Earle Raymond Hedrick Lecture Series
Olga Holtz, University of California Berkeley and Technical University Berlin
Lecture 1: Zeros of Polynomials via Structured Matrices and Continued Fractions
Thursday, August 1, 10:30 a.m. - 11:20 a.m., Connecticut Convention Center, Ballroom B
Going back to Descartes, Gauss, Laguerre, and other giants of our field, the theory of zero localization attempts to answer questions of the type: given a polynomial, how many of its roots are real? positive? have negative real part? lie in a given disk? etc. A fascinating algebro-analytic theory was gradually built to answer such questions, where structured matrices and continued fractions play a central role. This talk will be devoted to some of these intriguing connections, many classical, some new.
Lecture 2: Approximation Theory Meets Algebra and Combinatorics
Friday, August 2, 9:30 a.m. - 10:20 a.m., Connecticut Convention Center, Ballroom B
What (if anything) do the following things have in common?
integer points in polytopes
spanning trees of graphs
multivariate polynomial interpolation?
Surprisingly, these seemingly unrelated objects have been recently unified within the emerging theory of zonotopal algebra. I will offer its overview, state of the art, and some open problems.
Lecture 3: Communication Complexity of Algorithms
Saturday, August 3, 9:30 a.m. - 10:20 a.m., Connecticut Convention Center, Ballroom B
Unlike arithmetic complexity that measures the amount of computations performed, communication complexity of an algorithm measures the total communication (that is, the amount of data sent and received) between processors in a parallel cluster or levels of memory hierarchy. Since communication is much costlier than arithmetic, the main practical task in this area is minimizing communication and the main theoretical question is finding exact lower bounds on communication. The latter (rather technical) question turns out to have a very elegant answer having to do with graph theory. I will discuss the resulting novel approach to communication in algorithms, illustrate it on Strassen and Strassen-like algorithms for matrix multiplication, and point out some of its practical consequences.
Biography: Olga Holtz received her Diploma in Applied Mathematics from Southern Ural State University in Chelyabinsk, Russia, and her PhD in Mathematics from the University of Wisconsin-Madison under the guidance of Hans Schneider. She held a postdoctorate research position at the Computer Science Department of the University of Wisconsin-Madison, a Humboldt fellowship at the Institute of Mathematics of Technical University Berlin, a Morrey Assistant Professorship and an Associate Professorship at the Department of Mathematics of the University of California-Berkeley. Currently, Holtz is a Professor of Mathematics at the University of California-Berkeley, a Professor of Applied Mathematics at Technical University Berlin, and a Professor of Berlin Mathematical School. She is a Sofja Kovalevskaja awardee, a member of the Junge Akademie of Germany, and a European Mathematical Society Prize winner.
AMS-MAA Joint Invited Address
Coding Theory: A Cornucopia of Mathematics
Thursday, August 1, 9:30 a.m. - 10:20 a.m., Connecticut Convention Center, Ballroom B
Judy Walker, University of Nebraska at Lincoln
Whenever information is transmitted or stored, errors are bound to occur. It is the goal of coding theory to find efficient ways of adding redundancy to the information so that these errors can be corrected. The mathematical study of error-correcting codes began with Claude Shannon's groundbreaking 1948 paper, in which he proved probabilistically that good codes exist. The subsequent challenge has been to actually find or design these good codes; this problem has occupied the minds of many mathematicians, computer scientists and electrical engineers ever since. In addressing Shannon's challenge, many areas of mathematics have been drawn upon, including several that are not typically thought of as "applied math". This talk will give a mathematical tour through coding theory, focusing especially on the wide range of areas such as algebraic geometry, number theory, and graph theory that have played a crucial role in the development of this field.
