{"id":"https://openalex.org/W7204264291","doi":"https://doi.org/10.15479/at-ista-22694","title":"Equivariant K-theory of affine Grassmannians in representation theory and arithmetic","display_name":"Equivariant K-theory of affine Grassmannians in representation theory and arithmetic","publication_year":2026,"publication_date":"2026-08-12","ids":{"openalex":"https://openalex.org/W7204264291","doi":"https://doi.org/10.15479/at-ista-22694"},"language":"en","primary_location":{"id":"doi:10.15479/at-ista-22694","doi":"https://doi.org/10.15479/at-ista-22694","is_oa":true,"landing_page_url":"https://doi.org/10.15479/at-ista-22694","pdf_url":null,"source":{"id":"https://openalex.org/S7407055285","display_name":"Institute of Science and Technology Austria","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dissertation"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.15479/at-ista-22694","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013376726","display_name":"Jakub L\u00f6wit","orcid":"https://orcid.org/0009-0008-0361-7395","observed_orcids":["https://orcid.org/0009-0008-0361-7395"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"L\u00f6wit, Jakub","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5013376726"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.49000000953674316,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.49000000953674316,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.3959999978542328,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.07460000365972519,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equivariant-k-theory","display_name":"equivariant K-theory","score":0.9089999794960022},{"id":"https://openalex.org/keywords/affine-grassmannian","display_name":"affine Grassmannian","score":0.9399999976158142},{"id":"https://openalex.org/keywords/trace-map","display_name":"trace map","score":0.8100000023841858},{"id":"https://openalex.org/keywords/geometric-langlands-program","display_name":"geometric Langlands program","score":0.7319999933242798}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7285000085830688},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.6984999775886536},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.5766000151634216},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5580000281333923},{"id":"https://openalex.org/C77462122","wikidata":"https://www.wikidata.org/wiki/Q15176852","display_name":"Intersection theory","level":5,"score":0.5408999919891357},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.519599974155426},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5171999931335449},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4447999894618988},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.44350001215934753},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.42399999499320984},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.41929998993873596},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41920000314712524},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.41499999165534973},{"id":"https://openalex.org/C168393982","wikidata":"https://www.wikidata.org/wiki/Q6486188","display_name":"Langlands dual group","level":3,"score":0.3910999894142151},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.3898000121116638},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.3862999975681305},{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.3801000118255615},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.35659998655319214},{"id":"https://openalex.org/C31671712","wikidata":"https://www.wikidata.org/wiki/Q1393253","display_name":"Langlands program","level":3,"score":0.35530000925064087},{"id":"https://openalex.org/C199793520","wikidata":"https://www.wikidata.org/wiki/Q4723996","display_name":"Algebraic cycle","level":3,"score":0.3303000032901764},{"id":"https://openalex.org/C21555199","wikidata":"https://www.wikidata.org/wiki/Q5535491","display_name":"Geometric invariant theory","level":5,"score":0.32440000772476196},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.3231000006198883},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.305400013923645},{"id":"https://openalex.org/C187173678","wikidata":"https://www.wikidata.org/wiki/Q1695400","display_name":"Algebraic group","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C2776648750","wikidata":"https://www.wikidata.org/wiki/Q1622047","display_name":"Hochschild