{"id":14088,"date":"2024-03-04T12:07:10","date_gmt":"2024-03-04T18:07:10","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=14088"},"modified":"2024-03-04T12:08:49","modified_gmt":"2024-03-04T18:08:49","slug":"graduate-student-colloquium-dorian-smith","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/graduate-student-colloquium-dorian-smith\/","title":{"rendered":"Graduate Student Colloquium: Dorian Smith"},"content":{"rendered":"

\"\"<\/h1>\n

Sandpile Group For Cones Over Trees<\/h1>\n

Dorian Smith<\/a>
\nPhD Student<\/em>
\nUniversity of Minnesota Twin Cities<\/p>\n

The sandpile group $K(G)$ of a graph $G$ is a finite abelian group, isomorphic to the cokernel of the reduced graph Laplacian of $G.$ We study $K(G)$ when $G = Cone(T)$. The graph $Cone(T)$ is obtained from a tree $T$ on $n$ vertices by attaching a new cone vertex attached to all other vertices. For two such families of graphs, we will describe $K(G)$ exactly: the fan graphs $Cone(P_n)$ where $P_n$ is a path, and the thagomizer graph $Cone(S_n)$ where $S_n$ is the star-shaped tree. The motivation is that these two families turn out to be extreme cases among $Cone(T)$ for all trees $T$ on $n$ vertices.<\/p>\n","protected":false},"excerpt":{"rendered":"

Sandpile Group For Cones Over Trees Dorian Smith PhD Student University of Minnesota Twin Cities The sandpile group $K(G)$ of a graph $G$ is a finite abelian group, isomorphic to the cokernel of the reduced graph Laplacian of $G.$ We …<\/p>\n","protected":false},"author":4217,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","uwm_wg_additional_authors":[]},"tags":[],"tribe_events_cat":[70],"class_list":["post-14088","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-graduate-student-colloquia","cat_graduate-student-colloquia"],"yoast_head":"\nMathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/uwm.edu\/math\/event\/graduate-student-colloquium-dorian-smith\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Graduate Student Colloquium: Dorian Smith\" \/>\n<meta property=\"og:description\" content=\"Sandpile Group For Cones Over Trees Dorian Smith PhD Student University of Minnesota Twin Cities The sandpile group $K(G)$ of a graph $G$ is a finite abelian group, isomorphic to the cokernel of the reduced graph Laplacian of $G.$ We …\" \/>\n<meta property=\"og:url\" content=\"https:\/\/uwm.edu\/math\/event\/graduate-student-colloquium-dorian-smith\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2024-03-04T18:08:49+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/03\/BANNER_SMITH-1.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/graduate-student-colloquium-dorian-smith\\\/\",\"url\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/graduate-student-colloquium-dorian-smith\\\/\",\"name\":\"Graduate Student Colloquium: Dorian Smith - 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