Biography: Judy Walker received her undergraduate degree from the University of Michigan and both her master's degree and her Ph.D. from the University of Illinois at Urbana-Champaign. She has been at the University of Nebraska Lincoln since 1996, and currently serves as Aaron Douglas Professor and Chair of the Department of Mathematics there. Her research in algebraic coding theory has been continuously supported by the National Science Foundation, and she spent much of the fall 2011 semester as a Visiting Professor at Centre Interfacultaire Bernoulli, EPFL in Lausanne, Switzerland. Dr. Walker is a co-founder of the Nebraska Conference for Undergraduate Women in Mathematics and has served as an elected member of the AWM Executive Committee and the AMS Council. She was the lecturer for the undergraduate portion of the IAS/PCMI Mentoring Program for Women in 1999 and was one of three lecturers at the 2007 Summer School in Coding Theory at the Sophus Lie Conference Center, Nordfjordeid, Norway. She has won several teaching awards, including the Deborah and Franklin Tepper Haimo Award from the MAA, and she served as the MAA's Polya Lecturer for 2009-2011.
MAA Invited Addresses
Algebra, Analysis, and the Way You Eat Corn: The Complete Story
Thursday, August 1, 8:30 a.m. - 9:20 a.m., Connecticut Convention Center, Ballroom B
Susan Loepp, Williams College
It has been conjectured that one can tell an Algebraist from an Analyst by the way she eats corn on the cob. As this talk involves both Algebra and Analysis, all are welcome, regardless of your preferred corn on the cob eating technique. We start with a ring, define a metric on it, and proceed to construct the completion of the resulting metric space. We then consider which algebraic properties of the ring are, or are not, inherited by its completion. We give an overview of completions of rings for a general audience, including recent results, and open questions. Research results obtained by undergraduates will be highlighted. And if you don’t like corn, you’re probably a topologist.
Biography: Susan Loepp received a B.A. in mathematics and a B.S. in physics from Bethel College (N. Newton, KS) in 1989. She earned her Ph.D. in mathematics from the University of Texas at Austin in 1994. After a two-year postdoctoral position at the University of Nebraska, she joined the faculty at Williams College, where she now holds the rank of Professor. Dr. Loepp is currently the principal investigator on the Williams College SMALL REU grant, and has served as the director of the program three times. Her research area is commutative algebra and she has advised the research of many undergraduate students in that field. Loepp also loves teaching, and in 2012, she received the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching. Loepp and William K. Wootters, an expert in quantum information theory, are co-authors of the book "Protecting Information: From Classical Error Correction to Quantum Cryptography," published by Cambridge University Press in 2006.
Improving Numerical Weather Predictions Using Ideas from Nonlinear Dynamics
Friday, August 2, 10:30 a.m. - 11:20 a.m., Connecticut Convention Center, Ballroom B
Chris Danforth, University of Vermont
Modern weather forecasts are initialized with a 10 billion variable estimate of the Earth's atmospheric state. This initial condition is typically the result of 'data assimilation', the process by which satellite observations are combined with prior forecasts to produce a best guess. Predictions of the future state are then made by integrating a collection of perturbations of this best guess, and the resulting variance represents the forecast uncertainty. This talk will discuss the state-of-the-art in weather prediction in the context of our group's efforts to improve forecast methodology. We leverage results from low-dimensional nonlinear dynamical systems to suggest algorithms for reducing forecast error, and demonstrate success using an experimental apparatus analogous to Lorenz's 1963 model of convection.
Biography: Chris Danforth received his Ph.D in 2006 from the University of Maryland, where he worked under the direction of James Yorke and Eugenia Kalnay. Dr. Danforth is currently on the faculty of the University of Vermont where he co-directs the Computational Story Lab, a group of applied mathematicians working on large-scale, system-level problems in many fields including sociology, nonlinear dynamics, networks, ecology, and physics. His research has been covered by the New York Times, Science Magazine, and the BBC among others. Descriptions of his projects are available on his website and blog.
