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SUMMARY:Probability\, Symmetry\, Linearity (6/6)
DTSTART;VALUE=DATE-TIME:20141112T130000Z
DTEND;VALUE=DATE-TIME:20141112T150000Z
DTSTAMP;VALUE=DATE-TIME:20200806T073715Z
UID:indico-event-578@indico.math.cnrs.fr
DESCRIPTION:\nI plan six lectures on possible directions of modification/g
eneralization of the probability theory\, both concerning mathematical fou
ndations and applications within and without pure mathematics. Specificall
y\, I will address two issues. \n\n \n\n1. Enhancement of stochastic symm
etry by linearization and Hilbertization of set-theoretic categories. \n\n
2. Non-symmetric probability theory in heterogeneous environments of molec
ular biology and of linguistics. \n\n \nI will start with a category theo
retic view on probability and entropy. This includes\n\n \n repr
esentation of Lebesgue spaces as covariant functors from the category WF o
f weighted finite sets F into the category of set\;\n \n definit
ion of the Boltzmann-Shannon entropy of an F as an image of F in the topol
ogical Grothendieck semigroup of WF.\n\n(Much of this can be found in my a
rticle In a Search for a Structure\, Part 1: On Entropy).\n\n \nNext I wi
ll present several linearized measure-like structures\, and associated ent
ropies\, such as the homology measures and their appearance in many partic
le systems.\n(Some of it is presented in Singularities\, expanders and top
ology of map. Part 2: From combinatorics to topology via algebraic isoperi
metry. GAFA\, Geom. func. anal.\, 20 (2010)\, 416-526\, and in Geometry\,
Topology and Spectra of Non-Linear Spaces of Maps - Wolfgang Pauli Lecture
s\, May 25\, 2009.)\n\n \nAlso I say something about the von Neumann entr
opy.\n\n \nFinally I will dicuss possible concepts of probability for het
erogeneous systems\, such as natural languages and their applications to a
utomatic signals/texts analysis in the spirit of my article Ergostructures
\, Ergodic and the Universal Learning Problem: Chapters 1\, 2.\n\n \n(The
above mentioned papers can be found on my web page at IHES in the section
"recent").\n\nhttps://indico.math.cnrs.fr/event/578/
LOCATION:Université Pierre et Marie Curie Amphithéâtre 55 A
URL:https://indico.math.cnrs.fr/event/578/
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