Individual Choices, Cooperation and the Global Commons: Mathematical Challenges in Uniting Ecology and Socioeconomics for a Sustainable Environment.

Speaker: 

Professor Simon Levin

Institution: 

Princeton University

Time: 

Tuesday, February 13, 2007 - 11:00am

Location: 

NS2 1201

We live in a Global Commons, in which the actions of individuals bear costs for society as a whole. The resources we extract for our own uses are no longer available to others, and the toxicants we discharge affect others. The result of this mismatch between individual actions and individual costs is evidenced in the depletion of common resources, the toxification of the environment, and even the frightening loss of effectiveness of the antibiotics that are so fundamental to public health. In the terminology of economists, conventional markets have failed to restrain our harmful activities, like over-consumption, because those markets do not adequately incorporate the social costs, the externalities.

How can we resolve this situation, and develop patterns of social behavior that hold out greater hope for a sustainable future? What can we learn from evolutionary theory, and how can mathematical approaches improve our ability to devise strategies? Not only individuals and corporations, but also societies and nations, act in their own selfish interest, leading to problems for the biosphere as a whole. This lecture will explore how, and under what conditions, cooperation and altruism have arisen in the process of evolution; why social norms, including punishment, have arisen to reinforce socially beneficial behavior; and how those social norms can lead to inter-group conflicts. Attention will be addressed to the socioeconomic systems in which environmental management is based, and ask what lessons can be learned from our examination of natural systems, and how we can modify social norms to achieve global cooperation in managing our common future.

Recent progress on Serre's conjectures.

Speaker: 

Professor Kenneth Ribet

Institution: 

UC Berkeley

Time: 

Thursday, May 24, 2007 - 4:00pm

Location: 

MSTB 254

Over the last 15 years, there have been tremendous advances in our understanding of the connections among modular forms, Galois representations and algebraic varieties. Undoubtedly, the most spectacular development in this subject was the proof of Fermat's Last Theorem, which was completed in 1994. Beginning in the late 1960s, J-P. Serre proposed links of various kinds between modular forms and representations of Galois groups. In 1987, Serre wrote a seminal article that included precise conjectures relating mod p Galois representations and mod p modular forms. These conjectures were so powerful and general that they were inaccessible by then-current methods. Amazingly, these conjectures have been proved over the last two years, with the final step being contributed only several months ago. The main ideas are due to Khare and Wintenberger, with major contributions from Kisin and others. My talk will explain the history of the conjectures and some elements of the ingenious proof.

Knoted Solitons in the Faddeev and Skyrme Models

Speaker: 

Fanghua Lin

Institution: 

Courant Institute of New York University

Time: 

Wednesday, January 11, 2006 - 2:00pm

Location: 

MSTB 254

Here we give a brief survey on recent mathematical works concerning the Faddeev and Skyrme models.One of the most facinating phenomena descibed by these models are the knoted topological soliton solutions which are fundamentally different from many other well-known feild theory models such as instantons and monopoles in the Yang-Mills or the general gauge field theory,bubbles in the nonlinear sigma models or ferromagnetisms and vortices in superconductors and superfluids.In this lecture we shall illustrate some key features of these models that lead to the exisitence of stable knoted solitons and to discuss some possible implications in other problems.

Conserved Quantities and Analysis on Multiscale Problems

Speaker: 

Fanghua Lin

Institution: 

Courant Institute of New York University

Time: 

Monday, January 9, 2006 - 2:00pm

Location: 

MSTB 254

The importance of the conserved quantities were well recoganized in the physical sciences. In this lecture, through several examples, we shall illustrate the fundamental roles played by such conserved quatities in the multiscale analysis. One therefore has to put such quatities into serious considerations also in both modelings and computations.

How Useful is Mathematics to the Biosciences

Speaker: 

Distinguished Professor Avner Friedman

Institution: 

Math Biosciences Institute and Ohio State U.

Time: 

Tuesday, February 8, 2005 - 11:00am

Location: 

McDonnell Douglas Auditorium

The Mathematical Biosciences Institute (MBI) was established at The Ohio State University in 2002, with funding from the NSF. The MBI brings mathematicians and statisticians together with bio-scientists from all over the country and the world in order to work on significant problems in biology and medicine. In this talk, I shall give examples where mathematics does contribute to the solution of important problems in the biosciences. (i.e. tumor growth). I shall also briefly describe new mathematical problems, which arise from biological models.

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