D. Lukas B. Brantner

E-mail:  brantner@maths.ox.ac.uk

I am a Junior Research Fellow of Merton College at the University of Oxford . In the spring of 2019, I'm also a Della Pietra Fellow in the Derived Algebraic Geometry programme at the Mathematical Sciences Research Institute. Before this, I worked as a Researcher (Scientific Assistant) at the Max Planck Institute for Mathematics in Bonn. I was a graduate student of Jacob Lurie in the Department of Mathematics at Harvard University, after completing my undergraduate studies at the University of Cambridge (St. John's College).

My current research interests lie in chromatic homotopy theory, derived algebraic geometry, 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.

Here is my CV. If you would like to see my current research statement, please send me a message.

I co-organised the double-conference "Higher Algebra and Mathematical Physics" at the MPI in Bonn and the PI in Waterloo. In Oxford, I organised an advanced class on chromatic homotopy theory. While visiting Berkeley, I co-organised a block seminar on elliptic cohomology. 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".


Papers

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

The Action of Young Subgroups on the Partition Complex (with Arone). Recorded talk at BanffPaper (submitted).

The Lubin-Tate Theory of Spectral Lie Algebras. Extended version of Ch. 3 + Ch. 4 of my thesis.

The vn-periodic Goodwillie Tower on Wedges and Cofibres (with Heuts). Paper (accepted).

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 2018, I held Geometry tutorials 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.