# Affiliated Faculty

Wojtek Chacholski , Professor, Mathematics

"I believe the shape of data does matter and to further our abilities to analyze data it is therefore essential that statistical methods are adjusted and developed to incorporate geometrical and topological information. How to transform such information into signatures suitable for statistical analysis and validation is what drives my interest. I am particularly interested in homology based invariants and new ways of using them for data analysis purposes."

Anders Forsgren , Professor, Optimization and Systems Theory

"My main research interest is nonlinear optimization, in particular method development and applications in radiation therapy. The aim is development of efficient methods. The aim is not immediately about handing of complex data, but I envisage that the techniques we develop might be of use also in this setting."

Xiaoming Hu , Professor, Optimization and Systems Theory

"My main research interests are in complex and networked systems, active sensing and perception, control of multi-agent systems, nonlinear observer design, and mobile manipulation. A common key issue among these research areas is how to do modeling and control based on the large amount of data obtained from the various sensors that are usually noisy."

Elias Jarlebring , Professor, Numerical Analysis

"My research area is numerical linear algebra and matrix computations, i.e., the study of linear algebra for numerical computations. All computational problems in this field involve in some way huge amounts of data stored in matrices, vectors or tensor. The most common problems are linear systems of equations, eigenvalue problems, singular value problem, matrix equations, etc. These problems arise in most fields in science and technology, in particular in the topics of the lab, e.g., data analysis. In order to construct efficient and robust computational procedures for problems, we exploit the complex structures in the data (typically in the matrices)."

Johan Karlsson , Associate Professor, Optimization and Systems Theory

"My current research interests include: Analysis and identification of complex and stochastic systems with emphasis on reliability and robustness. Deformation models such as optimal mass transport for inverse problems with prior information and for modeling time-varying systems. Large scale optimization problems, moment problems and low complexity modeling. Applications in remote sensing, signal processing, and systems theory."

Jan Kronqvist , Associate Professor, Optimization and Systems Theory

"My main research interest is in mixed-integer optimization, specifically in developing methods and strong convex relaxations. Strong, and computationally tractable, relaxations are one of the key components for solving nonconvex optimization problems, and weak relaxations can render even small problems computationally intractable. The goal is to develop efficient methods for solving challenging optimization problems with both integer variables and nonlinear expressions. I am a developer of the open-source mixed-integer nonlinear optimization solver SHOT , which integrates several new methods. I am also interested in mixed-integer optimization techniques for ML and AI. For example, I have worked on efficient mixed-integer techniques for robust verification of trained neural networks."

Pierre Nyquist , Associate Professor, Mathematical Statistics

"My main research area is probability theory (broadly construed) and I work on questions at the intersection of probability, statistics and applied mathematics; topics of current interest include large deviations theory, stochastic numerical methods, interacting particle systems, stochastic control, partial differential equations and statistical learning. Within the scope of the activities of the Lab, I am currently interested in the foundations of statistical learning and the analysis and design of efficient computational methods. I approach these topics from the perspective of a probabilist, studying stochastic processes that correspond to different algorithms and techniques for handling complex data. "

Anders Szepessy , Professor, Numerical Analysis

"My research interest is partial differential equations, numerical analysis and stochastic analysis. At the moment it is primarily directed towards analysis of classical and quantum mechanical particle systems, stochastic partial differential equations and inverse problems realted to optimal control. In all these areas there are research questions based on mathematics for complex data. For instance, reconstruction of empirical potentials from ab initio computations of particle systems, determination of distributions of stochastic parameters in differential equations and solving inverse problems with given data."

Bo Wahlberg , Professor, Automatic Control

"My research interests are in learning and control of dynamical system. Current research projects include matrix rank regularization techniques, sparse methods in Markov Decision Process problems, inverse filtering for Hidden Markov Models and identification of nonlinear stochastic dynamical systems."