Everett Pitcher Lecture Series
The Pitcher lectures are held in honor of Everett Pitcher, who served in Lehigh's Department of Mathematics from 1938 until 1978, when he retired as Distinguished Professor of Mathematics. He was secretary of the American Mathematical Society from 1967 until 1988.
For more information call 610-758-3731.
Spring 2013 Everett Pitcher Lectures
Gunnar Carlsson
Anne & Bill Swindells Professor
Professor of Mathematics
Stanford University
In recent years, it has become possible to collect very large amount of data
of extremely varied types. Analyzing these data sets is a problem which is now
recognized as one of the fundamental intellectual problems facing the scientific
and mathematical communities. Topology can be characterized as the study of
shape, and most data sets are equipped with a notion of shape, via a metric
which captures the notion of similarity of data points. From this observation,
one can attempt to adapt topological methods to studying these data. In these
talks, we will present a number of methods based on topological methods and ways
of thinking, with examples.
Monday, March 18, 2013
Measuring the shape of data I : persistent homology
Lewis Lab 270 --- 7:30pm
Lobby reception at 6:45pm
Homology in standard topology is a methodology for "measuring" shape, in terms of
invariants which count occurrences of certain kinds of features or patterns in
topological spaces. It can be adapted to finite metric spaces via a construction
called the Vietoris-Rips complex, which builds an increasing family of complexes
parametrized by the positive real line. One can then evaluate homology groups on
these complexes, and obtain a diagram of vector spaces with shape the real line.
We will describe this construction, together with the associated diagrams of
homology groups, and discuss some applications.
Tuesday, March 19, 2013
Measuring the shape of data II : examples and generalized
persistence
Sinclair Auditorium --- 4:10pm
Persistent homology represents homology of finite metric spaces by diagrams of a
particular shape. Diagrams of other shapes are also useful for other data
analysis question. We will discuss some of these methods, including
multidimensional analogues of persistence, as well as zig-zag persistence,
another extension.
Wednesday, March 20, 2013
Mapping Big Data
Sinclair Auditorium --- 4:10pm
Another direction in topology is the combinatorial representation of shapes,
exemplified by triangulation theorems for manifolds of various kinds. One can
do similar things for point cloud data. We will describe such methods, with
numerous examples.
The lectures are held in honor of A. Everett Pitcher, who was secretary of the AMS from 1967 until 1988. Pitcher served in the mathematics department at Lehigh from 1938 until 1978, when he retired as Distinguished Professor of Mathematics. He died on December 4, 2006, at the age of 94.
Past talks are listed below. Click
hereto go back to the Math Department homepage.
|
Month,Year |
Speaker |
Title of the Talk |
| April, 1983 |
R. Bott |
Some Applications of Equivariant DeRahm Theory |
| December 1983 |
J.-P. Serre |
Rational Points on Algebraic Varieties |
| March, 1985 |
J. Moser |
Stability of Hamiltonian Systems |
| October, 1985 |
M. Atiyah |
The Mystery of Four Dimensions |
| April, 1987 |
J. Tate |
Elliptic Curves and Modular Symbols |
| October, 1987 |
J. Milnor |
Iterated Polynomial Maps |
| April, 1989 |
F. John |
Non-linear Wave Equations, Formation of Singularities |
| March, 1990 |
S. Smale |
Theory of Computation. On the Problem "P != NP" for the Real and Complex Numbers |
| November, 1990 |
J. Tits |
Monster and Moonshine: A Survey |
| April, 1992 |
J. Conway |
Geometry and Numbers |
| April, 1993 |
R. Graham |
Quasi-randomness and Combinatorics |
| October, 1993 |
P. Hall |
Statistical Estimation of Fractal Dimension |
| February, 1994 |
M. Talagrand |
Isoperimetric Inequalities and Concetration of Measure in Product Spaces |
| November, 1994 |
M. Hopkins |
Modular Forms and Stable Homotopy |
| April, 1996 |
C. Pomerance |
Primes: a computational approach |
| March, 1997 |
B. Mandelbrot |
Fractals in Mathematics and the Sciences |
| April, 1998 |
C. Morawetz |
Revisiting the Wave Equation |
| April, 1999 |
H.S. Wilf |
The Recursive Structure of Combinatorial Families |
| March, 2001 |
I. M. Singer |
Index Theory in Mathematics and Physics |
| November, 2001 |
P. Shor |
Quantum Information and Computation |
| July, 2002 |
J. Birman |
Recognizing the Unknot |
| April, 2003 |
J. Arthur |
Automorphic Forms and the Trace Formula |
March 2005
|
Peter Sarnak
|
Arithmetic and analysis on locally symmetric spaces
|
March 2006
|
Sir Roger Penrose
|
Before the Big Bang and Twistor Theory
|
April 2007
|
George E. Andrews
|
The Indian Genius, Ramanujan: His Life and the Excitement of His Mathematics
|
March 2008
|
Persi Diaconis
|
The Search for Randomness
|
March 2009
|
Maria Chudnovsky |
The Perfect Graphs - Structure and Recongition |
| March 2010 |
Rick Durrett |
Three Faces of Probability |
March 2011
|
Manjul Bhargava
|
Quadratic and Higher Degree Forms in Arithmetic
|
April 2012
|
William P. Minicozzi II
|
Singularities in Mean Curvature Flow
|