**Sergei OVCHINNIKOV**

Mathematics Department

San Francisco State University

1600 Holloway Ave.

San Francisco, CA 94132

sergei@sfsu.edu

Symposium: *Media Theory*
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**Abstract:**

Jean-Claude Falmagne introduced Media Theory in 1997 in an attempt to generalize models of subjective preference evolution developed earlier. The concept of a medium has a rich combinatorial flavor and the stochastic part of the theory has found applications, for instance, in studies of opinion polls.

The symposium will present media theory mostly from geometric point of view. First an overview of (finite and infinite) media theory including most interesting examples will be given with a focus on geometric features of the underlying concepts. In particular, homogeneity properties of a medium considered as metric space will be introduced. One of the main results of the media theory states that the graph of a medium can be isometrically embedded into a hypercube. This statement has far reached implications that will be mostly the subject of the second presentation. Finally, applications to opinion polls and probabilistic aspects of the theory will be a subject of discussion in the last presentation.