Spring 2005 schedule

Autumn 2004 schedule

Spring 2004 schedule

Mathematics Department Colloquium : Autumn 2005 schedule

 

   Monday, August 22, 1600-1700

Speaker : Anthony O'Farrell, NUI Maynooth, Ireland.

Title : Pervasive function spaces.

Abstract

 

   Monday, September 5, 1600-1700

Speaker : Oskar Sandberg, Matematisk Statistik, Chalmers.

Title : Small worlds and dark networks.

Abstract : The "small world" phenomenon - that we are all connected through a short series of acquaintances - has been part of folklore and popular culture for a long time. But it is only in recent years that effective mathematical models have come about for explaining the dynamics of small world networks. This talk discusses the question of navigating the small world. For efficient navigation, it is not enough that short paths exist between any two people, but one must also be able to find them. How to do this was first answered by Jon Kleinberg in 2000. Using his model, new algorithms are presented for teaching computers how to navigate in a small world, and the possibility of building large scale encrypted "dark" computer networks arises from these.

På svenska : Det så kallade "small world" fenomenet - att vi alla kan kopplas samman genom en kort serie vänner - har sedan länge blivit en del av vår folkliga tradition och populärkultur. Men det är bara på senare år som det har uppkommit matematiska modeller som kan förklara denna typ av nätverks dynamik. Talet handlar om frågan hur man navigerar i sådana små världar. För att göra detta krävs det inte bara att korta väger finns mellan vilka två personer som helst, utan även att det går att hitta dem effektivt. Hur det kan vara möjligt besvarades först av Jon Kleinberg för fem år sedan. Med hjälp av hans modell presenteras nya algoritmer för hur man kan lära datorer att hitta i små världar, och därmed uppstår möjligheten att bygga stora, krypterade, "mörka" dator-nätverk.

NOTE : The presentation will be in english.

 

 

   Monday, October 10, 1600-1700 (OBS! Rescheduled from the spring)

Speaker : Viktor Berbyuk, Mechanical Engineering, Chalmers.

Title : Control and optimization of semi-passively actuated mechatronic systems.

Abstract

 

   Monday, October 17, 1600-1700

Speaker : Douglas Rogers, University of Hawaii and Selmer Centre, University of Bergen.

Title : Indecomposable polyominoes.

Abstract : A polyomino is the natural generalization to many cells of the familar domino made from two square cells (the word seems to have been the coinage a little over fifty years ago of Solomon Golomb). Thus a polyomino is a finite collection of cells in the square grid with connected interior. The enumeration of polyominoes remains an outstanding problem, but some information can be found here.

A familiar technique in the enumeration of combinatorial objects of interest is according to the first occurrence of some feature. This leads naturally to consideration of those objects that are indecomposable in the sense of lacking the feature in question altogether. We illustrate the renewal recurrence relations and transfer matrices that arise with a problem in domino tiling.

But we can also ask about the enumeration of polyominos in a given class that cannot be dissected into smaller polyominoes in that class. Curiously enough, whereas problems of graph decompositions have been studied extensively, this type of polyomino problem seems almost completely open - and difficult - territory, unrecorded, as yet, in the Online Encyclopedia of Integer Sequences. The talk aims to provide a starting point for research.

Here is a link to a recent paper of mine on the subject of polyomino enumeration.

 

   Monday, October 31, 1600-1700

Speaker : Dan Nilsson, Lunds Universitet.

Title : Levande maskiner med ögon.

Abstrakt : De flesta djur är så komplexa att vi i ett och samma andetag inte kan förstå helheten, utan måste separat studera deras många specialiserade organsystem, där vart och ett i bästa fall låter sig beskrivas och förstås i någorlunda detalj. Även om djur i praktiken kan betraktas som maskiner som omsätter energi och information är det alltså sällan fruktbart att använda ett maskintänkande i forskning om hela djurs konstruktion och funktion. Det finns dock djur som är så enkla och maskinlika att man i princip skulle kunna bygga robotar med precis samma beteende. Föredraget handlar om kubmaneter som är ett bra exempel på denna typ av enkla maskinlika djur. De har dessutom ett mycket maskinlikt synsystem som erbjuder unika möjligheter att studera de ursprungliga anledningarna till att evolutionen hittade vägen till ögon och synsinne.

 

   Monday, November 7, 1600-1700

Speaker : Joerg Schmeling, Lunds Universitet.

Title : Some aspects of dimension theory in dynamical systems.

Abstract : In smooth dynamical systems several characteristics play a fundamental role. The most important dynamical characteristics are entropy, Lyapunov exponents and dimension. These characteristics are adjoint to invariant sets or invariant measures and reflect different aspects of the asymptotics of the system. Moreover there is a deep connection between them. We will survey the main methods and results of the theory of dimension-like characteristics. A special emphasis will be given to the fundamental difference between systems of low and high complexity. We will illustrate the concepts and results on several significant examples and also state some of the most important open questions.

 

   Monday, November 28, 1600-1700

Speaker : Mikael Passare, Stockholms Universitet.

Title : From real ovals to complex crystals.

Abstract : In 1876 Axel Harnack proved that a smooth real algebraic curve in the projective plane cannot have more than $1+(d-1)(d-2)/2$ connected components, where $d$ denotes the degree of the curve. He also gave a construction of curves having this maximal number of components, or ``ovals". These matters were pursued further by David Hilbert, who also included the study of ovals in problem 16 of his famous list. It has recently been discovered that the Harnack curves and their complexifications possess many other extremal properties. For instance, the amoeba of a complex Harnack curve is of maximal area, and it has the maximal number of ``holes" that precisely correspond to the ovals of the real curve. In fact, the area of the holes can be taken as coordinates for the moduli space of Harnack curves of a given degree. In the work of Andrei Okounkov and his collaborators the very same Harnack curves and their amoebas unexpectedly show up in combinatorial random surface models for partially dissolved crystals.