MATH+

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.

The semester is organized within the framework of the Berlin Mathematics Research Center MATH+ and supported by the Einstein Foundation Berlin.

Opening Event

April 13, 2021

• Ileana Streinu (Smith College)
• Daphne Klotsa (U North Carolina at Chapel Hill)
• Herbert Edelsbrunner (IST Austria)

April 14, 2021

• Stephen Hyde (U Sydney)
• Motoko Kotani (Tohoku U)
• Yasuaki Hiraoka (Kyoto U)

Collegiality

MATH+ Collegiality Statement

Contact

tes-summer2021@math.tu-berlin.de