics Seminar)

Presented by Asohan Amarasingham, Associate Professor, Department of Mathematics, City College of New York

**Abstract:** 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.?

**Semi-parametric dynamic factor models for non-stationary time series**

Wednesday, March 22, 2017 in Room 922 East Building, 12:15-1:05 pm (CUNY Applied Probability & Statistics Seminar)

Presented by **Giovanni Motta**, Pontificia Universidad Catolica de Chile

**Abstract:** 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.

**Groups as geometric objects**

Wednesday, March 15, 2017 in Room 921 East Building, 12:15-1:05 pm (GRECS Seminar)

Presented by **Ilya Kapovich**, the Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, University of Illinois at Urbana-Champaign

**Abstract:** 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.

**Groups and Semigroups with Applications to Computer Science**

Wednesday, March 1, 2017 in Room 920 East Building, 1:10-2:10 pm (GRECS Seminar)

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

**Abstract:** 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.

**The primitivity index function for a free group, and untangling closed geodesics on hyperbolic surfaces**

Wednesday, February 22, 2017 in Room 920 East Building, 1:10-2:10 pm (GRECS Seminar)

Presented by **Ilya Kapovich**, the Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, University of Illinois at Urbana-Champaign

**Abstract:** 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.

**First-Order Definable Languages and Counter-Free Automata**

Wednesday, November 16, 2016 in Room 920 East Building, 1:10-2:10 pm (GRECS Seminar)

Presented by **Pascal Weil**, the Ada Peluso Visiting Professor, Hunter College; Research Professor, National Centre for Scientific Research, Université Bordeaux, France

**Abstract:** 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

**Abstract:** 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.

**Algebra in Automata Theory**

Wednesday, September 28, 2016 in Room 920 East Building, 1:15 pm (GRECS Seminar)

Presented by **Pascal Weil**, the Ada Peluso Visiting Professor, Hunter College; Research Professor, National Centre for Scientific Research, Université Bordeaux, France

**Abstract:** 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.*

**Matrix Identities Involving Multiplication And Transposition**

Wednesday, April 20, 2016 in Room 920 East Building, 1:30-2:30 pm (GRECS Seminar)

Presented by Mikhail Volkov, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia

**Abstract:** 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;

**Road Coloring Theorem**

Wednesday, February 24, 2016 in Room 920 East Building, 1:00-2:00 pm (GRECS Seminar)

Presented by **Mikhail Volkov**, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia

**Abstract:** 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.

**Synchronizing finite automata: a problem everyone can understand but nobody can solve (so far)**

Wednesday, February 17, 2016 in Room 920 East Building, 1:00-2:00 pm (Departmental Lecture Series)

Presented by Mikhail Volkov, Ada Peluso Visiting Professor, Hunter College; Professor of Mathematics, Ural Federal University, Russia

**Abstract:** 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.

**Taxicabs and the Sum of Two Cubes**

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) Presented by **Joseph H. Silverman**.

**Abstract:** 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.

**A Knot's Tale For Halloween**

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)

Presented by **Tatyana Khodorovskiy**, Assistant Professor of Mathematics, Hunter College of the City University of New York.

**Abstract:** 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.

**Overgroup Lattices in Finite Groups**

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)

Presented by **Levi Biock**, BA/MA student in Mathematics, Hunter College of the City University of New York.

**Abstract**: 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.*

**On Motions-Continuous, Quasiconformal, and Holomorphic**

Wednesday, March 14, 2012 in Room 920 East Building, 3:00-4:00 pm (Departmental Lecture Series)

Presented by **Sudeb Mitra**, Queens College and the Graduate Center of the City University of New York.

**Abstract:** The idea of holomorphic motions was first introduced by Mane, Sad, and Sullivan, in their study of the dynamics of rational maps. Since then, it has found important applica- tions in many branches of complex analysis and dynamics. An important topic is the question of extending holomorphic motions. In this talk, we will relate that question to contin- uous motions and quasiconformal motions (in the sense of Sullivan and Thurston). We will also give simple examples of holomorphic motions of a finite set over the punctured unit disk, that cannot be extended to the Riemann sphere. If time permits, we will discuss an application in geometric function theory. All basic definitions and motivations will be given.

**Using Geometry To Classify Surfaces**

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

Presented by **Ara Basmajian**, Professor of Mathematics, Hunter College and the Graduate Center of the City University of New York.

**Abstract:** 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 that most surfaces admit a hyperbolic geometry. We will finish by mentioning some recent work on three dimensional spaces.

**Hochschild Complexes and Mapping Spaces**

Wednesday, April 13, 2011 in Room 920 East Building, 3:00-4:00 pm (Departmental Colloquium)

Presented by **Mahmoud Zeinalian**, Long Island University

**Abstract:** Free loop spaces, or more generally spaces of maps from one manifold into another, appear in many branches of mathematics including topology, analysis, differential geometry, quantum field and string theories. In this talk, I will explain, from an elementary view point, how some important geometric objects on these mapping spaces are described in terms of familiar and tractable data on their domains and targets. I will discuss how some rather sophisticated algebraic objects, such as the Hochschild complexes, and the higher dimensional analogues, have their roots in elementary calculus calculations.

