Wolfgang Bock

I am quite new at Linnaeus University as I started as Senior Lecturer in August 2023. Since December 2023 I am Docent, which could be translated as Associate Professor in the area of Stochastic Analysis.

I finished my PhD 2013 at the Technische Universität Kaiserslautern in Germany in the field of Stochastic Analysis under the supervision of Martin Grothaus. From August 2013 to August 2014 I was postdoctoral fellow at the Center of Mathematical Analysis and its Applications (CMAF) in Lisbon, Portugal. 

Starting from September 2014 I was on a lecturer position at TU Kaiserslautern and from 2015 I was permanent senior lecturer (Akademischer Rat) and responsible for the Engineering Mathematics in Kaiserslautern. 

During my academic life I have actively participated in several comissions and was also highly involved in internationalization. 

I want to use my knowledge to be a "change maker" and enhance the international visibility of LNU in Stochastic Analysis.  

Teaching

I am currently teaching

1MA441/1MA401 Basic Mathematics for Computer Science/ Mathematics

4MA901 Applied Analysis

Please see MyMoodle for the websites.

Research

Currently my research has 3 focal projects:

1.) Leavitt path algebras and their respresentation (wirth A. Sebandal)

My research within this project develops structural and dynamical tools for the classification of Leavitt path algebras (LPAs), with the long-term goal of contributing to a solution of Hazrat’s graded isomorphism conjecture, which predicts that the so-called talented monoid completely determines graded isomorphism. Among other things, we have shown how the adjacency matrix acts on the talented monoid and encodes hereditary/saturated subsets, thereby linking graph data directly to graded ideals; we have analyzed Lie algebras over LPAs and connected their simplicity and solvability to monoid invariants and GK-dimension; and we have introduced algebraic entropy as a robust quantitative invariant, proving its agreement for path algebras and LPAs as well as its stability under Morita equivalence. In addition, A. Sebandal has coauthored the classification of LPAs arising from graphs with disjoint cycles (with Hazrat and Vilela), an important special case of the conjecture. Taken together, these results strengthen the invariant framework and provide concrete methods for detecting graded isomorphisms, positioning our work as a step toward resolving Hazrat’s conjecture.

2.) Non-Gaussian Analysis and Random Time Change

(with O. Draouil from University of Tunis El Manar and Lorenzo Cristofaro from University of Luxembourg)

Aim is the development of a white noise like calculus for non-Gaussian measures which can be represented as randomly scaled Gaussian measures. Classical examples are Incomplete Gamma measures and the Mittag-Leffler measure. 

The corresponding processes have structural properties which are very close to that of Gaussian processes. We want to use these to develop a regularity theory in the sense of Meyer-Watanabe, based on the Hitsude-Skorokhod type integral. 

3.) White Noise Analysis and Mittag-Leffler Analysis

In this project, we have serval conributions to the theory of Gaussian Analysis and Mittag-Leffler Analysis. 

• Mosco convergence vs. Hida convergence

In this subproject, I established a sufficient condition for Kuwae-Shioya-Mosco convergence for Dirichlet forms over White Noise spaces. We linked the convergence to a uniform convergence of Hida-distributions. The result is also valid for changing reference measures. As an example we showed that the planar fractional Edwards measure can be used to approximate the stochastic quantization of the planar Brownian polymer measure.

• Operators and Regularity in Mittag-Leffler Analysis

In this subproject we established an operator calculus for non-Gaussian analysis using differential operators on polynomials. The challenge is that there is no Fock space in the Mittag-Leffler case. In addition we worked out concepts for regularity theory in non-Gaussian analysis, which are user friendly.