Thematic Einstein Semester on

Geometric and Topological Structure of Materials

Summer Semester 2021

Organizers

Myfanwy Evans (U Potsdam)
Kathryn Hess Bellwald (EPFL)
Frank H. Lutz (TU Berlin)
Dmitriy Morozov (LBNL)
Ileana Streinu (Smith College)

Scope

This Thematic Einstein Semester, devoted to recent developments in the field of computational materials science, brings together experts from the sciences with experts from computational topology, computational algebraic, discrete differential and stochastic geometry working on the structure and function of materials.

Physical properties of materials are governed to a large extent by their microstructure, on which various geometric and topological analyses can be performed to identify essential structural properties. This leads to improvements in production processes or to new designs of materials with controlled properties:

• The geometric form of material microstructures plays a critical role in macroscopic function and is subject to a myriad of energy constraints.
• The spatial geometry of framework materials is described precisely by a set of algebraic constraints. These reveal insight into the physically based descriptions of rigidity, flexibility and spatial deformations of the structures.
• Crystalline structure requires a more enumerative, data-driven approach to material characterization than disordered systems.
• Polycrystalline materials like rocks, metals or steel, but also foams can be regarded as cellular decompositions of three-dimensional space.
• Establishing phase transitions for topological properties provides understanding for how well material structures can be approximated by random topological spaces.
• Persistence helps to describe the changes that a material, like an amorphous solid or glass, undergoes during phase transitions.
• Research at the interface of topology and neuroscience includes the classification and synthesis of neuron morphologies.

Opening Event

• 02:15 pm to 02:45 pm   Virtual get-together
  
• 02:45 pm to 03:00 pm   Welcome address by Christof Schütte (President of ZIB Berlin, Chair of MATH+)
  
  
• 03:00 pm to 03:40 pm   Ileana Streinu (Smith College)
  Rigidity, Circuits and Resultants: a combinatorial elimination approach to localization
  
  
• 03:50 pm to 04:30 pm   Daphne Klotsa (U North Carolina at Chapel Hill)
  
  
• 04:30 pm to 05:00 pm   Virtual coffee break
  
  
• 05:00 pm to 05:40 pm   Herbert Edelsbrunner (IST Austria)
  

• 09:00 am to 09:40 am   Stephen Hyde (U Sydney)
  
• 09:50 am to 10:30 am   Motoko Kotani (Tohoku U)
  
  
• 10:30 am to 11:00 am   Virtual coffee break
  
  
• 11:00 am to 11:40 am   Yasuaki Hiraoka (Kyoto U)
  On characterizing rare events in persistent homology

Thematic Days

• James A. Sethian (UC Berkeley / LBNL) (to be confirmed)
• Lisbeth Fajstrup (Aalborg U)
• Jacek Brodzki (U Southampton)

• Francisco Garcia-Moreno (Helmholtz-Zentrum Berlin / TU Berlin)
• Emanuel (Menachem) Lazar (Bar-Ilan U)
• Michael Klatt (Saarland U)
• John M. Sullivan (TU Berlin)

• Claudia Redenbach (TU Kaiserslautern)
• Benedikt Jahnel (WIAS Berlin)
• Barbara Zwicknagl (HU Berlin)
• Wolfgang König (TU Berlin / WIAS Berlin)

• t.b.a.

Semester courses for local students

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