The Role of Topology in Materials

students on the topic of geometry and topology. 4. Mark Dennis (Univ. of Bristol), Mark.Dennis@bristol.ac.uk Geometry and topology of knots: electron vortices and wave dislocations.

Professor of Theoretical Physics in the Theoretical Physics Group of the School of Physics. His main research is in Optical Field Theory and Topological Physics. These topics involve his primary focus on geometric and topological aspects of wave physics, especially their manifestation in structured light and quantum wave functions:

· Singular and topological optics, including optical and electron vortices, wave dislocations and polarization singularities. · Statistical geometry and topology of random functions, with application to quantum chaos, statistical optics and cosmology. · Geometry and topology of knots, links, braids and ribbons, especially those in spatially-extended fields.

5. Rumiana Dimova and Roland Knorr (Max-Planck Inst. Of Colloids and Interfaces, Germany), Rumiana.Dimova@mpikg.mpg.de and Roland.Knorr@mpikg.mpg.de The main focus of research is on shape transformations in lipid vesicles. They are Team Leaders in the field of Biomembranes and giant vesicles. Their group employs giant vesicles for systematic measurements of the properties of lipid bilayers as a function of membrane composition and phase state, surrounding media, curvature, topology and temperature. They have investigated membrane responses to external factors such as ions, amphiphilic (biomacro-) molecules and polymers, membrane-wetting aqueous phases, hydrodynamic flows or electromagnetic fields and have measured topologies associated with genus. 6. Sanju Gupta (W. Kentucky Univ.) and Avadh Saxena (Los Alamos), Sanju.gupta@wku.edu and Avadh@lanl.gov Topology of nanocarbons and functional materials. 7. Erika Kauffman (Purdue University), ebkaufma@math.purdue.edu Wire networks, gyroids and triply periodic materials. Associate Professor of Mathematics and Physics. She is an expert in the modeling of non-equilibrium systems and quantum wire networks. Her research spans triply-periodic minimal surfaces and finite-size scaling in atomic models. She was awarded an NSF Career grant on Physical properties of new materials via mathematics -- methods and applications. 8. Jacob Kirkensgaard (University of Copenhagen), jjkk@nbi.ku.dk Triply periodic and gyroid sturctures. Associate Professor in the X-ray and Neutron Science group at the Niels Bohr Institute, His research is centered around mesoscale self-assembly and the formation of geometrically and topologically complex structures. He combines expertise in coarse-grained molecular dynamics simulations of soft matter self-assembly with structural investigations of soft matter systems using small-angle scattering techniques (i.e. metrology of topological systems). 9. Cristiano Nisoli (Los Alamos National Lab) and Gia-Wei Chern (University of Virginia), Cristiano@lanl.gov and gc6u@eservices.virginia.edu Designed frustration in artificial spin ice. Staff Member at the Theoretical Division and a pioneer of the Artifical Spin Ice (ASI) materials and their topological defects including monopoles. Many recent marquee publications including in Physics Today, Nature, Nature Physics, Reviews of Modern Physics and Physical Review Letters. Clearly an emerging world leader in this field of research. 10. Jun Onoe (Univ. Nagoya) and Hiroyuki Shima (Yamanashi Univ., Japan), j-onoe@nucl.nagoya-u.ac.jp and hshima@yamanashi.ac.jp Complex carbon nanomaterials and their topology. Leading professor at the Department of Materials, Physics and Energy Engineering in the Division of Quantum Science. Outstanding contributions to the synthesis and topological characterization of carbon nanomaterials; discoverer of the bucky-ball polymer. Frequently invited speaker and an authority on this topic. He has organized many workshops on this important and growing topic. 11. Tony Roberts (Univ. Queensland Australia), apr@maths.uq.edu.au Cellular structures and properties.

Associate Professor of Mathematics and Physics. His research interests are in Mathematical Materials Science. The properties of many important natural and manufactured materials are linked to their internal microstructure. The study of how these microstructural details influence macroscopic properties leads to fascinating scientific and mathematical questions. The results show how manufactured materials can be optimized via Topology Optimization: Design of artificial bone implants, Models of random structures: Gaussian random fields, 3D Poisson models, percolation models, diffusion limited aggregation, fractal networks and trees, Analysis of experimental techniques: Statistical reconstruction of 3D models from 2D images; Small angle neutron and x-ray scattering. 12. Tamar Schlick (New York Univ.), schlock@nyu.edu Topological soft matter. Professor of Chemistry, Mathematics and Computer Science, Courant Institute. Author of a textbook on Molecular Modeling. Fellow of APS, AAAS, SIAM and Biophysical Society. On the Editorial Boards of several journals. Substantial contributions to the topology of chromatin, RNA and various other biomolecules. She is a prolific researcher with about 6000 citations (according to the Web of Science) and an h-index of 44. 13. Gennady Shvets (Univ. Texas at Austin), gena@physics.utexas.edu Topological photonic materials. Professor of photonics (Ph.D. from MIT). Fellow of American Physical Society and the Optical Society of America. Frequent invited speaker who has made significant contributions to photonic metamaterials, plasmonics and photonic topological materials. Over 7000 citations with an h-index of 44 (Web of Science). 14. David Srolovitz and Menachem Lazar (Univ. Pennsylvania), srol@seas.upenn.edu and mlazar@seas.upenn.edu Topology of Microstructure Optimization Named Professor of Materials Science & Engineering, Mechanical Engineering and Applied Mechanics, and Computer and Information Science. Former chair at Princeton University and President of Yeshiva University. MRS Fellow, IoP Fellow, ASM International Fellow. He is a distinguished researcher with xtensive contributions to the topology of materials microstructure and topological defects such as dislocations. 15. Joanna Sulkowska (University of Warsaw), jsulkows@gmail.com DNA knotting and lasso topologies in biomaterials. eam leader of interdisciplinary laboratory of biological systems modeling at the Center of new Technologies. Her scientific interests and expertise are directly associated with knot theory in DNA and other biological molecules, such as the development of multi-dimensional models for the analysis of energy landscape of proteins with complex structures, as proteins with non-trivial topology; development of analytical methods as direct coupling analysis (DCA) and bioinformatics tools for analysis of amino acids evolution and their application to prediction of protein structures (including membrane proteins) and alternative protein folding mechanism; development and application of mathematical knot theory to determine the topology of open chain and its application to proteins and nucleic acids. 16. Mingliang Tian (Hefei, China), tianml@hmfl.ac.cn Skyrmions in confined geometries.

Professor of Physics at High Magnetic Field Lab (Hefei), University of Science and Technology of China, Chinese Academy of Science and former professor at Penn State University. Substantial contributions to quantum properties of topological materials including helical magnets and skyrmions. Many high profile papers published on this topic including a recent Nature Commun. paper on skyrmions in confined geometries.

textures called skyrmions, has been featured in Discovery News. He holds Adjunct Professor positions at the University of Barcelona, University of Arizona and Virginia Tech. Recently he was granted the prestigious Affiliate Professorship at the Royal Institute of Technology (KTH), Stockholm. He also serves as an advisor for the National Institute for Materials Science, Tsukuba, Japan.