{"659017":{"#nid":"659017","#data":{"type":"event","title":"Phd Defense by Maxie Schmidt","body":[{"value":"\u003Cp\u003EFACTORIZATION THEOREMS AND CANONICAL REPRESENTATIONS FOR GENERATING FUNCTIONS OF SPECIAL SUMS\u003C\/p\u003E\r\n\r\n\u003Ch3\u003E\u003Cstrong\u003EABSTRACT:\u003C\/strong\u003E\u003C\/h3\u003E\r\n\r\n\u003Cp\u003EThis manuscript explores many convolution (restricted summation) type sequences via certain types of matrix based factorizations that can be used to express their generating functions. These results are a main focus of the author\u0026#39;s publications from 2017-2021. The last primary (non-appendix) section of the thesis explores the topic of how to best rigorously define a so-termed \u0026quot;\u003Cem\u003Ecanonically best\u003C\/em\u003E\u0026quot; matrix based factorization for a given class of convolution sum sequences. The notion of a canonical factorization for the generating function of such sequences needs to match the qualitative properties we find in the factorization theorems for Lambert series generating functions (LGFs). The expected qualitatively most expressive expansion we find in the LGF case results naturally from algebraic constructions of the underlying LGF series type. We propose a precise quantitative requirement to generalize this notion in terms of optimal cross-correlation statistics for certain sequences that define the matrix based factorizations of the generating function expansions we study. We finally pose a few conjectures on the types of matrix factorizations we expect to find when we are able to attain the maximal (respectively minimal) correlation statistic for a given sum type.\u003C\/p\u003E\r\n\r\n\u003Cdiv\u003E\u0026nbsp;\u003C\/div\u003E\r\n\r\n\u003Ch3\u003E\u003Cstrong\u003ECOMMITTEE:\u003C\/strong\u003E\u003C\/h3\u003E\r\n\r\n\u003Cul\u003E\r\n\t\u003Cli\u003EDr. Josephine Yu, \u003Cem\u003EGeorgia Tech\u003C\/em\u003E\u003C\/li\u003E\r\n\t\u003Cli\u003EDr. Matthew Baker, \u003Cem\u003EGeorgia Tech\u003C\/em\u003E\u003C\/li\u003E\r\n\t\u003Cli\u003EDr. Rafael de la Llave, \u003Cem\u003EGeorgia Tech\u003C\/em\u003E\u003C\/li\u003E\r\n\t\u003Cli\u003EDr. Jayadev Athreya, \u003Cem\u003EUniversity of Washington\u003C\/em\u003E\u003C\/li\u003E\r\n\t\u003Cli\u003EDr. Bruce Berndt, \u003Cem\u003EUniversity of Illinois at Urbana-Champaign\u003C\/em\u003E\u003C\/li\u003E\r\n\u003C\/ul\u003E\r\n\r\n\u003Cdiv\u003E\u0026nbsp;\u003C\/div\u003E\r\n\r\n\u003Ch3\u003E\u003Cstrong\u003EHYBRID FORMAT LOCATIONS:\u003C\/strong\u003E\u003C\/h3\u003E\r\n\r\n\u003Cul\u003E\r\n\t\u003Cli\u003E\u003Cem\u003EIn-person location:\u003C\/em\u003E Skiles 006\u003C\/li\u003E\r\n\t\u003Cli\u003E\u003Cem\u003EOnline GT Zoom link:\u003C\/em\u003E \u003Ca href=\u0022https:\/\/gatech.zoom.us\/j\/99997438538?pwd=ZEptc2lpMU5XWUtwOVQrZm8xcDFrdz09\u0022 target=\u0022_blank\u0022\u003EGT Zoom -- Meeting ID (999 9743 8538) -- Passcode (057722)\u003C\/a\u003E\u003C\/li\u003E\r\n\u003C\/ul\u003E\r\n\r\n\u003Cdiv\u003E\u0026nbsp;\u003C\/div\u003E\r\n\r\n\u003Ch3\u003E\u003Cstrong\u003ELINKS:\u003C\/strong\u003E\u003C\/h3\u003E\r\n\r\n\u003Cul\u003E\r\n\t\u003Cli\u003E\u003Cem\u003EThesis manuscript (PDF format):\u003C\/em\u003E \u003Ca href=\u0022https:\/\/mschmidt34.math.gatech.edu\/thesis-manuscript-2022.06.21-v1.pdf\u0022 target=\u0022_blank\u0022\u003Ethesis-manuscript-2022.06.21-v1.pdf\u003C\/a\u003E\u003C\/li\u003E\r\n\t\u003Cli\u003E\u003Cem\u003EGT School of Math Seminar Announcement:\u003C\/em\u003E \u003Ca href=\u0022https:\/\/intranet.math.gatech.edu\/seminars-colloquia\/series\/dissertation-defense\/maxie-dion-schmidt-wed-07062022-1500\u0022 target=\u0022_blank\u0022\u003Ehttps:\/\/intranet.math.gatech.edu\/seminars-colloquia\/series\/dissertation-defense\/maxie-dion-schmidt-wed-07062022-1500\u003C\/a\u003E\u003C\/li\u003E\r\n\u003C\/ul\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"FACTORIZATION THEOREMS AND CANONICAL REPRESENTATIONS FOR GENERATING FUNCTIONS OF SPECIAL SUMS"}],"uid":"27707","created_gmt":"2022-06-22 13:18:27","changed_gmt":"2022-06-22 13:18:27","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2022-07-06T16:00:00-04:00","event_time_end":"2022-07-06T18:00:00-04:00","event_time_end_last":"2022-07-06T18:00:00-04:00","gmt_time_start":"2022-07-06 20:00:00","gmt_time_end":"2022-07-06 22:00:00","gmt_time_end_last":"2022-07-06 22:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}