Category theoretical approaches in technologies and sciences
Professor, Tokyo Institute of Technology
It is a recent trend in science and technology that mathematics, both pure or applied, appear in diverse areas and subjects in science and technology, and that such new and “unexpected” applications of mathematics are glowing more and more, and yet many others should be discovered in future. Among several special features of this recent movement, one of the most important is that, unlike the out-of-date view of “foundational role” of mathematics, the recent applications seem to reveal “new relationship” between mathematics and other sciences, not based on “foundation-vs-application” dichotomy, but more interactive, symmetric, and bidirectional relationships. Now, many of such new applications of mathematics are done with the so-called category theory, which deals with a relatively new objects, categories and functors. Although category theory has initially been plotted in the fairly abstract mathematical theory of algebraic topology, it nowadays reveals its power to afford vast applications, including, for example, logic, linguistics, music, cognitive science, artificial intelligence, and many others. In this talk, I will discuss one of such possible applications, category theoretic approaches to neural networks (Deep Learning), in which I discuss our recent, on-going and rather experimental, researches with DWANGO team.
Dr. Fumiharu KATO is professor of Department of Mathematics, Tokyo Institute of Technology (Tokyo Tech), JAPAN. He received his BSc (1993), MSc (1995), PhD (1997) in Mathematics from Kyoto University. He worked as assistant professor in Kyushu University (Feb. 1997 – Sept. 2000), lecturer and associate professor in Kyoto university (Oct. 2000 – Mar. 2011), full professor in Kumamoto University (Apr. 2011 – Sept. 2015), and finally in Tokyo Institut of Technology from Oct. 2015. In addition, he conducted his research in arithmetic geometry in Max-Planck-Institute für Mathematik (Oct. 1998 – Sept. 1999), and Institut Henri Poincaré (Apr. 1997 – Jun. 1997), and was invited as visiting professor to Université Rennes and Université Paris VI. He mainly works in several areas of algebraic and arithmetic geometry, and is one of the authors of the recent book “Foundations of rigid geometry” (with Kazuhiro Fujiwara) published from European Mathematical Society. Recently, he started collaborative research on Deep Learning with DWANGO team in Japan.