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 + 14, 2021, Titles and Abstracts
- 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
April 22, 2021, Thematic Day 1, Applied Facets of Geometry and Topology, Titles and Abstracts
- James A. Sethian (UC Berkeley / LBNL)
- Lisbeth Fajstrup (Aalborg U)
- Jacek Brodzki (U Southampton)
May 6, 2021, Thematic Day 2, Cellular Materials, Titles and Abstracts
- Francisco Garcia-Moreno (Helmholtz-Zentrum Berlin / TU Berlin)
- Emanuel (Menachem) Lazar (Bar-Ilan U)
- Michael Klatt (Saarland U)
- John M. Sullivan (TU Berlin)
May 20, 2021, Thematic Day 3, Stochastic Geometry and Materials, Titles and Abstracts
- Claudia Redenbach (TU Kaiserslautern)
- Benedikt Jahnel (WIAS Berlin)
- Barbara Zwicknagl (HU Berlin)
- Wolfgang König (TU Berlin / WIAS Berlin)
May 26, 2021, Thematic Day 4, Topological Data Analysis, Titles and Abstracts
- 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, Titles and Abstracts
- Bernd Sturmfels (MPI Leipzig / UC Berkeley)
- Xiaoming Mao (U Michigan)
- Alexander Heaton (The Fields Institute Toronto)
- Miranda Holmes-Cerfon (Courant Institute)
June 24, 2021, Thematic Day 6, Topological Ideas in Applications, Titles and Abstracts
- Erin Wolf Chambers (Saint Louis U)
- Senja Barthel (Vrije U Amsterdam)
- Elizabeth Munch (Michigan State U)
- Paweł Dłotko (Dioscuri Centre Warszawa)
July 1, 2021, Thematic Day 7, Modelling and Structure, Titles and Abstracts
- Sonia Mahmoudi (Tohoku U)
- Marta Panizzut (TU Berlin)
- Rhoslyn Coles (TU Berlin)
- Teresa Heiss (IST Austria)
July 2, 2021, MATH+ Friday Colloquium
- Kathryn Hess Bellwald (EPFL)
Thematic Mini-Conferences
September 21 + 22, 2021, Thematic Mini-Conference, Stochastic Topology, Titles and Abstracts
- Roy Meshulam (Technion)
- Sayan Mukherjee (Duke U)
- Érika Roldán (TU München / EPFL)
- Andrew Newman (Carnegie Mellon)
- Matthew Kahle (Ohio State U)
- Omer Bobrowski (Technion)
- Yuval Peled (Hebrew U)
- Benjamin Schweinhart (George Mason U)
September 28 + 29, 2021, Thematic Mini-Conference, Computational Topology and Machine Learning, Titles and Abstracts
- Jose Perea (Northeastern U)
- Bastian Rieck (ETH Zürich)
- Henry Adams (Colorado State U)
- Roland Kwitt (U Salzburg)
- Peter Bubenik (U Florida)
- Chao Chen (Stony Brook)
- Yusu Wang (UC San Diego)
- Mathieu Carrière (Inria Sophia Antipolis)
Semester courses for local students
Discrete and Computational Topology, Frank H. Lutz (TU Berlin)
Discrete Geometrie II, Matthias Beck (FU Berlin)
Discrete Geometry III, Michael Joswig (TU Berlin)
Geometry, Topology and Applications, Myfanwy Evans (U Potsdam)
Mathematical Visualization: The Symmetries of Things, John M. Sullivan (TU Berlin)
Zellulare Materialien Francisco Garcia-Moreno (Helmholtz-Zentrum Berlin / TU Berlin)
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))
Collegiality
MATH+ Collegiality Statement
Contact
tes-summer2021@math.tu-berlin.de