{"id":182,"date":"2019-06-19T11:51:49","date_gmt":"2019-06-19T15:51:49","guid":{"rendered":"http:\/\/sites.williams.edu\/10rem\/?page_id=182"},"modified":"2026-01-09T13:48:06","modified_gmt":"2026-01-09T18:48:06","slug":"work-with-and-by-students","status":"publish","type":"page","link":"https:\/\/sites.williams.edu\/10rem\/work-with-and-by-students\/","title":{"rendered":"Work with and by students"},"content":{"rendered":"<p><strong>The SMALL REU<\/strong><\/p>\n<p>I advised groups as part of Williams College&#8217;s SMALL REU in 2017, 2018, 2020, 2021, 2023, and 2025.\u00a0 Check out the <a href=\"https:\/\/sites.williams.edu\/10rem\/research\/\">research page<\/a> for our publications!<\/p>\n<div id=\"attachment_185\" style=\"width: 970px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-185\" class=\"wp-image-185 size-full\" src=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/YMC_photo.jpg\" alt=\"\" width=\"960\" height=\"720\" srcset=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/YMC_photo.jpg 960w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/YMC_photo-300x225.jpg 300w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/YMC_photo-768x576.jpg 768w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/YMC_photo-400x300.jpg 400w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><p id=\"caption-attachment-185\" class=\"wp-caption-text\">SMALL Tropical Geometry 2017 at the Young Mathematician&#8217;s Conference in Columbus, OH (Andrew Scharf &#8217;18, Sifan Jiang, Desmond Coles, Neelav Dutta, RM)<\/p><\/div>\n<div id=\"attachment_187\" style=\"width: 778px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-187\" class=\"wp-image-187 size-full\" src=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/38674333_10215190749620876_7893495611909996544_n-768x576.jpg\" alt=\"\" width=\"768\" height=\"576\" srcset=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/38674333_10215190749620876_7893495611909996544_n-768x576.jpg 768w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/38674333_10215190749620876_7893495611909996544_n-768x576-300x225.jpg 300w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/38674333_10215190749620876_7893495611909996544_n-768x576-400x300.jpg 400w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><p id=\"caption-attachment-187\" class=\"wp-caption-text\">SMALL Tropical Geometry 2018 at Mathfest in Denver, CO (Teresa Yu &#8217;20, Julie Yuan, Franny Dean &#8217;19, RM, Ivan Aidun, Sammy Rosofsky &#8217;19)<\/p><\/div>\n<div id=\"attachment_394\" style=\"width: 674px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-394\" class=\"wp-image-394 size-full\" src=\"https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small_2020.png\" alt=\"\" width=\"664\" height=\"415\" srcset=\"https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small_2020.png 664w, https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small_2020-300x188.png 300w, https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small_2020-480x300.png 480w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><p id=\"caption-attachment-394\" class=\"wp-caption-text\">SMALL Tropical and Algebraic Geometry 2020 on Zoom (Robin Huang &#8217;21, Liza Jacoby &#8217;22, Marino Echavarria, Ben Weber &#8217;21, Raluca Vlad, Max Everett &#8217;21)<\/p><\/div>\n<div id=\"attachment_395\" style=\"width: 594px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-395\" class=\"wp-image-395 size-large\" src=\"https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small2021-copy-1024x852.jpg\" alt=\"\" width=\"584\" height=\"486\" srcset=\"https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small2021-copy-1024x852.jpg 1024w, https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small2021-copy-300x250.jpg 300w, https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small2021-copy-768x639.jpg 768w, https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small2021-copy-1536x1279.jpg 1536w, https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small2021-copy-2048x1705.jpg 2048w, https:\/\/sites.williams.edu\/10rem\/files\/2022\/08\/small2021-copy-360x300.jpg 360w\" sizes=\"auto, (max-width: 584px) 100vw, 584px\" \/><p id=\"caption-attachment-395\" class=\"wp-caption-text\">SMALL 2021 Chip-Firing Games in the Frank Morgan Library (Jason Meintjes &#8217;22, Liz Ostemeyer &#8216;22.5, Lizzie Ferguson &#8217;22, Lisa Cenek, Shefali Ramakrishna, Eyobel Gebre &#8217;22, Cassandra Marcussen)<\/p><\/div>\n<div id=\"attachment_436\" style=\"width: 594px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-436\" class=\"wp-image-436 size-large\" src=\"https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/SMALL_2023_poster-1024x768.jpeg\" alt=\"\" width=\"584\" height=\"438\" srcset=\"https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/SMALL_2023_poster-1024x768.jpeg 1024w, https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/SMALL_2023_poster-300x225.jpeg 300w, https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/SMALL_2023_poster-768x576.jpeg 768w, https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/SMALL_2023_poster-400x300.jpeg 400w, https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/SMALL_2023_poster.jpeg 1330w\" sizes=\"auto, (max-width: 584px) 100vw, 584px\" \/><p id=\"caption-attachment-436\" class=\"wp-caption-text\">SMALL 2023 Chip-Firing Games at the Summer Science Poster Session (Cassie Ding, Sasha Kononova, Chan Lee &#8217;24, Marchelle Beougher, Nila Cibu, Steven DiSilvio, Krish Singal)<\/p><\/div>\n<div id=\"attachment_435\" style=\"width: 1013px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-435\" class=\"wp-image-435 size-full\" src=\"https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/chip_firers.jpeg\" alt=\"\" width=\"1003\" height=\"745\" srcset=\"https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/chip_firers.jpeg 1003w, https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/chip_firers-300x223.jpeg 