Talk #1 (1:00 - 2:30pm): Xuemiao Chen, University of Waterloo
"Boundary value problems for G2 holonomy equation and mapping problems for 3 forms on 5-d manifolds"
A result of Donaldson says: with the set-up motivated by Hitchin’s variational point of view, the G2 holonomy equation with boundary is elliptic mod related diffeomorphisms. Applications include the existence of a G2-cobordism between small deformations of Calabi-Yau threefolds. Similar discussions regarding boundary value problems can be also done for complex Calabi-Yau threefolds. However, it is not elliptic. Donaldson and Lehmann considered a variant of this problem called the mapping problem which asks: when could a three-form on a 5-d manifold be the pull-back of the real part of the holomorphic 3-form on a Calabi-Yau threefold under some embedding? For this, they define a class of closed strongly pseudo-convex 3-form corresponding to the CR geometry and prove that the perturbative version of this problem can be solved if a finite dimensional obstruction vector space vanishes. We will give an introduction to these results. Reference:arXiv:1802.09694, arXiv:2210.16208.
Talk #2 (2:30 - 4:00pm): Shubham Dwivedi, University of Humboldt Berlin
"Parabolic frequency on Ricci flows"
We will define a parabolic frequency function on Reimannian manifolds with metrics evolving by Ricci flows. We’ll prove the frequency monotonicity along the flow and use it to prove unique continuation theorems for certain 2nd order operators. This talk is based on the paper Parabolic Frequency on Ricci Flows by Julius Baldauf and Dain Kim.
MC 5403