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Monday, January 23, 1530-1630 |
Speaker :
Jeffrey Steif, Chalmers.
Title : Some results of Robert Aumann in game theory.
Abstract :
In the fall, Robert Aumann received
"Sveriges Riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne"
for his work in game theory. I will discuss a very small portion of his
research in order to give a flavor of his work.
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Wednesday, February 8, 1530-1630 (OBS! WEDNESDAY) |
Speaker :
Einar Steingrimsson, Chalmers.
Title : Combinatorics, Algebraic and
Enumerative.
Abstract
: I will show a few glimpses from the area of combinatorics, ranging from very
simple to fairly deep. However, the entire presentation should be
understandable for any graduate student. I will show some of the tools used
by combinatorialists, such as bijections and generating functions. I will
also talk about one of the major breakthroughs in algebraic combinatorics of
the last couple of decades, namely the solution of the Neggers-Stanley
conjecture, which was cracked in our very department a year and a half ago.
Monday, February
13, 1530-1630 Speaker :
Douglas Rogers, University of Hawaii and Mathematical Institute, University of Bergen. Title : Bounds Archimedes missed : exercises in geometric extrapolation. Abstract
: Pi is a topic of abiding fascination that engages the interest of all
mathematicians, pure and applied alike. We know, or think we know, that it
was Archimedes who early calculated pi to considerable accuracy by bounding
a circle inside and out by regular polygons. However, this program, with
an explicit argument in the case of inscribed polygons, is already contained
in Book XII of Euclid's Elements.
Closer examination of the works of Euclid and of Archimedes suggests that
everything you can do with inscribed and circumscribed polygons together can
be done just as well with inscribed polygons alone. Moreover, it seems that
the Chinese mathematician Liu Hui, working over seventeen hundred years ago,
was able to improve the lower bound on the area of a circle by interpolation
using only inscribed polygons.
Perhaps even more surprisingly, whereas the combined work of Euclid and
Archimedes shows that the difference between areas of circumscribed and
inscribed polygons more than halves on doubling the number of sides of
these polygons, an argument that would have been accessible to both of them,
as well as to Liu Hui, shows that, in fact, it more than quarters.
The talk is presented as an exercise in ''mathematics from history'',
where we take the mathematics from a given period and see what (more) can be
extracted by means of it alone. Thus, when we look back on this material from
the later perspective of the calculus, we find that these geometric arguments
remarkably powerful, giving results akin to Richardson-Romberg integration -
the quartering inequality just mentioned is accurate up to the term in the
sixth power of the reciprocal of the number of sides of the largest and
smallest polygons.
It seems that we - not just Archimedes - might have been missing something.
Monday, February
27, 1530-1630 Speaker :
Niklas Eriksen, Chalmers. Title : Släktförskning för bakterier (OBS! Föredraget kommer att hållas på svenska). Abstract
: Det finns miljontals barteriarter, som alla är släkt med varandra. Att
bestämma deras släktträd är en grannlaga uppgift. Dock visar det sig att
enkel kombinatorik är till stor hjälp när man ska bestämma bakteriernas
släktskap. Vi kommer att beskriva hur det går till, samt titta litet på
hur metoderna kan förfinas för att få mer realistiska släktskapsberäkningar.
Monday, April
10, 1530-1630 Speaker :
Johan Jonasson, Chalmers. Title : Circle coverign and Brownian motion. Abstract
:
Monday, May
22, 1530-1630 Speaker :
Patrik Albin, Chalmers. Title : Bootstrap : An overview of central principles and results. Abstract
: To be announced.