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DTSTAMP:20241108T153347Z
UID:1712755800@ist.ac.at
DTSTART:20240410T153000
DTEND:20240410T163000
DESCRIPTION:Speaker: László Lovász\nhosted by Tim Browning \nAbstract: F
rom Zeno's paradoxes to quantum physics\, the question of the continuous n
ature of our world has been prominent and remains unanswered. Does space-t
ime really exist\, or is it just a good model for an enormous\, but finite
number of elementary particles?Discrete structures behave quite different
ly from continuous ones. The great success story of mathematics in the 18-
th and 19-th centuries was the development of analysis\, with extremely po
werful tools such as differential equations or Fourier series\, and with b
y now very standard methods like the famous (infamous?) epsilon-delta tech
nique. Discrete mathematics had a later start\, but for importance of its
applications it is catching up. Its proof techniques are different\, such
as enumeration or induction. In the continuous world\, algorithms are most
ly computations\, with numerical analysis at the center. In the discrete w
orld\, algorithmic ideas are more diverse\, including searching\, recurren
ce\, and (yes!) pulling in methods from continuous mathematics.I will argu
e that these worlds are not as far apart as they seem. The use of computer
s forces us to approximate continuous structures by finite ones\; but perh
aps more surprisingly\, very large finite structures can be very well appr
oximated by continuous structures\, and this approximation gets rid of inc
onvenient and unnecessary details. Many fundamental questions of mathemati
cs\, probability\, or physics can be asked in both settings\, and their ap
proaches cross-fertilize each other.
LOCATION:Raiffeisen Lecture Hall\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:László Lovász: Discrete or continuous?
URL:https://talks-calendar.ista.ac.at/events/4399
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