**A Quick Trip Through Clifford Algebras**

Wednesday, March 9, 2011 in Room 920 East Building, 3:00-4:00 pm (Departmental Colloquium)

Presented by **Martin Bendersky**, Professor of Mathematics, Hunter College and the City University of New York Graduate Center

**Abstract:** Clifford algebras appear in myriad topics in mathematics. For example, they appear in Diracs quantization of the electron, the theory of elliptic operators (in particular, the Dirac operators) and the study of division algebras. I will focus on their application to constructing vector fields on spheres. The prerequisite is Linear Algebra. The word Tensor will appear in the talk.

**Romberg Integration Using the Midpoint Formula**

Wednesday, November 3, 2010 in Room 920 East Building, 1:10-2:00 pm (Departmental Colloquium)

Presented by **Roger Pinkham**, Professor Emeritus, Stevens Institute of Technology and Visiting Professor at Hunter College, CUNY

**Abstract:** An oft used technique of numerical integration bears the name Romberg. Romberg integration is the shrewd application of a general idea known as Richardson's method of "extrapolation to the limit". It involves repeated application of the trapezoidal rule and allows for repeated re-use of previous function evaluations. Now the midpoint rule uses half the function evaluations and has an error term half that of the trapezoidal rule. As a result, I wondered whether an analog of Romberg integration could be based on the midpoint rule. In this talk I show that it can.

**Unexpected Phenomena in High Dimensions**

Wednesday, April 28, 2010 in Room 920 East Building, 1:00-2:00 pm (Departmental Colloquium)

Presented by **Paul Goodey**, Professor of Mathematics and Chair, University of Oklahoma

**Abstract:** We will discuss a number of geometric phenomena which occur only in high dimensions. These will primarily comprise a mixture of geometry and analysis although some will be purely combinatorial.

**The function n -> n!**

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)

Presented by **Benedict Gross**, Professor of Mathematics, Harvard University

**Abstract:** 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.

**Adding and Counting**

Tuesday, March 8, 2010 in Room 510 North Building, 5:45 PM (Second Distinguished Undergraduate RTG Lecture in Number Theory, a Joint Project of Columbia University, CUNY, and New York University)

Presented by **Ken Ono**, Professor of Mathematics, Emory University / University of Wisconsin, Madison

**Abstract:** In mathematics, the stuff of partitions seems like mere child’s play. The speaker will explain how the simple task of adding and counting has fascinated many of the world’s leading mathematicians: Euler, Ramanu- jan, Hardy, Rademacher, Dyson, to name a few. And as is typical in number theory, many of the most fundamental (and simple to state) questions have remained open. In 2010 the speaker, with the support of the American In- stitute for Mathematics and the National Science Foundation, assembled an international team of distinguished researchers to attack some of these prob- lems. Come hear Professor Ono speak about their findings: new theories which solve some of the famous old questions.

**Supertropical Matrix Theory**

Tuesday, October 27, 2009 in Room 920 East Building, 12 noon (Departmental Lecture Series)

Presented by **Louis Rowen**, Professor, Bar-Ilan University, Israel

**Abstract:** 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.

**Supertropical Algebras**

Wednesday, September 9, 2009 in Room 920 East Building, 12:10-1:00 pm (Departmental Lecture Series)

Presented by **Louis Rowen**, Professor, Bar-Ilan University, Israel

**Abstract:** 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.

**The Discrete Charms of Topology**

Wednesday, March 18, 2009 in Room 920 East Building, 1:10-2:00 pm (Departmental Lecture Series)

Presented by **Murad Ozaydin**, Professor of Mathematics, University of Oklahoma

**Abstract:** 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).

**Computer Graphics and the Geometry of Complex Polynomials**

Wednesday, February 25, 2009 in Room 920 East Building, 1:10-2:00 pm (Departmental Lecture Series)

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 sequence *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.

**Order or Chaos? Understanding Careers in Different Labor Markets via Clusters for Nominal Longitudinal Data**

Wednesday, April 30, 2008 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)

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

**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.

**One sided quantum groups and the boson-fermion correspondence**

Wednesday, April 9, 2008 in Room 920 East Building, 1:10 -2:00 PM (Departmental Lecture Series)

Presented by **Earl Taft**, Professor of Mathematics, Rutgers University

**Abstract:** 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.

**Ben Shahn's Art and Mid-twentieth Century Science**

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)

Presented by **Ezra Shahn**, Professor of Biological Sciences at Hunter College

**Abstract:** 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.

**Propagation of Ultra-short Optical Pulses in Nonlinear and Random Media**

Wednesday, November 28, 2007 in 920 HE, 2:10-3:00 pm (Departmental Lecture Series)

Presented by **Tobias Schaefer** at 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.

**Mathematica as a Powerful Authoring Tool for the Classroom**

Wednesday, November 14, 2007 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)

Presented by **John Kiehl**, Adjunct Lecturer at 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.

**3D Mathematica in the CUBE**

Thursday, November 8, 2007 in 611 HN, 3:00 – 4:00 pm (Sigma Xi)

Presented by **Mimi Tsuruga**, student in Hunter's BA/MA Program in Mathematics

**Abstract:** 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.

**Meta-Modeling with Kriging in the Design of a Product with Multiple Outcomes**

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

Presented by **Terrence Murphy** at 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.

**A Buckling Problem for Graphene Sheets**

Wednesday, October 3, 2007 in 920 HE, 1:10-2:00 pm (Departmental Lecture Series)

Presented by **Yevgeniy Milman**, 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.