Financial Mathematics: A Two-Way Bridge Between Finance and Mathematics
Saturday, August 3, 10:30 a.m. – 11:20 a.m., Connecticut Convention Center, Ballroom B
Gordan Zitkovic, University of Texas at Austin
Financial mathematics is a relatively recent addition to the spectrum of mathematical disciplines. Like many other mathematical specialties, it aims to provide a rigorous analysis and an abstract reductionist view of a circle of ideas, intuitions, models, observations and beliefs related to a specific "facet of reality". In the case of financial mathematics, the focus is on the structure and dynamics of financial markets and the role played by financial agents acting in them. It builds on fundamental ideas of financial economics, but goes beyond the toy models and does not shy away from embracing the powerful analytical tools contemporary mathematics has to offer. A major attraction of the subject is the breadth of the array of such tools that can be effectively used; they range from classical analysis, partial differential equations and their numerical counterparts over the Banach-space theory and non-locally-convex functional analysis through convex analysis and optimization to probability theory and stochastic analysis. Another -- in a sense dual -- source of appeal of financial mathematics is the degree of enrichment these purely mathematical fields have gained from the relationship. Indeed, problems first encountered in analysis of financial problems led to many mathematical developments in a variety of disciplines. The talk will focus on an assortment of problems illustrating the above mutually beneficial interactions and provide a glimpse of contemporary frontiers of research in this exciting field. It is meant to be accessible to a mathematically mature audience, but no previous exposure to the subject is required.
Biography: Gordan Zitkovic received his PhD in 2003 from Columbia University, under the mentorship of Ioannis Karatzas. After a postdoc at Carnegie Mellon University he joined the Department of Mathematics at the University of Texas at Austin, where he currently holds the position of Associate Professor. His research interests focus on stochastic analysis and optimal control with applications to financial mathematics.
AWM-MAA Etta Z. Falconer Lecture
Improving Equity and Education: Why and How
Friday, August 2, 8:30 a.m. - 9:20 a.m., Connecticut Convention Center, Ballroom B
Patricia Kenschaft, Montclair University
Drawing on both the speaker's own experiences and research and that of others, this talk will explore ideas and behaviors that would improve equity and education, especially in mathematics. She will emphasize the importance of elementary school teachers' knowing the mathematics they are supposed to teach. Why are some powerful people so opposed to teaching them the requisite mathematics? What is equity? How does mathematics education affect equity issues including those of race and gender, but also of economics, ability and personality? What is the connection between innumeracy and the pressing economic and environmental issues of our time? What roles do testing, homework and nurturing responsibility in children play?
Biography: Patricia Clark Kenschaft is Professor Emerita of Mathematics at Montclair State University. She is P.I. on fourteen grants for helping elementary school teachers mathematically, the mother of two, and author, co-author, or co-editor of nine published books, including "Change is Possible: Stories of Women and Minorities in Mathematics" and "Math Power: How to Help Your Child Love Math Even If You Don.t." She holds an A.B from Swarthmore College and a Ph.D. from the University of Pennsylvania. She moderated a radio talk show "Math Medley" for six years, interviewing over 300 people about their relationship to mathematics, including presidents of mathematical organizations, elementary school teachers, and those in apparently unrelated fields. In the national MAA she has been Governor from New Jersey, chair of the Committee on Environmental Mathematics, and first chair of the Committee on Participation of Women. In the latter capacity she moderated and directed micro-inequity skits at national meetings, depicting actual experiences of women in the previous year. She has interviewed over 100 African American mathematicians.
James R. Leitzel Lecture
Statistics Isn’t Mathematics: So How’s That Working Out?
Saturday, August 3, 8:30 a.m. - 9:20 a.m., Connecticut Convention Center, Ballroom B
Ann Watkins, California State University Northridge
Mathematics and statistics faculty have different priorities concerning their overlapping interests in the school mathematics curriculum, the training of teachers, the Advanced Placement program, undergraduate majors, and the introductory statistics course. Has this tension worked to the benefit of our common students? A survey of current issues shows mixed results, some surprising trends, and a need for a continuing emphasis on respectful cooperation.
