Saman Habibi Esfahani (Duke) will speak in the geometry seminar at 5pm on 18th November. The talk will take place online. We will hopefully organise a group viewing in the Salle des Profs (9th floor of building NO). Saman’s title is “Fueter sections and Z2-harmonic 1-forms” and his abstract is below.

*This talk is based on joint work with Yang Li. Non-linear Dirac operators appear in various problems in gauge theory, calibrated geometry, and Floer theory. They are used to define generalized Seiberg-Witten equations on 3- and 4-manifolds. Taubes proposed that counting harmonic spinors with respect to these operators on 3-manifolds could lead to new 3-manifold invariants. Similarly, Donaldson and Segal suggested counting spinors over special Lagrangians to produce Calabi-Yau invariants, while Doan-Rezchikov outlined a Fukaya 2-category for hyperkähler manifolds based on such counts. The central question in all these proposals is whether the space of solutions (called Fueter sections) is compact. We address this question in certain cases, proving and disproving several conjectures in the field, with the key observation that Z2-harmonic forms play a crucial role in the problem.*