The Undergraduate Faculty Program (UFP) at PCMI is aimed at faculty members from all types of colleges and universities with a strong interest in teaching undergraduates. Some participants are looking to rekindle their engagement with mathematical research and to interact with the broader mathematical community, and others are looking for new teaching approaches. The focus of the UFP varies from year to year, although its mathematical content is always aligned with the main research theme of PCMI that summer—the 2019 theme is Quantum Field Theory and Manifold Invariants. In some years it is mainly a small group seminar devoted to some interesting parts of mathematics, in a setting which emphasizes participants working on ideas and problems together; in other years some part of it is also devoted to pedagogical issues or curriculum development. The UFP typically has around 15 participants, which allows for close and informal interactions with other UFP participants.
The lecturers and topics for the Undergraduate Faculty Program in 2019 will be:
John Etnyre (Georgia Tech) and Paul Melvin (Bryn Mawr) —
Topics will include Morse theory, handlebody theory, the h-cobordism theorem, and Kirby's framed link calculus (for the study of 3-dimensional and 4-dimensional manifolds), aiming toward quantum invariants of 3-manifolds. There are many accessible open problems that can be attacked once one has the computational tools of the link calculus available, and in the UFP we will emphasize using these tools to explore solutions together.
UFP participants also interact with the participants and lecturers in the Undergraduate Summer School, and may choose to attend some of the Graduate Summer School minicourses. Members from all parts of PCMI may take part in the Experimental Math Lab, in which small groups of participants with close mentorship from a more senior mathematician investigate open-ended problems and report on their findings at the end of the three-week Summer Session. Interaction among everyone at PCMI is fostered by various informal social activities open to all PCMI participants, as well as daily “cross-program activities’’ that include lectures and presentations on topics of general mathematical interest.
The 29th Annual PCMI Summer Session will be held June 30 - July 20, 2019.