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Monday, January 17, 1530-1630. |
SPEAKER :
Alexandra Pettet, Oxford University.
TITLE : Topology and dynamics of the outer automorphism group of a free group.
ABSTRACT :
The outer autormorphism group Out(F) of a finite rank free group shares many
properties with lattices in Lie groups and with the mapping class group Mod(S)
of a surface, although the techniques for studying Out(F) are often quite
different from the latter two. Motivated by analogy, I will
describe some recent results about Out(F), previously well-known for the
mapping class group, while highlighting some of the features which distinguish
it from Mod(S).
|
Monday, January 24, 1530-1630. |
SPEAKER :
Carl Lindberg, Chalmers/GU.
TITLE : Options, trading and optimal portfolios.
ABSTRACT :
In this lecture, we will analyze two financial investment
problems. It is shown that, under natural model assumptions, these
problems have intuitively appealing solutions which both have
diversification as a common theme.
|
Thursday, April 14, 1000-1100 (OBS! unusual time). |
SPEAKER :
Svante Linusson, KTH.
TITLE : Mathematics of elections.
ABSTRACT :
I will first give a survey of the mathematical history of the problem of
distributing seats in a parliament proportionally. I will explain known
advantages and disadvantages with various methods. I will also give some
examples of more modern work about what is impossible to obtain in any
election system.
At the end I will speak about the Swedish election system in more detail.
I will also discuss the general problem of achieving proportionality both
between parties and between regions and some mathematics to obtain this. At
the very end I hope the audience will present their own suggestions for how
the Swedish election system should be formulated.
|
Monday, May 9, 1530-1630. |
SPEAKER :
Kathryn Hare, University of Waterloo and Chalmers Hedersdoktor.
TITLE : When does a sum of nothings give you something ?
ABSTRACT :
By the orbit of an n x n Hermitian matrix X, we mean the
orbit of X under unitary similarity transformations. Orbits have
interesting geometric properties. Having measure zero, they are invisible
sets as far as Lebesgue measure is concerned, and yet a sum of n^2 - 1
orbits is so large it has non-empty interior.
This fact generalizes to orbits of elements of Lie algebras under the action
of a compact, simple Lie group. By using techniques from harmonic analysis
we can determine the index k where the k-fold sum of orbits switches
from being "nothing" to being large. Applications will be given to the study
of the spectrum of sums of Hermitian matrices.
|
Monday, May 16, 1530-1630. |
SPEAKER :
Sture Holm, Chalmers/GU.
TITLE : Är kritiken av PISA-analysen berättigad ? ( Obs! Föredraget är på svenska)
|
Monday, May 23, 1315-1415. (Obs! Unusual time) |
SPEAKER :
Marc-Hubert Nicole, Luminy/Bonn.
TITLE : Modular forms and the Langlands programme.
ABSTRACT :
The Langlands programme is a conjectural web of relations between
certain arithmetic objects and certain analytic ones. A fascinating
aspect thereof is that basic constructions on the arithmetic (or
Galois) side are easy to come by, while the conjectural corresponding
analytic (or automorphic) operations are very difficult to establish,
often requiring sophisticated use of the Arthur-Selberg trace formula.
The analytic objects, in their simplest guise, are modular forms. We
shall start by presenting their definition as complex analytic
functions on the upper-half plane, with the example of Eisenstein
series. We will then briefly review representations of the Galois
group of the rational numbers, which provide the arithmetic side of
the picture. After sketching the links between modular forms and
Galois representations, we will discuss on-going attempts at refining
further Langlands's ideas. One of the basic ideas is to study the
reduction modulo p of modular forms, where p is a prime number. For
example, the reduction modulo p of the Eisenstein series E_{p-1} is
the so-called Hasse invariant, which is a stepping stone in the theory
of p-adic analytic modular forms.
This talk is aimed at non-experts.
|
Monday, May 23, 1515-1615. (Obs! Unusual time) |
SPEAKER :
Volodymyr Mazorchuk, Uppsala University.
TITLE : 2-representations of 2-categories.
ABSTRACT :
In this talk I will try to generally describe
what is now called the "higher representation theory".
The first nontrivial level of this can be roughly
understood as study of functorial actions on
categories. The latter can be reformulated in terms
of 2-categories and their 2-representations.
I plan to mention how this theory appeared, what it
studies, and what kind of results are known.