300w, https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/chip_firers-768x570.jpeg 768w, https:\/\/sites.williams.edu\/10rem\/files\/2026\/01\/chip_firers-404x300.jpeg 404w\" sizes=\"auto, (max-width: 1003px) 100vw, 1003px\" \/><p id=\"caption-attachment-435\" class=\"wp-caption-text\">SMALL 2025 Chip-Firing Games in Wachenheim (Desmond Leitz, Thor Gabrielsen, Noam Pasman &#8217;28, Charlotte Chen &#8217;27, Vincent Wang, S\u00f8ren Newman-Taylor &#8217;27, Maddie Reeves, Benham Cobb &#8217;26<\/p><\/div>\n<p><strong>Thesis students<\/strong><\/p>\n<p>I have advised eleven senior honors theses at Williams College, as well as a minithesis:<\/p>\n<ul>\n<li>Madeleine Elyze &#8217;18:\u00a0 <em>On higher distance commuting matrices<\/em><\/li>\n<li>Andrew Scharf &#8217;18:\u00a0 <em>Intersections of tropical surfaces<\/em><\/li>\n<li>Jian Lu &#8217;19:\u00a0 <em>Time complexities in max-linear systems<\/em><\/li>\n<li>Max Everett &#8217;21:\u00a0 <em>Multiplicity-free gonality on graphs<\/em><\/li>\n<li>Robin Huang &#8217;21:\u00a0 <em>The tropical Three Conics Theorem<\/em><\/li>\n<li>Ben Weber &#8217;21:\u00a0 <em>On gonality-related graph parameters<\/em><\/li>\n<li>Jason Meintjes &#8217;22:\u00a0\u00a0<em>Tropical Brianchon&#8217;s Theorem<\/em><\/li>\n<li>Lucas Tolley &#8217;22: <em>Higher order gonalities of graphs<\/em><\/li>\n<li>Robin Eagleton &#8216;22.5:\u00a0 <em>Characterizing graphs of small scramble number (minithesis)<\/em><\/li>\n<li>Em Lindheim-Marx &#8217;23:\u00a0 <em>Higher critical groups under suspension<\/em><\/li>\n<li>Noah Cape &#8217;25:\u00a0 <em>Tropical crossing number of finite graphs<\/em><\/li>\n<li>Felix Nusbaum &#8217;25:\u00a0 <em>Generalizing parking polytopes to non-complete graphs<\/em><\/li>\n<\/ul>\n<p><strong>Class projects<\/strong><\/p>\n<p>Most of my upper level classes include a final project.\u00a0 Here are a few of those!<\/p>\n<p><em>Nullstellenfont<\/em> (by Ben Logsdon &#8217;20 and Anya Michaelsen &#8217;19, for Math 487: Computational Algebraic Geometry in Spring 2019)<\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-205\" src=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/quick-brown-fox-300x94.png\" alt=\"\" width=\"300\" height=\"94\" srcset=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/quick-brown-fox-300x94.png 300w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/quick-brown-fox-768x241.png 768w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/quick-brown-fox-1024x321.png 1024w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/quick-brown-fox-500x157.png 500w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Algebraic geometry studies varieties, which are shapes defined by polynomial equations.\u00a0 For instance, polynomials in two variables define curves in the plane.\u00a0 For their final project, Ben and Anya designed a typographical font called &#8220;Nullstellensatz&#8221;, which lets you represent any string of letters using a single polynomial equation! For instance, <a href=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/Ralph-Morrison-Nullstellenfont.pdf\">here&#8217;s a polynomial<\/a> defining a curve that looks like my name. If you&#8217;d like to make your own, you can download their code <a href=\"https:\/\/github.com\/bclogsdon\/nullstellenfont\">here<\/a>.<\/p>\n<p><em>Chip-firing tool<\/em>\u00a0(by Markus Feng &#8217;21 for Math 334: Graph Theory in Spring 2019)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-192 aligncenter\" src=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/chip_fire-300x176.png\" alt=\"\" width=\"300\" height=\"176\" srcset=\"https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/chip_fire-300x176.png 300w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/chip_fire-500x293.png 500w, https:\/\/sites.williams.edu\/10rem\/files\/2019\/06\/chip_fire.png 618w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Chip-firing games on graphs involve placing an integer number of chips on the vertices of the graph, and then moving those chips around by &#8220;firing&#8221; vertices, which makes them donate a chip to each neighbor.\u00a0 For his final project in my Graph Theory class, Markus designed a <a href=\"https:\/\/markusfeng.com\/projects\/graph\/\">great tool<\/a> for drawing graphs and then performing chip-firing moves on them.<\/p>\n<p>This one isn&#8217;t really a final project, but the students in Math 474:\u00a0 Tropical Geometry in Spring 2021 put together a gallery of tropical curves.\u00a0 Check it out <a href=\"https:\/\/sites.williams.edu\/10rem\/files\/2021\/05\/landscape.pdf\">here<\/a>!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The SMALL REU I advised groups as part of Williams College&#8217;s SMALL REU in 2017, 2018, 2020, 2021, 2023, and 2025.\u00a0 Check out the research page for our publications! Thesis students I have advised eleven senior honors theses at Williams &hellip; <a href=\"https:\/\/sites.williams.edu\/10rem\/work-with-and-by-students\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1294,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-182","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/10rem\/wp-json\/wp\/v2\/pages\/182","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.williams.edu\/10rem\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.williams.edu\/10rem\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/10rem\/wp-json\/wp\/v2\/users\/1294"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/10rem\/wp-json\/wp\/v2\/comments?post=182"}],"version-history":[{"count":17,"href":"https:\/\/sites.williams.edu\/10rem\/wp-json\/wp\/v2\/pages\/182\/revisions"}],"predecessor-version":[{"id":438,"href":"https:\/\/sites.williams.edu\/10rem\/wp-json\/wp\/v2\/pages\/182\/revisions\/438"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/10rem\/wp-json\/wp\/v2\/media?parent=182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}