homology","level":3,"score":0.2757999897003174},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.2632000148296356},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.2612999975681305},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.25839999318122864}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.15479/at-ista-22694","doi":"https://doi.org/10.15479/at-ista-22694","is_oa":true,"landing_page_url":"https://doi.org/10.15479/at-ista-22694","pdf_url":null,"source":{"id":"https://openalex.org/S7407055285","display_name":"Institute of Science and Technology Austria","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dissertation"}],"best_oa_location":{"id":"doi:10.15479/at-ista-22694","doi":"https://doi.org/10.15479/at-ista-22694","is_oa":true,"landing_page_url":"https://doi.org/10.15479/at-ista-22694","pdf_url":null,"source":{"id":"https://openalex.org/S7407055285","display_name":"Institute of Science and Technology Austria","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dissertation"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4403799656","https://openalex.org/W7212490883","https://openalex.org/W7134036211","https://openalex.org/W1980536054","https://openalex.org/W4403054563","https://openalex.org/W2030105072","https://openalex.org/W2006482861","https://openalex.org/W1647571282","https://openalex.org/W7097618861","https://openalex.org/W4413637464"],"abstract_inverted_index":{"We":[0,25,191,211,221,239,248,260,297],"develop":[1],"and":[2,9,22,91,137,184,225,275,289,316],"employ":[3],"techniques":[4,31,104],"from":[5,132],"equivariant":[6,195,215,281],"algebraic":[7,65,75,89,129,133],"K-theory":[8,216,283,303],"related":[10],"invariants":[11,87,127,142,178,229],"in":[12,19,42,109,128,159,179,198,234,255,294,330],"the":[13,27,33,43,55,72,100,110,117,180,218,262,267,272,295,301,306],"context":[14],"of":[15,29,39,52,54,74,79,88,94,119,125,146,168,182,200,208,227,230,253,266,309,327],"geometric":[16,44,120,160],"representation":[17,121,161,332],"theory,":[18],"both":[20],"arithmetic":[21,237],"topological":[23,258,282],"situations.":[24,238],"showcase":[26,173],"use":[28,185,276],"such":[30,177,228],"on":[32,202,271],"affine":[34,231,273],"Grassmannian":[35],"Gr,":[36,235],"a":[37,49,256,324],"space":[38],"fundamental":[40],"interest":[41,80,183],"Langlands":[45,111],"program.":[46],"It":[47],"is":[48,171,287],"deep":[50],"development":[51],"mathematics":[53],"last":[56],"century":[57],"that":[58,241],"many":[59],"concrete,":[60],"yet":[61],"combina-":[62],"torially":[63],"complex":[64],"problems":[66],"may":[67],"be":[68,82],"effectively":[69],"studied":[70],"through":[71],"lens":[73],"geometry.":[76],"The":[77,166,285],"objects":[78],"can":[81],"often":[83],"realized":[84],"as":[85],"cohomological":[86],"varieties,":[90],"good":[92],"understanding":[93],"their":[95,138,157],"geometry":[96,130],"sheds":[97],"light":[98],"into":[99],"original":[101],"questions.":[102],"Such":[103],"have":[105],"seen":[106],"immense":[107],"applications":[108],"program,":[112],"where":[113],"they":[114,242],"go":[115],"under":[116],"label":[118],"theory.":[122,333],"One":[123],"source":[124],"powerful":[126],"comes":[131],"K-theory,":[134],"Hochschild":[135,196],"homology,":[136],"relatives.":[139],"These":[140],"localizing":[141],"contain":[143],"large":[144],"amount":[145],"information,":[147],"but":[148],"are":[149,207],"quite":[150],"hard":[151],"to":[152,172,175,187,214,278,305],"compute.":[153],"For":[154],"this":[155,169,251],"reason,":[156],"usage":[158],"theory":[162],"has":[163],"been":[164],"limited.":[165],"aim":[167],"thesis":[170],"how":[174],"control":[176],"situations":[181],"them":[186],"obtain":[188],"new":[189,223],"insights.":[190],"start":[192],"by":[193],"reinterpreting":[194],"homology":[197],"terms":[199],"functions":[201],"certain":[203],"fixed-point":[204],"schemes,":[205],"which":[206],"independent":[209],"interest.":[210],"compare":[212],"it":[213,277],"via":[217],"trace":[219],"map.":[220],"give":[222],"computations":[224,329],"comparisons":[226],"Schubert":[232],"varieties":[233],"including":[236],"show":[240],"behave":[243],"much":[244],"better":[245],"than":[246],"expected.":[247],"finally":[249],"utilize":[250],"circle":[252],"ideas":[254],"purely":[257],"setting.":[259],"describe":[261],"varying":[263],"fixed":[264],"points":[265],"extended":[268],"torus":[269],"action":[270],"Grassmannian,":[274],"compute":[279],"its":[280,317],"ring.":[284],"answer":[286],"nontrivial":[288],"verifies":[290],"an":[291,310],"outstanding":[292],"conjecture":[293],"subject.":[296],"compare,":[298],"partly":[299],"conjecturally,":[300],"resulting":[302],"ring":[304],"completed":[307],"center":[308],"integral":[311],"even":[312],"hybrid":[313],"quantum":[314,319],"group":[315],"deformed":[318],"category":[320],"O.":[321],"This":[322],"gives":[323],"genuine":[325],"application":[326],"our":[328],"pure":[331]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-27T00:00:00"}