Dr. Dennis Ulbrich

About

I am a mathematician with a research background in nonlinear analysis, dynamical systems, ergodic theory, and kinetic theory, with several years of proficiency and a strong commitment to undergraduate teaching, student supervision, and academic course organization.

Among other things, I was a postdoc at the Institute for Analysis and Numerics of the University of Münster and earned my PhD (Dr. rer. nat.) in Mathematics at the University of Bremen.

Research

Research interests

• ◆ Ordinary and partial differential equations and their dynamics
• ◆ Nonlinear wave solutions and their ergodic properties
• ◆ Kinetic theory, in particular entropy methods
• ◆ Boltzmann equation and its BGK-type approximations
• ◆ Long-time behavior of solutions (hypocoercivity)
• ◆ Physical applications
• ◆ Models of chemical reactions

Project Participation

Publications

Journal articles (peer-reviewed)

• ◆
  A. Pauthier, J.D.M. Rademacher, D. Ulbrich
  Weak and strong interaction of excitation kinks in scalar parabolic equations
  J Dyn Diff Equat35, 2199–2235, (2023)

  [DOI] [arXiv:2021.00309]
• ◆
  M. Keßeböhmer, J.D.M. Rademacher, D. Ulbrich
  Dynamics and topological entropy of 1D Greenberg-Hastings cellular automata
  Ergodic Theory and Dynamical Systems, 41 (2020), no. 5, 1397–1430

  [DOI] [arXiv:1903.02459]

Ongoing work

• ◆
  L. Liu, M. Pirner, D. Ulbrich
  Discrete hypocoercivity for a nonlinear kinetic reaction model without initial close-to-equilibrium assumption (working title)

Thesis

• ◆
  D. Ulbrich
  Ergodic theory of nonlinear waves in discrete and continuous excitable media
  Diss., 2021

  [DOI]

Teaching

Hochschule Bremen (Winter 2024/25):

• ◆ Mathematik 1 (lectures, tutorials, exams)

Jacobs University Bremen (Spring 2022):

• ◆ Finite Mathematics (lectures, tutorials, exams)
• ◆ Introduction to Dynamical Systems (pro-seminar)

Short CV