Homotopy theory and quantum field theories

          @misc{ scivideos_PIRSA:24030109,
            doi = {10.48660/24030109},
            url = {https://pirsa.org/24030109},
            author = {Yamashita, Mayuko},
            keywords = {Other Physics},
            language = {en},
            title = {Homotopy theory and quantum field theories},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030109 see, \url{https://scivideos.org/pirsa/24030109}}
          }
          

Abstract

Recently, there has been a growing interest in the relations between homotopy theory in mathematics and theoretical physics. Homotopy theory is used to classify and study physical systems. Also, physically motivated conjectures have led to many interesting developments in homotopy theory. I have been studying this subject as a mathematician. 

My recent works have been motivated by the Segal-Stolz-Teichner program, which is one of the most deep and important subjects relating homotopy theory and physics. They propose a geometric model, in terms of supersymmetric quantum field theories, of a homotopy-theoretic object "Topological Modular Forms". Based on this, we show the absence of anomaly in heterotic string theory (joint work with Yuji Tachikawa), and found a new physical and geometric understanding of duality (with Y.Tachikawa) and periodicity (with Theo Jonhson-Freyd) in homotopy theory. These works lead us to further interesting conjectures to explore. I would like to illustrate this exciting interplay between mathematics and physics. 

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