Colloquium Schedule
1998-1999 Colloquia
- An Asteroid Impact Model: A Tale of Two Ice
Shelves
Jamie Gordon, Jeff Mintz, and Andy Oster, Mathematics Department, Cal Poly
One of Cal Poly's Mathematics Modeling Teams presented their Meritorious-Award-winning solution paper in the 1999 Mathematical Contest in Modeling.
Abstract
During the 1999 Mathematical Contest in Modeling the team was asked to study the effects of an asteroid impact at the South Pole. They began with a simple model in which all of the asteroid's kinetic energy was converted into thermal energy used solely to melt ice. This model indicated that the ice melted would not extend beyond the continent's borders. Thus there would be no coastal flooding or damage to food production, and minimal human casualties. They then analyzed the seismic effects of the impact. This new model suggested that there might be an increase in the rate of ice flow to the ocean. If this were the case, there would be some coastal flooding, but still minimal human casualties and no significant damage to food production. - Operator Theory
Seminar
Riemann-Hilbert Approach to Integrable Fredholm Operators
Alexander Its, Indiana University-Purdue University Indianapolis (visiting MSRI, Berkeley)
Abstract
Integrable Fredholm operators, i.e. the integral operators whose commutator with the operator of multiplication by the independent variable has finite rank, play an important role in the theory of random matrices and exactly solvable statistical mechanics and quantum field models. These operators possess a number of remarkable properties which have been extensively discussed in the literature during the last ten years. In particular, the corresponding resolvent kernel can be explicitly evaluated in terms of the solutions of a certain matrix Riemann-Hilbert problem. This observation brings the Riemann-Hilbert asymptotic method of the theory of integrable nonlinear systems into random matrices and statistical mechanics. In the talk, the Riemann-Hilbert approach to the asymptotic analysis of integrable operators will be demonstrated for some concrete examples. - Universality and Scaling for Zeros of
Random
Polynomials
Pavel Bleher, Indiana University-Purdue University Indianapolis (visiting MSRI, Berkeley)
Abstract
A random polynomial is a polynomial whose coefficients are (independent) random variables, real or complex. The basic questions about real random polynomials are:
How many zeros of the polynomial are real on the average?
What is the probability distribution of real zeros?
What is the probability distribution of complex zeros?
What are the correlations between zeros?
etc., asymptotically as the degree N of the random polynomial goes to infinity. Remarkably, in the limit when N goes to infinity the joint distribution of zeros approaches, after an appropriate rescaling, some universal limit, which is characterized by repulsion between zeros at small distances and fast decay of correlations at large distances. - Water, Heat, and
Antarctic Thermodynamics, or Massive Asteroid: Tiny
Hole
Joel Fish, Nathan Royer, and Ryan Tully-Doyle, Mathematics Department, Cal Poly
One of Cal Poly's Mathematics Modeling Teams presented their Meritorious-Award-winning solution paper in the 1999 Mathematical Contest in Modeling.
Abstract
During the 1999 Mathematical Contest in Modeling the team was asked to study the effects of an asteroid impact at the South Pole. They determined that an impact by an asteroid of the dimensions given would have no significant effect. They then generalized the problem to larger asteroids, different impact locations and angles and in each case examined potential casualties and damage. They concluded that either an oblique impact at the pole or a land strike in a non-polar region could result in a significant opaque dust cloud with long term catastrophic effects. An ocean strike could create tsunamis large enough to result in coastal damage, but more importantly would inject enough water into the middle atmosphere to cause a change in the world climate.
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