Spring 2010 schedule

# MathematicsDepartmentColloquium : Autumn 2010 schedule

 Monday, September 20, 1530-1630.

SPEAKER : Lloyd Demetrius, Department of Organismic and Evolutionary Biology, Harvard University.

TITLE : An entropic principle for evolutionary processes.

ABSTRACT : Competition between an incumbent and a mutant type is the process that determines changes in the composition of types within a population. Two notions play a critical role in the analysis of this process:

(a) evolutionary stability: the invulnerability of the incumbent population to displacement by a mutant type

(b) evolutionary entropy: the uncertainty in the state, i.e. in age, size, energy of the ancestor of a randomly chosen descendant

The outcome of this process of competition can be characterized by the following principle: The evolutionarily stable states of a population are extremal states of entropy.

I will appeal to the ergodic theory of dynamical systems to outline the mathematical basis of this evolutionary principle. I will also describe the application of this principle to the understanding of three biological phenomena:

(1) Aging: the large variation in life span between species.

(2) Oncology: the origin and proliferation of cancer.

(3) Sociality: the origin and evolution of cooperation.

 Monday, October 4, 1345-1445 (OBS! unusual time).

SPEAKER : Maria Gorelik, Weizmann Institute of Science, Israel.

TITLE : On MacDonald and Kac-Wakimoto identities.

ABSTRACT : In 1972, I. G. Macdonald generalized a classical formula of H. Weyl, obtaining, in particular, a formula for certain powers of the $\eta$-function which include some classical identities of Jacobi. In 1994, V. Kac and M. Wakimoto conjectured a super-analogue of Macdonald's identities and proved it in some special cases. Specializations of these identities give, in particular, the Jacobi and Legendre formulas for representing an integer as a sum of squares or a sum of triangular numbers, respectively. In my talk I will explain the ideas behind the proof of the Kac-Wakimoto formulas.

 Monday, October 11, 1530-1630.

SPEAKER : Sandra Pott, Lunds Universitet.

TITLE : Factorisation of H^p spaces on the polydisk.

ABSTRACT : A classical result in the theory of Hardy spaces on the unit disc D asserts that for any 0 < p,r,s < \infty satisfying 1/r + 1/s = 1/p, and for each f \in H^p(D), f may be factorized as f = g h, where g \in H^s(D), h \in H^r(D).

The situation in the case of Hardy spaces on the polydisc D^n, so-called product Hardy spaces, is much more subtle. A direct factorization into two functions cannot be expected here. We look instead at weak factorisation properties, which can be expressed on the dual side as boundedness properties of Hankel operators on product Hardy spaces. The case p=1 was finally solved by Ferguson, Lacey and Terwilleger in 2002 and 2007. In the talk, I shall present new factorization results for the case 1/2 <= p <= 3/2.

 Monday, October 18, 1530-1630.

SPEAKER : Torbjörn Lundh, Chalmers/GU.

TITLE : Wanted : New mathematics for old biological enigmas.

ABSTRACT : Mathematical Biology can come in many different shapes. Here I would like to present three grand challenges in biology that are in serious need for new mathematical tools.

The problem of morphogenesis: How does a more or less uniform egg turn into a complete and complex organism by itself?

The problem of sympatric speciation: Is it possible that a species will split into two separate species in the same environment? And if so, what are the mechanisms behind it?

The problem of circular wound healing: The medical grand father Hippocrates himself is said to have stated this still open question: Why doesn't a circular wound heal?

 Monday, October 25, 1530-1630.

SPEAKER : Jeff Steif, Chalmers/GU.

TITLE : An overview of Stanislav Smirnov's Fields medal work.

ABSTRACT : I will give an overview of the work that Smirnov did for which he received the Fields medal. I will mostly discuss his so-called conformal invariance theorem for percolation as well as its consequences for computation of so-called critical exponents. My plan is that the talk will be accessible to a general mathematical audience.

 Monday, November 8, 1530-1630.

SPEAKER : Dag Wedelin, Data- och Informationsteknik, Chalmers.

TITLE : Mathematical modelling for the IT program.

ABSTRACT : I will describe my experiences in giving the course Mathematical Modelling at the end of the second year of the Chalmers IT-program. The course is based on the observation that without a course like this, many students do not understand how mathematics is useful in their area or how they can themselves use mathematics in their profession.

The course teaches mathematical modelling and structured problem solving, with an emphasis on basic skills and insights, since this appears to be what the students need most. It does not introduce any advanced theory, and rather intends to show how relatively simple mathematics is useful if you are just able to see how. The students typically confirm that the course has changed their view of mathematics and its application.

 Monday, November 15, 1530-1630.

SPEAKER : Håkan Andreasson, GU/Chalmers.

TITLE : General relativity and some mathematical results on the Einstein equations.

ABSTRACT : I will give a brief introduction to general relativity and the Einstein equations and then I will discuss some of my research projects in recent years: gravitational collapse and weak cosmic censorship, bounds on M/R for spherically symmetric static objects and the existence of axisymmetric solutions of the Einstein-Vlasov system.

 Monday, November 29, 1530-1630.

SPEAKER : Torgny Almgren, Volvo Aero Corporation, Trollhättan.

TITLE : Optimization in logistics - an opportunity if doen with care.

ABSTRACT : The purpose of logistics, and production logistics, is to ensure that each resource is being fed with the right product in the right quantity and quality at the right time - at minimum cost. This is not always as easy as it may seem, as the problem context is often a complex environment, and is also constantly subjected to variations. Optimization is one powerful way, in theory, to handle this complexity. It is, however, often very expensive and time consuming to build models that are useful in industrial settings. It is therefore essential that the "right" models are built at every occasion.

The seminar will give a general presentation of optimization in a logistical context; discuss the different considerations that need to be taken into account by the industrial modeler; and present some examples of models that have been developed.

Torgny Almgren earned his PhD at Luleå with a thesis on mining production planning. He has been working as a logistics specialist at Volvo Aero in Trollhättan since 1997. One of the main topics of his period as an adjunct professor is to assist in the application of mathematical optimization to real life problems.

 Monday, December 13, 1530-1630.

SPEAKER : Ole Warnaar, University of Queensland, Australia.

TITLE : The Selberg integral.

ABSTRACT : In this talk I will give an introduction to the Selberg integral. This integral, which first appeared in two rather unusual papers by Atle Selberg in the 1940s, has become famous as much for its association with mathematical greats such as Enrico Bombieri, Freeman Dyson and Ian Macdonald as for its importance in algebra (Coxeter groups), geometry (hyperplane arrangements) and number theory (the Riemann hypothesis). In this talk I will review some of these developments as well as my own recent work on Selberg integrals related to Lie algebras.