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Geometry and Topology in Contemporary Material Science - International Summer School 2022
Provider: Faculty of Science

Activity no.: 5876-22-11-31 
Enrollment deadline: 01/08/2022
Date and timeAugust 2022
Regular seats30
ECTS credits5.00
Contact personJulie Meier Hansen    E-mail address: juliemh@nbi.ku.dk
Enrolment Handling/Course OrganiserJacob Judas Kain Kirkensgaard    E-mail address: jjkk@food.ku.dk
Written languageEnglish
Teaching languageEnglish
Block noteDuration: 1 week
Course workload
Course workload categoryHours
Preparation / Self-Study75.00
Course hours50.00



To apply:

Due to summer holidays, we ask that you - in addition to applying using the form below - send an email to Jacob Judas Kain Kirkensgaard <jjkk@food.ku.dk> and inform him that you have applied. Please include your school affiliation, educational level/position and contact information. 

Thank you!


For more information on the summer school, please visit --> home page for the school.

Aim and content
This 5 ECTS point course will explore the geometry and topology of ordered cellular patterns such as foams, bicontinuous and polycontinuous forms and nets found in synthetic and biological materials, including:

• Mesoporous silicates
• Metal organic frameworks and coordination polymers
• Amphiphiles, lipids, star polyphiles forming lyotropic liquid crystals
• Block copolymers including star miktoarm copolymers

Lectures will emphasise the fundamental structural aspects, with an introduction to the following concepts from modern geometry, crystallography and topology:

• Two-dimensional symmetries and orbifolds (wallpaper and point groups)
• Graph theory and net embeddings, knots and entanglement
• Triply-periodic minimal surfaces and related polycontinuous patterns
• 2D hyperbolic tilings and their embedding in 3D

No specialised mathematical knowledge is assumed, apart from some elementary familiarity with the shape of space, polyhedra and symmetry. The course will introduce students to unifying structural concepts in a range of ordered multi-phase hard/soft materials. We encourage students with theoretical or experimental backgrounds to attend.

The course will familiarise students with open-source software for construction and characterisation of structures from nets to surfaces. Hands-on tutorials will explore the concepts, via models and software like Kaleidotile, Surface Evolver, Houdini, GAVROG (3dt and Systre), RCSR, EPINET and HooMD for molecular simulations.

Stand-alone evening / afternoon lectures will be presented by active material researchers explaining current understanding of mesoporous materials and associated biological assemblies.

The course is free to attend, but all travel, accommodation and meals are at participants' own expense. A limited number of participants will be chosen from the applicants.

Stephen Hyde
University of Sydney, Australia

Gerd Schröder-Turk
Murdoch University, Australia

Myfanwy Evans
University of Potsdam, Germany

Martin Cramer Pedersen
University of Copenhagen, Denmark

Jacob Kirkensgaard
University of Copenhagen, Denmark

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