## Lukas Niebel

PhD student
Institute of Applied Analysis
Faculty for Mathematics and Economics
Ulm University
niebel.math@gmail.com

Welcome to my web page! I am a last-year PhD student at Ulm University. My research is mainly focused on the regularity theory of kinetic partial differential equations. Together with my supervisor Rico Zacher, I have published some articles on the $$L^p$$-theory of linear kinetic PDEs. Currently, we are trying to extend these results and ultimatively apply the findings to study quasilinear kinetic PDE's. I explain my research interests more detailed in the Research tab.

Feel free to contact me if you have any questions.

#### News

• December 2022   —   I am visiting Nicola De Nitti in Erlangen from 14.3 till 17.3. I will give a talk on "Parabolic trajectories and the Harnack inequality" on Wednesday. You are invited to join! [Event] [Slides]
• February 2023   —   I gave a talk on kinetic maximal $$L^p$$-regularity at the TULKKA at the KIT in Karlsruhe. [Slides]
• December 2022   —   New Preprint on the ArXiv. We use parabolic trajectories to prove Moser's Harnack inequality. [ArXiv]
• December 2022   —   New Preprint on the ArXiv. We investigate Poincaré inequalities for kinetic/hypoelliptic equations. [ArXiv]
• November 2022   —   I participated in the winter school "Kinetic Theory" at CIRM and presented my work as poster. [Poster]
• October 2022   —   I am happy to announce the program for the Mathematical Colloquium Ulm for winter 2022. [Poster]
• September 2022   —   Welcome to the summer school "Horizons in non-linear PDEs" at Ulm University. I am going to give a talk and present a poster. I am looking forward to discuss with you. [Slides] [Poster]
• July 2022   —   I am going to attend the Conference "When Kinetic Theory meets Fluid Mechanics" in Zürich (Switzerland) and the 2nd IST Austria Summer School in Analysis and PDEs in Klosterneuburg (Austria).
• June 2022   —   I am going to attend the Summer school "Methods and Models in Kinetic Theory" in Pesaro (Italy) and the Workshop of the 25th Internet Seminar in Agropoli (Italy). [Poster]

#### Short Bio

• Since 2019 I am a PhD student at Ulm University under the supervision of Prof. Rico Zacher
• 2014-2019 BSc and Msc in Mathematics at Ulm University, Germany