Technion Math Club
All the lectures are in Hebrew unless stated otherwise
Wednesday, December 31, 2008
Irad Yavneh (Technion)
Title: Multiscale Computation
16:30 // Taub 2 (computer science)
Wednesday, April 22, 2009
Uri Bader (Technion)
Title: The Miracle of the Loaves and Fish
16:30 // Location: Amado 233
Wednesday, May 20, 2009
Leo Corry Tel Aviv University
Title: Einstein Meets Hilbert on the Way to General Relativity: Who Arrives First?
16:30 // Location: TBA
Wednesday, June 24, 2009
Robert Adler (Technion)
Title: Making Decisions on the Basis of Shape
16:30 // Location: Amado 233
Abstract: : What do the following two problems have in common?
(1) Getting a bunch of soldiers to stand in a straight line.
(2) Ranking internet pages by relevance.
A: Both can be solved efficiently by multiscale methods.
Multiscale methods are well-established as an important approach for solving
various types of large problems in science and engineering. Based on these
two problems - the first borrowed from Alfred M. "Freddy" Bruckstein and the
second from Sergey M. Brin and Lawrence E. "Larry" Page - this talk will
strive to expose the immense promise and grave challenges associated with
multiscale computational techniques.
Abstract: Recently we came to familiarity with Ponzi schemes - type of frauds that are doomed
to be collapsed eventually because of the finiteness of population/resources/money.
Mathematical objects are often infinite, though, and the Ponzi dream might very well come true.
In 1924 Banach and Tarski, following Hausdorff, showed that one can decompose a sphere
into finitely many pieces and reconstruct from these pieces two copies of the same sphere.
This is now called the Hausdorff-Banach-Tarski paradox, though it is not a paradox - it is a
mathematical fact! It shows, among other things, that the collection of subsets of the sphere
is too rich to support a reasonable preservation low. This insight is one of the corner stones
of measure theory. Some mathematical objects do admit preservation laws, they are called
Others do not. The definition of amenability of groups was given by Von-Neuman, following
the HBT paradox. It influenced many branches of mathematics ever since.
Abstract: On November 25, 1915, Albert Einstein presented to the Berlin Academy of
Sciences the explicit,
complete and correct, generally-covariant field
equations of gravitation, lying at the heart of his
General Theory of Relativity.
This was the fourth consecutive week in which he presented, at the
meetings of the Academy, what he believed to be the culmination of many
years of intense efforts to
generalize his principle of relativity so as
to cover cases of relatively moving reference systems more general
the inertial ones, and so as to apply to gravitation. In the previous
three opportunities he soon realized
that the version he had just
presented was still in need of further improvement. After his talk of
Einstein was euphoric about his achievement, which he was
ever to consider the most important one of his
entire scientific career.
Five days earlier, on November 20, David Hilbert presented in Gottingen
his own version of the equations
that, in the published version that
appeared in print several months later, contained the correct and
equations of the theory. According to a view that was commonly
accepted for many years, Hilbert had
anticipated Einstein in five days
in correctly formulating this important part of the latter's work. Recent
archival research, however, has shown that this was not really the case,
and the actual historical situation
was much more complex.
Einstein had visited Gottingen in the summer of 1915 and there he
presented the current state of his theory,
including the problems that
were yet to be solved before it could be considered to be complete. Einstein
was absolutely delighted by the audience, one of the few in the world that
included a considerable number
of people who could follow his ideas, ask
difficult questions and perhaps even help him overcome some
difficulties. Above all, the presence of Hilbert in the audience was of
great impact for him. A strong
personal and scientific friendship
developed. Over the following months, and especially over the crucial
months of November, they corresponded intensely. This correspondence has
been thoroughly analyzed as
part of the story of their encounter and
their respective talks in November. As this interesting episode involves
two of the foremost scientists and
one of the most momentous developments of the beginning of the twentieth
century, the discovery and publication of the relevant documents aroused
much interest and debate within
historians of science as well as in
broader circles. Still, despite the intrinsic curiosity that it arises,
disputes ("Who arrived first?") are not the kind of foremost
questions that attract the interest and research
efforts of historians of
science. This is also the case in the story of Hilbert and Einstein.
The main point of historical interest in the story concerns the first half
of the title of this talk:
"Einstein meets Hilbert on the Way to General
Relativity". Here we have these two prominent scientists
working out their
long-term research programs, each one with his specific aims in mind,
different disciplines, using different methodologies, and
based on different bodies of knowledge as their
Their scientific and personal encounter raises important and difficult
questions: What was the essence of their research programs?
Where was each of them heading with their
work? How did their programs meet
and what kind of interaction ensued? How this influenced each of
their programs? Where did the meeting ultimate lead to?
My talk will address all of these questions and will attempt to provide
some of the answers that recent
research by several historians has brought