@article{8816,
  abstract     = {Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.},
  author       = {Runkel, Ingo and Szegedy, Lorant},
  issn         = {14320916},
  journal      = {Communications in Mathematical Physics},
  number       = {1},
  pages        = {83–117},
  publisher    = {Springer Nature},
  title        = {{Area-dependent quantum field theory}},
  doi          = {10.1007/s00220-020-03902-1},
  volume       = {381},
  year         = {2021},
}

@article{8325,
  abstract     = {Let 𝐹:ℤ2→ℤ be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes. },
  author       = {Kalinin, Nikita and Shkolnikov, Mikhail},
  issn         = {14320916},
  journal      = {Communications in Mathematical Physics},
  number       = {9},
  pages        = {1649--1675},
  publisher    = {Springer Nature},
  title        = {{Sandpile solitons via smoothing of superharmonic functions}},
  doi          = {10.1007/s00220-020-03828-8},
  volume       = {378},
  year         = {2020},
}