Modular forms are ubiquitous in modern number theory.\u00a0 For instance, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat’s Last Theorem.\u00a0 In addition to number theory, modular forms show up in diverse areas such as coding theory and particle physics.\u00a0 Roughly speaking, a modular form is a complex-valued function defined on the complex upper half-plane that satisfies a large number of symmetries.\u00a0 A modular form has two invariants: weight and level.\u00a0 If one fixes a weight and level, the collection of modular forms of that weight and level form a finite-dimensional complex vector space.\u00a0 One has a collection of operators on these spaces referred to as Hecke operators.\u00a0 A natural question is if one takes two eigenforms of these operators and multiplies them, when is the product still an eigenform?\u00a0 It was shown in independent work by Duke and Ghate that there is a finite list of pairs of eigenforms whose product is again an eigenform.\u00a0 In this talk we will report on the case when one replaces modular forms with the more general case of Siegel modular forms.\u00a0 This is work that was partially conducted during an REU in summer 2018.\u00a0 No prior familiarity with modular forms is assumed.<\/p>\n","protected":false},"excerpt":{"rendered":"
Modular forms are ubiquitous in modern number theory.\u00a0 For instance, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat’s Last Theorem.\u00a0 In addition […]<\/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-1047","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"\n