# Mathematics Colloquium Spring 2009

Jack Baskin Engineering Room 301A

Refreshments served at 3:40

For further information please contact the Mathematics Department at 459-2969

**April 7, 2009**

**Video: ***The Trillion Dollar Bet*

*The Trillion Dollar Bet*

This NOVA special describes the development of the (in)famous Black-Scholes model of the market for an equity, introduced in the 1973 paper, "The Pricing of Options and Corporate Liabilities." This model has played a pivotal role in the rise of the "quant" in the financial community. http://www.pbs.org/wgbh/nova/stockmarket/ http://en.wikipedia.org/wiki/Black-Scholes

**April 14, 2009**

**Differentiating Between Contact Structures: From Contact Homology to Elementary Invariants**

**Differentiating Between Contact Structures: From Contact Homology to Elementary Invariants**

**Viktor Ginzburg, Professor of Mathematics, UCSC**

**April 21, 2009**

**Talking to the Public about Math**

**Talking to the Public about Math**

**Dana MacKenzie (Freelance Math Writer)**

In this short, half-hour presentation, I will discuss some of the differences between writing about math for other mathematicians and writing about math for the public. Some of the differences are trivial (use active verbs!) and others are important (it's not an article or a paper -- it's a story!). I will also talk about what reporters are looking for in a story, what makes a good press release, and how little most reporters know about math. Mathematicians need to sell their subject and their message to the outside world; after all, other scientists do it. There will be plenty of time for questions after my talk.

**May 12, 2009**

**Exploring Body Shape and Motion**

**Exploring Body Shape and Motion**

**James Davis - Computer Science, UCSC**

Directly sensing the shape and motion of people would enable many new applications. Unfortunately no such sensor yet exists. We hypothesize that a high quality surface prior model of human shape will be sufficient to enable sensing using todays inadequate sensors. We introduce a data-driven method for building a human shape model that spans variation in both subject shape and pose. The method is based on a representation that incorporates both articulated and nonrigid deformations. We learn a pose deformation model that derives the nonrigid surface deformation as a function of the pose of the articulated skeleton. We also learn a separate model of variation based on body shape. Our two models can be combined to produce 3D surface models with realistic muscle deformation for different people in different poses, when neither appear in the training set. We show how the model can be used for shape completion --- generating a complete surface mesh given a limited set of markers specifying the target shape. We present applications of shape completion to partial view completion and motion capture animation. In particular, our method is capable of constructing a high-quality animated surface model of a moving person, with realistic muscle deformation, using just a single static scan of that person. We also show results using this model to recover shape and motion from traditional cameras.

**May 19, 2009**

**Landscape Dynamics in Population Games**

**Landscape Dynamics in Population Games**

**Dan Friedman, Professor, Economics, UCSC and Dan Ostrove, Professor, Math & Computer Science, Santa Clara University**

The payoff or fitness function in a population game defines a "landscape", and each player adjusts her action to move up the payoff gradient. In many cases, the evolution of the action distribution (and of the landscape itself) is described by a non-linear partial differential equation. Such models describe a range of situations in biology, behavioral ecology, politics, economics, and finance.In this talk, we discuss the mathematical properties of these evolution equations and present two applications. The first application is for a financial market. Local interactions are described by a variant of Burgers' equation, and the resulting behavior involves bubbles, crashes and herding behavior described by shock waves. The second is a guessing game with non-local interactions described by an integro-partial differential equation that we will solve explicitly.

**May 22, 2009**

**Minimal Surfaces, Conformal Geometery and Steklov Eigenvalues**

**Minimal Surfaces, Conformal Geometery and Steklov Eigenvalues**

**Ailana Fraser, Stanford University and UBC **

***SPECIAL TIME!!*** Friday, May 22, 2009 3:30-4:30 P.M. Jack Baskin Engineering 301A Refreshments Served at 3:00 P.M.

**May 26, 2009**

**Today's Colloquium has been CANCELLED**

**June 2, 2009**

**Regional Estimates of Greenhouse Gas Emissions from California**

**Regional Estimates of Greenhouse Gas Emissions from California**

**Marc L. Fischer, Staff Scientist, Atmospheric Science Dept., Lawrence Berkeley National Lab**

In 2006, California passed the landmark assembly bill AB-32 to reduce California’s emissions of greenhouse gases (GHGs) that contribute to global climate change. AB-32 commits California to reduce total GHG emissions to 1990 levels by 2020, a reduction of 25 percent from current levels. To verify that GHG emission reductions are actually taking place, it will be necessary to measure emissions. We describe atmospheric inverse model estimates of GHG emissions obtained from the California Greenhouse Gas Emissions Measurement (CALGEM) project. In collaboration with NOAA, we are measuring the dominant long-lived GHGs at two tall-towers in central California. Here, we present estimates of CH4 and N2O emissions obtained by statistical comparison of measured and predicted atmospheric mixing ratios. The predicted mixing ratios are calculated using spatially resolved a priori CH4 and N2O emissions and surface footprints, that provide a proportional relationship between the surface emissions and the mixing ratio signal at tower locations. The footprints are computed using the Weather Research and Forecast (WRF) coupled to the Stochastic Time-Inverted Lagrangian Transport (STILT) model. Integral to the inverse estimates, we perform a quantitative analysis of errors in atmospheric transport and other factors to provide quantitative uncertainties in estimated emissions. Regressions of modeled and measured mixing ratios suggest that total CH4 emissions are within 25% of the inventory estimates but N2O emissions are underestimated by a factor of two. A Bayesian source sector analysis obtains posterior scaling factors for CH4 emissions, indicating that emissions from several of the sources (e.g., landfills, natural gas use, petroleum production, crops, and wetlands) are roughly consistent with inventory estimates, but livestock emissions are significantly higher than the inventory. A Bayesian “region” analysis is used to identify spatial variations in CH4 emissions from 13 sub-regions within California. Although, only regions near the tower are significantly constrained by the tower measurements, CH4 emissions from the south Central Valley appear to be underestimated in a manner consistent with the under-prediction of livestock emissions. Finally, we describe a pseudo-experiment using predicted CH4 signals to explore the uncertainty reductions that might be obtained if additional measurements were made by a future network of tall-tower stations spread over California. These results show that it should be possible to provide high-accuracy estimates of surface CH4 emissions for multiple regions as a means to verify future emissions reductions.