• Geometric topology: Topological graph theory
• Mathematical chemistry: Shape modelling

Topological graph theory investigates embeddings of graphs in 3-manifolds. The properties of a graph embedding are partly dependent on the graph, and partly by the particular embedding. The flavours of research questions are somewhere between graph theory and knot theory. After all, a knot is just an embedding of a cycle graph. 

I am equally interested in understanding shapes and their impact in the physical world around us. I am working interdisciplinary to model shapes in physics, biology, and in particular chemistry and material sciences. Emeddings of graphs are commonly used to describe molecules. But shapes are also found at many other places, such as in the form of pores in porous materials, or the shapes of potential energy surfaces and charge densitites.

Group members:

Fabio Buccoliero PhD student working on cellular embeddings of spatial graphs.

Hannes Gustafsson PhD student co-supervised with Amber Mace (Uppsala Universitet) developing a cost-efficient multi-scale model for diffusion in crystalline materials. 

Riya Dogra PhD student working on the topology of molecular braids. 

Possible master thesis topics, contact me if you are interested:

• Studying knots formed from DNA in Bacteriophages
• Deriving counts for sets of non-adjacent vertices in periodic graphs from their fundamental domain to predict grand ensemble quantities for simulating methane storage.

Currently teaching:

Differential Topology for mathematicians

Supervision BSc math project on Cayley graphs. 

In Amsterdam, I taught so far

• Calculus at AUC
• Calculus for mechanical engineering of the mechanical engineering BSc that is joined between the VU Amsterdam and UTwente.
• Calculus 2 for business analytics
• Differential Topology for mathematicians
• Mentored several 1st year projects for mech engs (developing a mechanical cutter for under water pipes, designing power plants) 
• Mentored 2nd year student projects for mech engs (diagnostics and maintainance of the grinders in coffee machines)
• Supervised seven 2nd year Math BSc projects (Graph theory in Chemistry, tuning systems in music, geometric knot invariants)
• Co-supervision master project Business Analytics

Previously,

I have taught or assisted the following courses

• Differential equations
• Algebraic topology
• Linear algebra and Geometry
• Metric spaces and Topology
• Mathematical Analysis 1
• Mathematical Analysis 2
• Quantitative methods of data analysis
• Linear algebra for engineers
• Mathematical analysis and Calculus for engineers

Service:

• Confidential Counsellor Academic Integrity Faculty of Science
• Member of the Management team Mathematics department
• Social events committee Mathematics department

Previously at the VU Amsterdam:

VPR committee (outreach, communication, open days, webmaster, etc)

Reviewing for:

• Discrete & Computational Geometry
• Nature Communications
• Canadian Journal of Mathematics
• Frontiers in Chemistry (section Physical Chemistry and Chemical Physics)
• Materials research express
• New Journal of Chemistry
• Proceedings of the Royal Society A
• Acta Crystallographica Section A
• The Journal of Chemical Physics
• Materials Advances
• Langmuir
• The Journal of Physical Chemistry Letters
• Inverse Problems
• Mathematics, Symmetry, Minerals
• Zentralblatt Math
• Biomedical Physics & Engineering Express
• Applied Sciences
• Journal of Physics A: Mathematical and Theoretical

I am born and raised in Berlin, Germany. Before coming to Amsterdam, I lived in Switzerland, Austria, England, Japan (for a summer research stay), South Africa, and Germany. My scientific CV:

• Since 2019 Assitant professor at Vrije Univeriteit Amsterdam
• 2015-2019 Postdoc at EPFL Valais/Wallis in Berend Smit's molecular simulations group (chemistry/chemical engineering department)
• 2015 PhD from Imperial College London (Geometric topology, some modelling in topological cystallography)
• 2009 Diplom Mathematics from TU Berlin (Differential topology, master thesis on Gravitational lensing joined with Astronomy)
• 2006 Vordiplom Physics from TU Berlin

In a parallel life I graduated in

• 2007 Diplom Music Pedagogics from UdK Berlin (thesis on mathematial music theory, and on the theory and pedagogics of musical temperaments)

and worked as instrumental teacher and general music educator at the Musikschule Fanny Hensel Berlin (2007-2009) and at the Keiskamma Music Academy in Hamburg, South Africa (for 6 months in 2010). I taught recorder in groups and individually, gave ensemble lessons, taught music theory, history, and improvisation. My students won the Grahamtown Eisteddfod and we toured South Africa in concert. I won the first price of the South African "Rising star" music competition. After returning to Europe, I co-founded a recorder ensemble. We were awarded a Yehudi Menuhin fellowship 2011-2015 and performed in concerts.

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