{"id":14508,"date":"2024-10-01T08:33:57","date_gmt":"2024-10-01T13:33:57","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&#038;p=14508"},"modified":"2024-10-01T08:34:17","modified_gmt":"2024-10-01T13:34:17","slug":"colloquium-dr-daniel-stoertz","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/colloquium-dr-daniel-stoertz\/","title":{"rendered":"Colloquium: Dr. Daniel Stoertz"},"content":{"rendered":"<h1><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-14509 aligncenter\" src=\"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/10\/BANNER_STOERTZ.png\" alt=\"\" width=\"492\" height=\"252\" srcset=\"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/10\/BANNER_STOERTZ.png 492w, https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/10\/BANNER_STOERTZ-300x154.png 300w\" sizes=\"auto, (max-width: 492px) 100vw, 492px\" \/><\/h1>\n<h1>Baby Mandelbrot Sets for Maximally Generalized McMullen Maps<\/h1>\n<p>Dr. Daniel Stoertz<br \/>\n<em>Visiting Assistant Professor of Mathematics<\/em><br \/>\nSt. Olaf College<\/p>\n<p>In Complex Dynamics, we study the iteration of holomorphic or meromorphic functions on the complex plane or the Riemann sphere. Of particular interest is the behavior of the critical orbits of function families with one or more parameters. The simplest of such families, z^2 +c, is well-known to define the famous Mandelbrot set fractal as the set of c-values for which the unique critical orbit is bounded. In this talk we will examine the function family R(z) = z^n +b +a\/(z^d), and we will explore old and new results establishing the location of baby Mandelbrot sets in parameter space for increasingly general versions of this family. In the most general case, which we call maximally generalized McMullen maps, this family has multiple independent critical orbits, and the dynamics in this case are not yet well understood.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-14510 aligncenter\" src=\"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/10\/Beauty.png\" alt=\"\" width=\"794\" height=\"789\" srcset=\"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/10\/Beauty.png 794w, https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/10\/Beauty-300x298.png 300w, https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/10\/Beauty-150x150.png 150w, https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/10\/Beauty-768x763.png 768w\" sizes=\"auto, (max-width: 794px) 100vw, 794px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Baby Mandelbrot Sets for Maximally Generalized McMullen Maps Dr. Daniel Stoertz Visiting Assistant Professor of Mathematics St. Olaf College In Complex Dynamics, we study the iteration of holomorphic or meromorphic functions on the complex plane or the Riemann sphere. Of &hellip;<\/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":[41],"class_list":["post-14508","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-colloquia","cat_colloquia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Mathematical 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\/colloquium-dr-daniel-stoertz\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Colloquium: Dr. Daniel Stoertz\" \/>\n<meta property=\"og:description\" content=\"Baby Mandelbrot Sets for Maximally Generalized McMullen Maps Dr. Daniel Stoertz Visiting Assistant Professor of Mathematics St. Olaf College In Complex Dynamics, we study the iteration of holomorphic or meromorphic functions on the complex plane or the Riemann sphere. 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