• Geometric topology: Spatial graphs
• Mathematical chemistry: Shape modelling

Spatial graphs are embeddings of graphs in 3-manifolds. Graphs in themselves are purely combinatorial objects. However, in the tangible world around us, graphs manifest as physical objects in physical space. Properties of these spatial graphs are dependent on both the abstract underlying graphs and their specific realizations in space, which places their study between graph theory and knot theory. I am working interdisciplinary to model shapes in physics, biology, and in particular chemistry and material sciences. 

I study entanglements in spatial graphs and their embeddings in surfaces, often motivated by applications. Embeddings of graphs are traditionally 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 densities. I use geometrical and topological tools to e.g. develop descriptor of arrangements, model (diffusion) networks, quantify discorder, detect topologically critical values, quantify geometric-topological similarities, study crystal net topologies and their tilings. 

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 (ideally at the begin of your master studies):

• 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.

Teaching 2023\2024:

Mathematics 2 for BSc Creative Technology

Mathematics 3 for BSc Creative Technology

Calculus 2 for BSc Business Analytics

Differential Topology for BSc Mathematics

Winter School 'Introduction to Topological Data Analysis'

BSc Math project supervision 'Analysing relations between musical scales and cycles using filtered point symmetry'

MSc Business analytics project co-supervision: 'Assortment planning at IKEA'

In Amsterdam, I taught so far

• Calculus at AUC
• Calculus for mechanical engineering for BSc Mechanical Engineering
• Calculus 2 for Business Analytics

• Differential Topology for BSc Mathematics

• Mentored several 1st year projects for BSc Mech Engs (developing a mechanical cutter for under water pipes, designing power plants) 
• Mentored 2nd year student projects for BSc Mech Engs (diagnostics and maintainance of the grinders in coffee machines)
• Supervised seven 2nd year BSc Mathematics projects (Graph theory in Chemistry, tuning systems in music, geometric knot invariants)
• Supervision BSc Mathematics bachelor project on Cayley graphs
• Co-supervision master projects in MSc Business Analytics (Inventory level planning for Bols, gate scheduling for Schiphol airport)

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 was 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 (tenured 2022)
• 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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