@article{14244,
  abstract     = {In this paper, we determine the motivic class — in particular, the weight polynomial and conjecturally the Poincaré polynomial — of the open de Rham space, defined and studied by Boalch, of certain moduli spaces of irregular meromorphic connections on the trivial rank 
 bundle on P1. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild character variety. We also identify the open de Rham spaces with quiver varieties with multiplicities of Yamakawa and Geiss–Leclerc–Schröer. We finish with constructing natural complete hyperkähler metrics on them, which in the four-dimensional cases are expected to be of type ALF.},
  author       = {Hausel, Tamás and Wong, Michael Lennox and Wyss, Dimitri},
  issn         = {1460-244X},
  journal      = {Proceedings of the London Mathematical Society},
  number       = {4},
  pages        = {958--1027},
  publisher    = {Wiley},
  title        = {{Arithmetic and metric aspects of open de Rham spaces}},
  doi          = {10.1112/plms.12555},
  volume       = {127},
  year         = {2023},
}

@article{9581,
  abstract     = {We show that for any  𝑛  divisible by 3, almost all order-  𝑛  Steiner triple systems have a perfect matching (also known as a parallel class or resolution class). In fact, we prove a general upper bound on the number of perfect matchings in a Steiner triple system and show that almost all Steiner triple systems essentially attain this maximum. We accomplish this via a general theorem comparing a uniformly random Steiner triple system to the outcome of the triangle removal process, which we hope will be useful for other problems. Our methods can also be adapted to other types of designs; for example, we sketch a proof of the theorem that almost all Latin squares have transversals.},
  author       = {Kwan, Matthew Alan},
  issn         = {1460-244X},
  journal      = {Proceedings of the London Mathematical Society},
  number       = {6},
  pages        = {1468--1495},
  publisher    = {Wiley},
  title        = {{Almost all Steiner triple systems have perfect matchings}},
  doi          = {10.1112/plms.12373},
  volume       = {121},
  year         = {2020},
}