BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sabetta Matsumoto (Georgia Tech) DTSTART:20230811T160000Z DTEND:20230811T170000Z DTSTAMP:20260423T021033Z UID:IMSO/4 DESCRIPTION:Title: Twi sted topological tangles or: the knot theory of knitting\nby Sabetta M atsumoto (Georgia Tech) as part of Illustrating Math Seminar Online\n\n\nA bstract\nImagine a 1D curve\, then use it to fill a 2D manifold that cover s an arbitrary 3D object – this computationally intensive materials chal lenge has been realized in the ancient technology known as knitting. This process for making functional materials 2D materials from 1D portable clot h dates back to prehistory\, with the oldest known examples dating from th e 11th century CE. Knitted textiles are ubiquitous as they are easy and ch eap to create\, lightweight\, portable\, flexible and stretchy. As with ma ny functional materials\, the key to knitting’s extraordinary properties lies in its microstructure. At the 1D level\, knits are composed of an in terlocking series of slip knots. At the most basic level there is only one manipulation that creates a knitted stitch – pulling a loop of yarn thr ough another loop. However\, there exist hundreds of books with thousands of patterns of stitches with seemingly unbounded complexity. The topology of knitted stitches has a profound impact on the geometry and elasticity o f the resulting fabric. We have developed a formalization of the topology of two-periodic weft knitted textiles using a construction we call the swa tch [1]. Using this construction\, we can prove that all two-periodic weft knits form ribbon links [2]. This puts a new spin on additive manufacturi ng – not only can stitch pattern control the local and global geometry o f a textile\, but the creation process encodes mechanical properties withi n the material itself. Unlike standard additive manufacturing techniques\, the innate properties of the yarn and the stitch microstructure has a dir ect effect on the global geometric and mechanical outcome of knitted fabri cs.\n\nThe authors were partially supported by National Science Foundation grant DMR-1847172\, by the Research Corporation for Science Advancement a nd by the International Center for Sustainability with Chiral Knotted Meta Matter (SKCM²). We would like to thank sarah-marie belcastro\, Jen Hom\, Jim McCann\, Agniva Roy\, Saul Schleimer and Henry Segerman for many frui tful conversations. [1] S. Markande and S. Matsumoto\, in: Proceedings of Bridges 2020: Mathematics\, Art\, Music\, Architecture\, Culture\, (Tessel ations Publishing\, 2020)\, pp. 103–112. [2] M. Kuzbary\, S. Markande\, S. Matsumoto and S. Pritchard\, 2022.\n LOCATION:https://researchseminars.org/talk/IMSO/4/ END:VEVENT END:VCALENDAR