Biography: Ann Watkins is Professor of Mathematics at California State University, Northridge (CSUN) and specializes in statistics education. Beginning as co-chair of the joint committee of the American Statistical Association and National Council of Teachers of Mathematics, Ann has worked for many years with high school teachers and statisticians to develop materials for teaching statistics and probability in secondary schools and the introductory courses in colleges and to design opportunities for professional development for teachers. She is a co-author of textbooks published as a result of the Quantitative Literacy, Activity-Based Statistics, and Core-Plus Mathematics projects. She chaired the College Board's Development Committee for Advanced Placement Statistics, was exam leader at AP Statistics readings, and was primary author of the AP Statistics Teacher's Guide. She was a member of the Board of Editors of the Journal of Statistics Education. She served as president of the Mathematical Association of America from 2001 to 2003, and has been MAA second vice-president, sectional governor, co-editor of the College Mathematics Journal, and associate editor of the American Mathematical Monthly. She has won the following CSUN awards: Outstanding Professor, Advancement of Teaching Effectiveness, and Extraordinary Service. In 1999, she was elected a Fellow of the American Statistical Association “for innovative contributions to curriculum and pedagogy; for masterful teaching, and teaching of teachers; and for an extraordinary record of sustained and successful efforts to institutionalize reform in statistics education.”
Pi Mu Epsilon J. Sutherland Frame Lecture
Matrices I Admire
Friday, August 2, 8:00 p.m. - 8:50 p.m., Connecticut Convention Center, Ballroom B
Gilbert Strang, Massachusetts Institute of Technology
I will start with my absolute favorite among all matrices. It has 2's down the main diagonal and -1 's on the diagonals just above and just below. It is a Toeplitz matrix (constant diagonals), a second difference matrix (because of -1, 2, -1), and a highpass filter. The matrix is tridiagonal and positive definite and you see it all over pure mathematics too. Its determinant is n+1, and most important are its eigenvectors which are pure sines.
Recently I came back to this well-loved matrix, realizing that I didn't know its symmetric square root, its exponential or its cosine. Those are all badly needed for the heat equation and wave equation. They are not tridiagonal but still amazing. I will speak about another matrix too (the graph Laplacian) as well as the combination of differential equations and linear algebra.
Biography: Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT and an Honorary Fellow of Balliol College. Professor Strang has published eight textbooks: Introduction to Linear Algebra (1993, 1998, 2003, 2009) Linear Algebra and Its Applications (1976, 1980, 1988, 2005) An Analysis of the Finite Element Method, with George Fix (1973, 2008) Introduction to Applied Mathematics (1986) Calculus (1991) Wavelets and Filter Banks, with Truong Nguyen (1996) Linear Algebra, Geodesy, and GPS, with Kai Borre (1997) Computational Science and Engineering (2007) Strang was the President of SIAM during 1999 and 2000, and Chair of the Joint Policy Board for Mathematics. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world. His home page is math.mit.edu/~gs/ and his video lectures on linear algebra and on computational science and engineering are on ocw.mit.edu (mathematics/18.06 and 18.085).
NAM David Blackwell Lecture
Bridging a Gap Between Creative Literacy and Quantitative Literacy: Using Poetry to Improve Quantitative Reasoning
Friday, August 2, 1:00 p.m. – 1:50 p.m., Connecticut Convention Center, Ballroom B
Karen Morgan Ivy, New Jersey City University
How do we as mathematics educators provide alternative ways in which students engage in mathematical discourse and explore mathematical ideas, thereby improving students’ quantitative literacy? How do creative literacy and quantitative literacy conjointly enhance the cognitive and affective domains in the mathematics classroom? The use of mathematics in poetry extends beyond more obvious platforms such as counting syllables or lines and stresses in meter and structure. This talk will offer that teaching mathematics with poetry provides an opportunity to not only address quantitative reasoning, but to also improve students’ quantitative literacy. Writing poetry inspired by mathematics offers students the opportunity to frame mathematical reasoning with arguments grounded in succinctness and clarity of thought processes. Additionally, writing poetry inspired by mathematics bolsters students’ confidence in performing mathematics.
