Math Club Colloquium This is an archive of previous colloquia. For current colloquia, please join the facebook group or contact one of the officers. If you would like to give a talk, please send one of us a message. Past Events: 2006-2007 2005-2006 2006 - 2007 Thursday, May 31st at 3:00PM in SH 6617, "Doing research in Number Theory" by Adebisi Agboola, Professor at University of California, Santa Barbara. Thursday, May 24th at 3:00PM in SH 6617, "Doing research in Geometry" by Guofang Wei, Professor at University of California, Santa Barbara. Thursday, May 10th at 3:00PM in SH 6617, "Doing research in Topology" by Stephen Bigelow, Professor at University of California, Santa Barbara. Thursday, April 26th at 3:00PM in SH 6617, "Doing research in Applied Mathematics" by Paul Atzberger, Professor at University of California, Santa Barbara. Thursday, April 26th at 3:00PM in SH 6617, "Doing research in Mathematics" by Jon McCammond and Jeff Stopple, Professor at University of California, Santa Barbara. January 19th 2007: "Consequences of the ABC Conjecture" by Simon Rubinstein-Salzedo, Student at University of California, Santa Barbara The abc conjecture is one of the most important open problems in number theory. Roughly, the abc conjecture says that if a, b, and c are relatively prime, and a+b=c, then at least one of a, b, and c doesn't divide very large powers of any prime. In this talk, we will see some applications of the abc conjecture to other problems and show that it is "almost" good enough to prove Fermat's Last Theorem. November 30th 2006: "Dynamics and Migrations of Schools of Fish" by Bjorn Birnir, Professor at University of California, Santa Barbara The migrations of schools of fish, flocks of birds and herds of mammals can be simulated on computers and computational clusters and analyzed using dynamical systems theory and methods from the emerging theory of complex systems in biology. The recent discovery of migratory, stationary and swarming solutions of models that describe the interactions between individuals can now be used to construct global migrations including environmental effects. These solutions describe migratory, stationary and swarming phases of the schools, flocks and herds. The current focus is on how the animals switch from one phase (say migratory) to another (say stationary) and how environmental and internal effects can implement these changes. Fluctuations in the migratory patterns can be analyzed, and how the migratory patterns are influenced by variations in the environment. These methods are used to study the schools of capelin, a pelagic fish, that have a very extensive (hundreds of miles) migration in the North Atlantic. Newly found solutions that describe very large schools with millions of individuals, based on complex solutions of the Kuromoto model, can be simulated and the results compared to existing data. This data has been collected since the 1970s and shows the spatial distribution of the fish both by acoustic measurements and tagging. Other species of fish for example the herring in the North Atlantic and sardines and anchovies migrating in the Pacific can be simulated using similar methods. These methods can also be used to study the flocking of birds and herding of other animals. November 16th 2006: "Linking and Knotting With Sticks" by Ken Millet, Professor at University of California, Santa Barbara With rods and rubber tubes, we can make flexible polygons of increasing complexity as we increase the number of rods. How many rods are needed to build a specific knot? How many knots can we build with a given number of rods? How much linking can one achieve with a given number of rods? If one constructs something of this sort randomly, what do you most likely get? We will explore what is known about such questions, what is not known, and talk about why anybody would care. November 2nd 2006: "A Summer at Scientific American: Mathematics Writing for the neighbors, your mother, and other math-novices" by Brie Finegold, Graduate Student at University of California, Santa Barbara Ever want to translate that high you get from figuring out a problem after it's stumped you for days? I spent 10 weeks this summer in Manhattan and DC as an AAAS Mass Media Fellow where I learned how to write about science and math for the general public. I'll talk to you about why a world-renown magazine would ever want me, a mathematics graduate student, working for them and why you might want to try the experience yourself. October 19th 2006: "Regular Polytopes Are Everywhere" by Jon McCammond, Professor at University of California, Santa Barbara Most mathematicians know the 2-dimensional regular polygons, the 5 platonic solids (the regular tetrahedron, cube, octahedron, dodecahedron, and icosahedron) and higher dimensional generalizations such as the n-simplex and the n-cube, but not everyone realizes how close this list is to a complete classification of all regular polytopes, or how central this classification is to large portions of current research. In a one-hour talk it should be possible to 1) completely prove the classification theorem for regular polytopes and 2) to give some sense of the range of areas that are influenced by this classification (which includes large portions of algebra, geometry, topology, number theory, even differential equations and mathematical physics). The form in which the regular polytopes and their relatives are visible is usually through the simple graphs called Dynkin diagrams or more cryptically via their names in the Cartan-Killing classification (A_n, B_n, C_n, D_n, G_2, F_4, E_6, E_7, E_8, H_3, and I_2(m)). October 4th 2006: "The Riemann Hypothesis" by Jeff Stopple, Professor at University of California, Santa Barbara RH is one of the Clay Math Institutes million dollar Millenium Prize Problems http://www.claymath.org/millennium/Riemann_Hypothesis/ What does it say about prime numbers? This talk uses only Math 3B level calculus, (as well as some cool computer generated video and audio) to explore the question. 2005 - 2006 August 9th 2006: "Fair Division Games" by Peter Tannenbaum, Professor at California State University, Fresno Imagine dividing a plot of land, an estate, the assets of a bankrupt corporation or just a pizza among a group of players all having a rightful claim to the “goods.” Is it possible to accomplish the division in such a way that each player believes the division is fair? If so, how? Because fairness is such a broad and universal notion, these questions can be approached from ethical, political, economic and psychological perspectives. In this talk I will describe a mathematical approach to the problem. Over the last 50 years, mathematicians have developed procedures that can be viewed as non-strategic games: the players make moves according to a prescribed set of rules and following a set process. If the players play honestly, the process guarantees that each player ends up with at least a fair share (often more). I will illustrate several classic fair division games and discuss some of their limitations and applications. (Many of these games work equally well when the “goods” being divided are really “bads”—duties, obligations, etc.—opening interesting potential applications to issues of pollution control, environmental cleanup, etc.) January 25th 2006: "Visualize Whirled Peas: Efficient Simulation of Many Deformable Objects" by Jeff Danciger, UCSB student It is possible to simulate the interaction of elastic deformable objects to a very high degree of physical accuracy by numerically integrating the differential equations of elastic deformation. However, for this process to be stable we must impose a time step restriction and such a restriction slows down the simulation immensely. For computer animation purposes, these simulations are just too slow. We explore a geomteric method which, while sacrificing physical accuracy, is much more efficient and is therefore more appropriate for use in animation. This project was sponsored in part by Pixar Animation Studios and was completed as part of the 2005 Research in Industrial Projects for Students Program at the Institute for Pure and Applied Mathematics at UCLA. Also, there are several short movies in the presentation! January 18th 2006: "Alcohol's Effect on Neuron Firing" by Arpy Mikaelian, UCSB student