More details about our activity

# Information about the analysis and PDE group

Here you can find more information related to the Analysis and PDE group, its members and topics of research. This page is currently a work in progress.

Photo:

Sindre Lund Lomås

## Main content

### Topics of research

To be completed

### Permanent members of the group

**Henrik Kalish**,*Professor*: Henrik Kalisch is Professor of Applied Mathematics. He received his Ph.D. in 2001 from the University of Texas at Austin. His research is centered on the mathematical modeling of nearshore processes such as wave breaking, surfzone circulation and wave hazards in the coastal zone. He has co-authored more than one hundred scientific publications in fluid mechanics, partial differential equations, numerical analysis and scientific computation. He is currently Deputy Head of the Department and co-editor-in-chief for “Water Waves: An interdisciplinary journal”, published by Birkhäuser-Springer-Nature.**Irina Markina**,*Professor*: My research interests are differential geometry with non-holonomic constrains, Lie groups and Lie algebras, geometric measure theory and geometric theory of real and complex functions.**Didier Pilod**,*Associate Professor:*My research concerns mathematical analysis and partial differential equations. It aims at expanding our knowledge of dynamic properties of solutions to nonlinear dispersive evolution equations arising in mathematical physics and mathematical fluid mechanics. More precisely, I am interested in the following aspects of nonlinear dispersive equations:- Local and global well-posedness at low regularity in connexion with harmonic analysis.
- Orbital and asymptotic stability properties for solitons, multi-solitons or other special solutions.
- Long time dynamics: scattering, singularity formation and the soliton resolution conjecture.

**Sigmund Selberg**,*Professor*: I work with non-linear PDE and Harmonic analysis.

### Non-permament members

**Arnaud Eychenne**,*Doctoral student with Didier Pilod*: My thesis is about the non-linear dispersive PDE with non local operator on a generalized dispersive Benjamin-Ono equation.I'm also interested by quantum mechanics and variational methods.**Erlend Grong**,*Researcher:*My research is centered around sub-Riemannian geometry, and branches out in any direction linked to this subject. I began by studying problems related to geodesics and control theory. After my Ph.D., I have mostly been working on the relationship between sub-Riemannian geometry and second order operators that are not elliptic, but still hypoelliptic. On of the main tools to investigate this relationship has been to apply the geometry of stochastic differential equations. Another tool of increasing importance has been investigating holonomy groups defined only by loops tangent to a subbundle, which has powerful applications to sub-Riemannian metrics as well as Riemannian metrics on foliations. Recently, I have also look into the sub-Riemannian equivalence problem using Cartan geometry and have looked into applications in statistics on manifolds.**Adrien Ange Andre Laurent,***Post-doctoral fellow with Hans Zanna Munthe-Kaas:*My research focuses on the creation of numerical integrators for the numerical integration of a variety of stochastic problems. More specifically, I introduce new tools in the spirit of geometric integration and study their algebraic and geometric properties, as well as their numerous applications in the approximation of stochastic (partial) differential equations.**Martin Oen Paulsen,***Doctoral student with Didier Pilod.***Jonatan Stava,***Doctoral student with Hans Zanna Munthe-Kaas and Erlend Grong:***Frédéric Fernand Jacques Valet,***Post-doctoral fellow with Didier Pilod*. I am interested in the long time behavior of dispersive equations : solitons, multisolitons, and strong interaction of different objects.**Gianmarco Vega-Molino,***Post-doctoral fellow with Erlend Grong.*

21.03.2022