September 25, 2025 (Thursday), 4:10 pm<\/p>\n
Spencer Dowdall, Vanderbilt University<\/p>\n
Counting Mapping Classes by Type<\/strong><\/p>\n In the classic “lattice point counting problem” for a group acting on a metric space, the goal is to count the number of orbit points of the action in a ball of radius R, and to find the growth rate of this count as the radius R tends to infinity. For example, what is the growth rate for the integer lattice Z^2 acting on the Euclidean plane?<\/p>\n This talk will look at the lattice point counting problem for the case of everyone’s favorite group, namely, the mapping class group acting on Teichmuller space. I’ll explain what these objects are, why you might care about them, and what is known about the lattice point counting problem. Since elements of the mapping class group come in 3 distinct types, it’s also interesting to look at a refinement of the problem that counts lattice points for each type of element separately. Joint work with Howard Masur.<\/p>\n","protected":false},"excerpt":{"rendered":" September 25, 2025 (Thursday), 4:10 pm Spencer Dowdall, Vanderbilt University Counting Mapping Classes by Type In the classic “lattice point counting problem” for a group acting on a metric space, the goal is to count the number of orbit points of the action in a ball of radius R, and to find the growth rate…<\/p>\n","protected":false},"author":208,"featured_media":1671,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7],"tags":[],"acf":[],"jetpack_featured_media_url":"https:\/\/as.vanderbilt.edu\/math\/wp-content\/uploads\/sites\/69\/2025\/09\/spencer-dowdall.jpg","_links":{"self":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1452"}],"collection":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/users\/208"}],"replies":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/comments?post=1452"}],"version-history":[{"count":1,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1452\/revisions"}],"predecessor-version":[{"id":1453,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/posts\/1452\/revisions\/1453"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media\/1671"}],"wp:attachment":[{"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/media?parent=1452"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/categories?post=1452"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/as.vanderbilt.edu\/math\/wp-json\/wp\/v2\/tags?post=1452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}