|
Monday, August 22, 1600-1700 |
Speaker :
Anthony O'Farrell, NUI Maynooth, Ireland.
Title : Pervasive function spaces.
|
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.
|
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.
|
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.