A BioMath view of critical thresholds and tipping

September 27, 20124:00 PM – 5:00 PM

Druckenmiller Hall, Room 020

BIOLOGY DEPARTMENT WEEKLY SEMINAR SERIES

Mary Lou Zeeman, R. Wells Johnson Professor of Mathematics, "*A BioMath view of critical thresholds and tipping*"

Research Interests:

Geometric dynamical systems, mathematical biology, population dynamics, neuroendocrinology and hormone oscillations, hypothalamus-pituitary interactions, climate modeling and sustainability

Mathematics Department Seminar - Jonathan Lubin

October 23, 20124:15 PM – 5:15 PM

Searles Science Building, Room 217

"The Cantor Set: Source of Surprises, Unlikely Constructions and Counterexamples". ABSTRACT: The Cantor Set is a subset of the unit interval of the real line that gives us many counterexamples to plausible propositions, and examples of interesting phenomena. One surprising use of this set is to define a space-filling curve, that is a continuous map of the unit interval onto the unit square, or indeed onto any convex compact subset of n-dimensional space.

Christie Lecture: "The Pythagorean Theorem Seen from a More Modern Viewpoint" by Jonathan Lubin Oct. 23

October 23, 20127:30 PM – 8:30 PM

Searles Science Building, Room 315

Jonathan Lubin, Professor Emeritus from Brown University, will present the Dan E. Christie Mathematics Lecture on Tuesday, October 23, at 7:30 pm in Searles Science Building, Room 315. The title of his talk is "The Pythagorean Theorem Seen From A More Modern Viewpoint."

Professor Lubin provided the following abstract of his talk:

The Pythagorean Theorem is one of the triumphs of Greek mathematics from around the time of Euclid. They thought of it purely geometrically, speaking of the areas of squares built on the three sides of a right triangle, but we have the advantage of algebra, and express the Theorem in the equation a^{2}+b^{2}=c^{2}, where the three letters represent the lengths of the two legs and the hypotenuse of any right triangle. The most interesting examples of a^{2}+b^{2}=c^{2} are where a,b,c are whole numbers-then a,b,c form a Pythagorean triple. The standard example that comes up again and again in geometric examples is a=3, b=4, c=5, and there are a few others thrown at high-school students. But in fact there are infinitely many essentially different Pythagorean triples.

The Hellenistic-period mathematician Diophantos gave a formula for finding them all, expressed in the cumbersome non-algebraic language of the time, and there is some evidence that the Babylonians about two millennia earlier had pretty much the same information. More modern methods, now taught in all our high schools, allow a clear and understandable method not only to find Diophantos' formulas, but to see why they hold.

Mathematics Department Seminar - Jonathan Lubin

October 24, 20124:15 PM – 5:15 PM

Searles Science Building, Room 217

"Elliptic Curves: A Corner of Mathematics That Became Central". ABSTRACT: The study of elliptic curves sits at the junction of Number Theory and Algebraic Geometry. The field was dormant for a time after an explosion of activity in the nineteenth century, but the Theorem of Mordell, in 1922, about the algebraic structure of the group of rational points of an elliptic curve, stimulated more research, which took flight from the 1960's on. The field provided an essential ingredient to the final proof of Fermat's "Last Theorem", and elliptic curves are being used in some of the most active areas of today's research, for instance they have furnished a tool for attempting to factor the immense composite numbers that are used for many public-key codes. The field has gotten so large and so active that in this talk, it will be possible only to give a taste of the ideas and methods that are encompassed.