{"id":891,"date":"2016-07-22T12:24:19","date_gmt":"2016-07-22T16:24:19","guid":{"rendered":"https:\/\/jasoncantarella.com\/wordpress\/?page_id=891"},"modified":"2016-07-30T22:11:26","modified_gmt":"2016-07-31T02:11:26","slug":"summer-minicourse-polygons-and-grassmannians","status":"publish","type":"page","link":"https:\/\/jasoncantarella.com\/wordpress\/courses\/summer-minicourse-polygons-and-grassmannians\/","title":{"rendered":"Summer Minicourse: Polygons and Grassmannians"},"content":{"rendered":"<p>In the summer of 2016, I gave a short summer minicourse for graduate students on polygons, grassmannians, and linkages. These are scans of my notes for the lectures, along with some supplemental reading suggestions.<\/p>\n<ol>\n<li><a href=\"https:\/\/jasoncantarella.com\/downloads\/polygons-and-grassmannians.pdf\">Introduction: Polygons and Grassmannians<\/a>\u00a0(7\/19\/2016)\n<ul>\n<li>Random triangles and polygons in the plane. Cantarella, Needham, Shonkwiler (in preparation).<\/li>\n<li>Hausmann, J.-C., &amp; Knutson, A. (1997). Polygon spaces and Grassmannians. L&#8217;Enseignement Mathematique. Revue Internationale. 2e Serie, 43(1-2), 173\u2013198.<\/li>\n<li>Cantarella, J., Deguchi, T., &amp; Shonkwiler, C. (2013). Probability Theory of Random Polygons from the Quaternionic Viewpoint. Communications on Pure and Applied Mathematics. http:\/\/doi.org\/10.1002\/cpa.21480<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"https:\/\/jasoncantarella.com\/downloads\/carpenters-ruler-1.pdf\">The Carpenter&#8217;s Ruler Problem: Background from Tensegrity Theory<\/a>\u00a0(7\/20\/2016)\n<ul>\n<li>Roth, B., &amp; Whiteley, W. (1981). Tensegrity frameworks. Trans. Amer. Math. Soc., 265(2), 419\u2013446.<\/li>\n<li>Connelly, R., Demaine, E., &amp; Rote, G. (2003). Straightening polygonal arcs and convexifying polygonal cycles. Discrete &amp; Computational Geometry, 30(2), 205\u2013239.<\/li>\n<li>Streinu, I. (2000). A combinatorial approach to planar non-colliding robot arm motion planning. Collection (pp. 443\u2013453).<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"https:\/\/jasoncantarella.com\/downloads\/carpenters-rule-2.pdf\">The Carpenter&#8217;s Ruler Problem: Main Argument.<\/a>\u00a0(7\/22\/2016)\n<ul>\n<li>Cantarella, J., Demaine, E., Iben, H. N., Iben, H. N., O&#8217;Brien, J. F., &amp; O&#8217;Brien, J. F. (2004). An energy-driven approach to linkage unfolding. Presented at the SCG &#8217;04: Proceedings of the twentieth annual symposium on Computational geometry, \u00a0ACM \u00a0Request Permissions. http:\/\/doi.org\/10.1145\/997817.997840<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"https:\/\/jasoncantarella.com\/downloads\/distance-geometry-1.pdf\">Distance Geometry I: Gower&#8217;s Theorem constructing point clouds from distance matrices.<\/a> (7\/25\/16)\n<ul>\n<li>Gower, J. C. (1982). Euclidean distance geometry. The Mathematical Scientist, 7(1), 1\u201314.<\/li>\n<li>Liberti, L., Lavor, C., Maculan, N., &amp; Mucherino, A. (2014). Euclidean Distance Geometry and Applications. SIAM Rev., 56(1), 3\u201369. http:\/\/doi.org\/10.1137\/120875909<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"https:\/\/jasoncantarella.com\/downloads\/distance-geometry-2.pdf\">Distance Geometry II: More on Gower&#8217;s Theorem, the Cayley-Menger Determinant.<\/a> (7\/26\/16)\n<ul>\n<li><a href=\"http:\/\/www.mathpages.com\/home\/kmath664\/kmath664.htm\">A web proof of the Cayley-Menger formula.<\/a><\/li>\n<li>Liberti, L., &amp; Lavor, C. (2016). Six mathematical gems from the history of distance geometry. International Transactions in Operational Research, 23(5), 897\u2013920. http:\/\/doi.org\/10.1111\/itor.12170<\/li>\n<\/ul>\n<\/li>\n<li><a href=\"http:\/\/ww.jasoncantarella.com\/downloads\/distance-geometry-3.pdf\">Distance Geometry III: Tay&#8217;s Proof of Laman&#8217;s Theorem and the 3T2 decomposition<\/a> (7\/29\/16)\n<ul>\n<li>Tay, T.-S. (1993). <a href=\"https:\/\/jasoncantarella.com\/downloads\/tay-laman-theorem.pdf\">A new proof of Laman&#8217;s theorem<\/a>. Graphs and Combinatorics, 9(4), 365\u2013370. http:\/\/doi.org\/10.1007\/BF02988323<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>In the summer of 2016, I gave a short summer minicourse for graduate students on polygons, grassmannians, and linkages. These are scans of my notes for the lectures, along with some supplemental reading suggestions. Introduction: Polygons and Grassmannians\u00a0(7\/19\/2016) Random triangles and polygons in the plane. Cantarella, Needham, Shonkwiler (in preparation). Hausmann, J.-C., &amp; Knutson, A. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":78,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-notitle.php","meta":{"footnotes":""},"class_list":["post-891","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/891","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/comments?post=891"}],"version-history":[{"count":6,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/891\/revisions"}],"predecessor-version":[{"id":900,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/891\/revisions\/900"}],"up":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/78"}],"wp:attachment":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/media?parent=891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}