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IMA Thematic Year on Mathematics of Multimedia
September 2000 - June 2001

The past few years have seen an explosion in the use of digital media. Industry is making significant investments to deliver digital audio, image and video information to consumers and customers. A new infrastructure of digital audio, image and video recorders and players, on-line services and electronic commerce is rapidly being deployed. At the same time, major corporations are converting their audio, image and video archives to an electronic form. Individual consumers may also soon be able to convert their image and video archives to digital form.

This burgeoning of digital information coupled with advances in computing, interface and communication technologies has paved the way for multimedia. The most distinctive characteristic of a multimedia product is that it carries and delivers digital information in mixed modes on a single platform. What makes multimedia different from traditional information products is a much richer variety of underlying works. A multimedia product may contain graphics, film, video, music, photographs, paintings, animation, text, data, maps, games, and multimedia software.

Current and future challenges in multimedia technologies include (i) better understanding of the interaction between different media, (ii) two-way man-machine interaction in speech recognition and computer vision, (iii) improved quality of computer generated media, (iv) developing communication protocols that protect data privacy, and (v) restructuring existing data bases to respond to real-time performance demands.

Mathematics, with its reliance on exposing and exploiting the hidden patterns and structures in physical phenomena, will play a key role in uniting and synthesizing the different modalities inherent in the ongoing multimedia revolution. The mathematical disciplines that are required cover a broad spectrum, ranging from pure algebra and group theory, through geometry and topology, and, naturally, analysis - both analytical and numerical - with probabilistic and stochastic methods playing a particularly important role. The interface between mathematics and multimedia applications forms a two-way street - not only do existing mathematical theories acquire new and unexpected applications, but the multimedia applications themselves point to new problems requiring solutions, which in turn will stimulate new developments in mathematics itself. Thus, we can view multimedia in the role of a twenty-first century reincarnation of the old mathematical paradigm that inseparably synergizes research in pure mathematics and its applications.

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