D. Lukas B. Brantner

David Lukas Benjamin Brantner


I am a Royal Society University Research Fellow at the University of Oxford and a chargé de recherche en détachement (CNRS, Orsay).

My current research interests lie in derived algebraic geometry, chromatic homotopy theory, and combinatorial topology. Previously, I have carried out some research in geometric group theory with Danny Calegari. I am also interested in abelian, non-abelian, and p-adic Hodge theory.

I completed my PhD as a graduate student of Jacob Lurie at Harvard, and was an undergraduate at the University of Cambridge (St. John's College).

Here is my CV. If you would like to find out more about my current research, please send me a message here.


Research Papers

Deformations and Lifts of Calabi-Yau Varieties in Characteristic p (with Taelman), submitted.   Paper

PD Operads and Explicit Partition Lie Algebras (with Campos and Nuiten), to appear in the Memoirs of the AMS.   Paper.

Purely Inseparable Galois theory I: The Fundamental Theorem (with Waldron), submitted.   Paper.

The Lubin-Tate Theory of Configuration Spaces: I (with Hahn and Knudsen), to appear in the Journal of Topology.   Paper.

Deformation Theory and Partition Lie Algebras (with Mathew), submitted. Oberwolfach report.   Paper.

The Action of Young Subgroups on the Partition Complex (with Arone). Paper published in the Publications Mathématiques de l'IHÉS.

The Lubin-Tate Theory of Spectral Lie Algebras. Thesis.

The vn-periodic Goodwillie Tower on Wedges and Cofibres (with Heuts). Paper published in Homology, Homotopy and Applications.

On the Complexity of Sails (Appendix by Freddie Manners). Paper published in the Pacific Journal of Mathematics.


Expository Articles

Abelian and Nonabelian Hodge Theory. Article.

The p-adic Hodge Theory of Semistable Galois Representations. Article.


Teaching

In Michaelmas 2024, I will be teaching the Part C course on Category Theory at Oxford.

In Trinity 2024, I'm teaching a TCC course on ∞-Categories and Deformation Theory at Oxford.
In the spring of 2022, I held lectures on ∞-categories in algebraic geometry at Orsay. In Michaelmas 2021/2022, I organised an advanced class on prismatic cohomology (following Bhatt-Scholze) and delivered Geometry tutorials at Oxford.
In 2020/2021, I organised an advanced class on condensed mathematics (following Clausen-Scholze), supervised five Part B/Part C dissertations, and held tutorials in Geometry, Group Theory, Linear Algebra, Number Theory, Rings and Modules, and Topology. Moreover, I acted as Director of Studies for Merton's fourth year students in Mathematics.
In 2019/2020, I taught a topics class on Koszul duality, organised an advanced class on the rational homotopy theory of automorphisms of manifolds (following Berglund-Madsen), and held tutorials in Geometry, Group Theory, Linear Algebra, and Topology.
In 2018/2019, I held tutorials in Geometry and Analytic Topology and organised an advanced class on chromatic homotopy theory at Oxford.
In January 2018, I gave a Mini-Course on the Partition Complex at the MPI in Bonn.
At Harvard, I delivered Vector Calculus lectures ("Math 21a") in the Fall of 2015 and in the Spring of 2017.


Supervision

PhD students: Jiaqi Fu (joint supervision with Toën, 2022-), Sofía Marlasca Aparicio (2022-), Sam Moore (with Henriques, 2024-), Noe Sotto (with Harpaz, 2022-).
Postdoc: Simon Felten (2024-).
Undergraduates: I have supervised 13 undergraduate dissertations (Part B and C) and 5 summer reading/research projects (Nathan Adlam, Inés Borchers Arias (x2), Maliha Islam, Samuel Moore) at Oxford.


Service

I am currently serving as a guest editor for a special issue on “Derived Lie Algebras in Geometry and Topology” for Philosophical Transactions of the Royal Society A.

I recently co-organised the workshop "Generalised Lie Algebras in Derived Geometry" (29/05/23-02/06/23) in Utrecht. I also co-organised the conference "Homotopical Methods in Algebraic Geometry" (Institut Henri Poincare), the "Twinned Conference on Homotopy Theory with Applications to Arithmetic and Geometry" (MPI/Fields Institute) and the double-conference "Higher Algebra and Mathematical Physics" (MPI/Perimeter Institute).

While visiting Berkeley, I co-organised a block seminar on elliptic cohomology with Peter Teichner.
In Boston, I organised three rounds of the Harvard-MIT graduate topology seminar "Juvitop" on the Kervaire Invariant One Problem, Rational Homotopy and Formality, and Algebraic K-Theory. I also co-organised the Harvard graduate seminar "Trivial Notions".