Biography: Karen Morgan Ivy, an Associate Professor of Mathematics at New Jersey City University, is a mathematics educator who earned a Ph.D. from the University of Mississippi in 2001. Her current research interests include examining affective dimensions of math anxiety through student poetry; investigating pre-service teachers’ conceptualization of regrouping and placement value using base n arithmetic; examining the connection between mathematics memories and feelings toward mathematics; integrative learning; and the connection between general education and STEM disciplines, especially Mathematics.
She was awarded the Phi Eta Sigma Outstanding Teacher Award because of her excellence in classroom instruction, her exceptional ability to intellectually stimulate her students, and her genuine concern for the welfare of her students. She was a member of the Steering Committee for the 2012 Infinite Possibilities Conference (IPC), a national initiative designed to promote, educate, encourage and support minority women who are interested in mathematics and statistics.
She welcomes the opportunity to engage in student-learning, pedagogical and content issues at all levels as evidenced by her commitment to serve on the Mathematical Association of America (MAA) Committee for the Teaching of Undergraduate Mathematics (CTUM) for two consecutive terms, on the MAA Committee on Minority Participation in Mathematics (CMPM), and on the New Jersey Association of Mathematics Teacher Educators (NJ AMTE) Executive Board.
She is also a member of several other professional organizations including the National Council of Teachers of Mathematics (NCTM); the National Association of Mathematicians (NAM); the School Science and Mathematics Association (SSMA); the Association of Mathematics Teacher Educators (AMTE ); and the Association of Mathematics Teachers of New Jersey (AMTNJ).
CSHPM Kenneth O. May Lecture
Henri Poincaré: Mathematician, Physicist, Philosopher
Saturday, August 3, 1:00 p.m. – 1:50 p.m., Connecticut Convention Center, Ballroom B
Jeremy Gray, Open University
Henri Poincaré held strong views about human knowledge that animated his work in both mathematics and physics. He held views on the possibly non-Euclidean nature of space, on the foundations of mathematics, on the fundamental ‘laws’ of physics, on why the basic equations of mathematical physics are linear, on space and time, and on theory change in science. These views, and the debates they generated, give a rich insight into the frontiers of research a century ago.
Biography: Jeremy Gray’s first degree is in mathematics from Oxford, and his PhD is from the University of Warwick. In1983—84 he was a Visiting Assistant Professor of Mathematics at Brandeis University, Waltham, Mass, USA, and from September to December 1996 a Resident Fellow at the Dibner Institute for the History of Science and Technology, MIT, Cambridge, USA. In 1998 he gave a 45-minute Invited Lecture at the International Congress of Mathematicians in Berlin on ‘The Riemann-Roch Theorem, 1854--1914’. He is presently a Professor of the History of Mathematics at the Open University, and an Honorary Professor at the University of Warwick, where he lectures on the history of mathematics. In 2009 he was awarded the Albert Leon Whiteman Memorial Prize of the American Mathematical Society for his work on the history of mathematics. His book Plato’s Ghost: The Modernist Transformation of Mathematics, was published by Princeton University Press in 2008, and his scientific biography of Henri Poincaré was published by them in November 2012.
MAA Lecture for Students
Optimal Pentagonal Tilings
Thursday, August 1, 1:00 p.m. - 1:50 p.m., Connecticut Convention Center, Ballroom B
Frank Morgan, Williams College
Hales proved that the least-perimeter way to tile the plane with unit areas is by regular hexagons. What is the least-perimeter way to tile the plane with unit-area pentagons? We will discuss some new results, examples, and open questions, including work by undergraduates.
Biography: Frank Morgan studies optimal shapes and minimal surfaces. He has published over 150 articles and six books, including "Calculus" and "The Math Chat Book," based on his live, call-in TV show and column. He now has a blog at the Huffington Post. Founder of the NSF "SMALL" Undergraduate Research Project, inaugural winner of the MAA’s Haimo teaching award, past vice-president of the MAA and of the AMS, he is Atwell Professor of Mathematics at Williams College.