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

• Ileana Streinu (Smith College)
• Daphne Klotsa (U North Carolina at Chapel Hill)
• Herbert Edelsbrunner (IST Austria)
• Stephen Hyde (U Sydney)
  
• Motoko Kotani (Tohoku U)
  
• Yasuaki Hiraoka (Kyoto U)
  

Thematic Days

• James A. Sethian (UC Berkeley / LBNL)
• 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)

• Vanessa Robins (ANU)
• Ippei Obayashi (Okayama U)
• Katharine Turner (ANU)
• Wojciech Chachólski (KTH Stockholm)

June 10, 2021, Thematic Day 5, Algebraic Geometry and Framework Materials

Time Zone: Berlin Time (Central European Summer Time, CEST)

Chair: Miranda Holmes-Cerfon / Bernd Sturmfels

• 04:00 pm to 04:40 pm   Bernd Sturmfels   (MPI Leipzig)

  
  3264 Conics in A Second
  
  

• 04:50 pm to 05:30 pm   Xiaoming Mao   (U Michigan)

  
  Frustrated Self-Assembly of Non-Euclidean Crystals of Nanoparticles
  
  

• 05:30 am to 06:00 am   Virtual coffee break
  

• 06:00 pm to 06:40 pm   Alexander Heaton   (The Fields Institute Toronto)

  
  Auxetic tensegrity and constrained optimization on algebraic varieties
  
  

• 06:50 pm to 07:30 pm   Miranda Holmes-Cerfon   (Courant Institute)

  
  Almost-rigidity of frameworks

June 24, 2021, Thematic Day 6, Topological Ideas in Applications

• Erin Wolf Chambers (Saint Louis U)
• Senja Barthel (Vrije U Amsterdam)
• Elizabeth Munch (Michigan State U)
• t.b.a.

July 1, 2021, Thematic Day 7, t.b.a.

• t.b.a.

July 2, 2021, MATH+ Friday Colloquium

• 02:15 pm to 03:15 pm   Kathryn Hess Bellwald (EPFL)
  Topological insights in neuroscience

External Activities

April 26-30, 2021, Topological Data Analysis, IMSI

(organized by Brittany Fasy (Montana), Kathryn Hess (EPFL), Matthew Kahle (Ohio State), Sayan Mukherjee (Duke), Jose Perea (Michigan State))

May 4--11, 2021, Hot Topics: Topological Insights in Neuroscience, MSRI

(organized by Carina Curto (Penn State U), Chad Giusti (U Delaware), Kathryn Hess (EPFL), Ran Levi (U Aberdeen))

May 20--21, 2021, Interdisciplinary Workshop Mathematics, Materials Science & Design: The Geometry & Topology behind Fabrics at Multiple Scales

(organized by Sonia Mahmoudi (Tohoku U) and the Tohoku University Advanced Institute for Materials Research)

May 31 -- June 2, 2021, Workshop on Software and Applications of Numerical Nonlinear Algebra, MPI MIS

(organized by Paul Breiding, Taylor Brysiewicz, Simon Telen (MPI MIS Leizig) and Sascha Timme (TU Berlin))

Semester courses for local students

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