There is a rich connection between homogeneous dynamics and number theory. \u00a0Often in such applications it is desirable for dynamical results to be effective (i.e. the rates of convergence for dynamical phenomena are known). \u00a0In the first part of this talk, I will provide the necessary background and relevant history to state an effective equidistribution result for horospherical flows on the space of unimodular lattices in R^n. \u00a0I will then describe an application to studying the distribution of almost-prime times (integer times having fewer than a fixed number of prime factors) in horospherical orbits and discuss connections of this work to Sarnak\u2019s Mobius disjointness conjecture. \u00a0In the second part of the talk I will describe some of the ingredients and key steps that go into proving these results. If time allows, I will conclude by discussing recent results and ongoing work with M. Luethi that strengthens and generalizes this work.<\/p>\n","protected":false},"excerpt":{"rendered":"
There is a rich connection between homogeneous dynamics and number theory. \u00a0Often in such applications it is desirable for dynamical results to be effective (i.e. the rates of convergence for […]<\/p>\n","protected":false},"author":73,"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":[13],"class_list":["post-3302","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"\n