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PRODID:-//Memento EPFL//
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SUMMARY:Applied category theory: Information structures and modular system
 s
DTSTART:20150915T101500
DTEND:20150918T120000
DTSTAMP:20260501T185243Z
UID:0370ba7358a579a6dfd8d8d6244fee30195f01b7103a95866f03c073
CATEGORIES:Conferences - Seminars
DESCRIPTION:David Spivak (MIT)\nOver the past 75 years\, category theory h
 as organized and standardized much of the discipline of pure mathematics. 
 In this 8-hour mini-course\, we will consider how and in what respects it 
 may have a similar effect outside of math\, namely in science and industry
 . Indeed\, category theory's success stems from its ability to connect\, c
 haracterize\, and translate between\, disparate subjects.\nWe will begin w
 ith a short\, non-standard review of category theory\, where we will discu
 ss its 35-year role in computer science\, as the semantics of functional p
 rogramming languages. This will take us through the definition of symmetri
 c monoidal categories\, which can be thought of as governing the arithmeti
 c of parallel and serial composition. After the review\, we will turn our 
 attention to information-bearing structures\, such as databases and ontolo
 gies. We will see how querying a database is a special case of translating
  data from one structure to another\, which itself can be modeled by the c
 ategory theoretic notion of Kan extensions.\nIn the second part of the cou
 rse\, we will discuss the notion of modularity---from data flow diagrams\,
  to hierarchical protein materials\, to connected arrangements of dynamica
 l systems---and model each of these modular systems with operads and their
  algebras. Operads are a category-theoretic framework that controls how a 
 higher-level system can be formed as an arrangement of interacting compone
 nts. For example\, we will spell out a case in which an operad models hive
 s made up of agents\, which interact by sending signals to each other. The
 se signals control the internal states of each agent\, and\, in turn\, the
  agents' internal states determine the communication pattern connecting ag
 ents in the hive. The operadic nature of this model amounts to a formal se
 nse in which the hive itself forms an agent like any other. Finally\, we w
 ill consider databases\, programs\, and matrices again\, this time from th
 e perspective of modular systems.\nThe audience for this mini-course is me
 ant to include both mathematicians and scientists. One goal is to increase
  communication between scientific disciplines and pure math\, a subject to
  which I consider category theory as a primary gateway. I hope that this m
 ini-course will foster collaborations between mathematicians and other res
 earchers.
LOCATION:CM 10 (T\, Th\, F) & CM 113 (W)
STATUS:CONFIRMED
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