Topological Quantum Field Theory and Categorification

点击翻译按钮获取中文摘要

This award will fund the participation of US-based junior researchers in the "TQFT and Categorification" conference to be held at the Institut d'Etudes Scientifiques de Cargese on April 15-20, 2018. The subject of Topological Quantum Field Theory (TQFT) has provided a critical testing ground where ideas from theoretical physics inform rigorous mathematical frameworks that lay the foundation for a quantum theory of gravity. TQFTs have been particularly well studied in 3-dimensions, bringing about unprecedented interaction between mathematics and theoretical physics. Since the world we live in is 4-dimensional (including time), truly understand it requires an extension of the techniques of 3-dimensional TQFTs into 4-dimensions. This enhancement of mathematical structures has come to be called "Categorification". This conference will advance this ambitious program to understand 4-dimensional TQFTs, while proving important opportunities for the establishment of new collaborations and the scientific development of young scientists.The "TQFT and Categorification" conference aims to bring together researchers from different horizons around the central question of lifting the techniques from the study of 3-dimensional TQFTs to 4-dimensions. The conference will be organized around three central themes: Heegaard-Floer homologies and symplectic geometry, Algebraic categorification (including Khovanov homology, categorified quantum groups, and categorification at roots of the unity), and TQFT (including connections to physics, super homologies, and non-semisimple invariants). The organizers expect this conference to be a catalyst for establishing lasting collaborations and new avenues of research. More information about this conference can be found at https://tqft.sciencesconf.org/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.