Wednesday, April 26, 2023
04/26/2023 - 1:00pm
Elliptic PDEs defined on surfaces occur frequently in computer graphics, and in many areas of physics, including electromagnetism, fluid dynamics, and molecular dynamics. Despite this broad range of applications, there are few efficient and accurate numerical methods for this class of PDEs. In this talk, I present a method for converting PDEs of this type into an integral equation over the surface. Unlike PDEs on surfaces, integral equations on surfaces have been thoroughly studied and existing tools may be used to construct fast and high-order numerical solvers.
04/26/2023 - 4:15pm
It is well-known that for any finite group G, there exists a closed 3-manifold M with G as a quotient of the fundamental group of M. However, we can ask more detailed questions about the possible finite quotients of 3-manifold groups, e.g. for G and H_1,…,H_n finite groups, does there exist a 3-manifold group with G as a quotient but no H_i as a quotient? We answer all such questions. To prove non-existence, we prove new parity properties of the fundamental