12 citations · 17 across the 6 of their papers we have counts for
8 papers
Formal Integration of Derived Foliations
Lukas Brantner, Kirill Magidson, Joost Nuiten
Frobenius' theorem in differential geometry asserts that every involutive subbundle of the tangent bundle of a manifold integrates to a decomposition of into smooth leaves.…
Poincaré-Birkhoff-Witt Theorems in Higher Algebra
Omar Antolín-Camarena, Lukas Brantner, Gijs Heuts
We extend the classical Poincaré-Birkhoff-Witt theorem to higher algebra by establishing a version that applies to spectral Lie algebras. We deduce this statement from a basic rela…
Deformations and Lifts of Calabi-Yau Varieties in Characteristic
Lukas Brantner, Lenny Taelman
We study deformations of Calabi-Yau varieties in characteristic using techniques from derived algebraic geometry. We prove a mixed characteristic analogue of the Bogomolov-Tian…
PD Operads and Explicit Partition Lie Algebras
Lukas Brantner, Ricardo Campos, Joost Nuiten
Infinitesimal deformations are governed by partition Lie algebras. In characteristic , these higher categorical structures are modelled by differential graded Lie algebras, but…
Purely Inseparable Galois theory I: The Fundamental Theorem
Lukas Brantner, Joe Waldron
We construct a Galois correspondence for finite purely inseparable field extensions , generalising a classical result of Jacobson for extensions of exponent one (where $x^p \i…
Deformation Theory and Partition Lie Algebras
Lukas Brantner, Akhil Mathew
A theorem of Lurie and Pridham establishes a correspondence between formal moduli problems and differential graded Lie algebras in characteristic zero, thereby formalising a well-k…
The -periodic Goodwillie tower on Wedges and Cofibres
Lukas Brantner, Gijs Heuts
We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge of spaces (using the Hilton-Milnor theorem) and on the cofibre $\mathrm{c…
On the Complexity of Sails
Lukas Brantner
This paper analyses stable commutator length in groups Z^r * Z^s. We bound scl from above in terms of the reduced wordlength (sharply in the limit) and from below in terms of the a…