@article{BaerMazzeo2021,
  author    = {B{\"a}r, Christian and Mazzeo, Rafe},
  title     = {Manifolds with many Rarita-Schwinger fields},
  series = {Communications in mathematical physics},
  volume    = {384},
  journal   = {Communications in mathematical physics},
  number    = {1},
  publisher = {Springer},
  address   = {Berlin},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-021-04030-0},
  pages     = {533 -- 548},
  year      = {2021},
  abstract  = {The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.},
  language  = {en}
}
@article{Baer2021,
  author    = {B{\"a}r, Christian},
  title     = {The Faddeev-LeVerrier algorithm and the Pfaffian},
  series = {Linear algebra and its applications},
  volume    = {630},
  journal   = {Linear algebra and its applications},
  publisher = {Elsevier},
  address   = {New York},
  issn      = {0024-3795},
  doi       = {10.1016/j.laa.2021.07.023},
  pages     = {39 -- 55},
  year      = {2021},
  abstract  = {We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of computational cost O(n(beta+1)) where nis the size of the matrix and O(n(beta)) is the cost of multiplying n x n-matrices, beta is an element of [2, 2.37286). We compare its performance to that of other algorithms and show how it can be used to compute the Euler form of a Riemannian manifold using computer algebra.},
  language  = {en}
}