{"id":520,"date":"2018-09-10T00:35:43","date_gmt":"2018-09-10T07:35:43","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=520"},"modified":"2018-10-16T15:26:30","modified_gmt":"2018-10-16T22:26:30","slug":"applied-math-seminar-given-by-prof-steven-heilman","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/applied-math-seminar-given-by-prof-steven-heilman\/","title":{"rendered":"Minimal Gaussian Partitions, Clustering Hardness and Voting (Steven Heilman, USC)"},"content":{"rendered":"<p>A single soap bubble has a spherical shape since it minimizes its surface area subject to a fixed enclosed volume of air.\u00a0 When two soap bubbles collide, they form a &#8220;double-bubble&#8221; composed of three spherical caps.\u00a0 The double-bubble minimizes total surface area among all sets enclosing two fixed volumes.\u00a0 This was proven mathematically in a landmark result by Hutchings-Morgan-Ritore-Ros and Reichardt using the calculus of variations in the early 2000s.\u00a0 The analogous case of three or more Euclidean sets is considered difficult if not impossible.\u00a0 However, if we replace Lebesgue measure in these problems with the Gaussian measure, then recent work of myself (for 3 sets) and of Milman-Neeman (for any number of sets) can actually solve these problems.\u00a0 We also use the calculus of variations.\u00a0 We will discuss applications of this Gaussian &#8220;multi-bubble&#8221; problem to optimal clustering of data and to designing elections that are resilient to hacking.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A single soap bubble has a spherical shape since it minimizes its surface area subject to a fixed enclosed volume of air.\u00a0 When two soap bubbles collide, they form a [&hellip;]<\/p>\n","protected":false},"author":58,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":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":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[15],"class_list":["post-520","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-applied-math-seminar","cat_applied-math-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - 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