Project Grant 2627740

COLLABORATIVE RESEARCH: CONFERENCE: TEXAS-OKLAHOMA REPRESENTATIONS AND AUTOMORPHIC FORMS (TORA) -THIS AWARD PROVIDES FUNDING FOR THE TEXAS-OKLAHOMA REPRESENTATIONS AND AUTOMORPHIC FORMS (TORA) MATHEMATICS CONFERENCE SERIES FROM 2027 TO 2029. THE CONFERENCE WILL BE HELD AT THE UNIVERSITY OF NORTH TEXAS FROM APRIL 9-11, 2027; AT OKLAHOMA STATE UNIVERSITY IN SPRING 2028; AND AT THE UNIVERSITY OF OKLAHOMA IN SPRING 2029. EACH OF THESE MEETINGS WILL FOCUS ON RECENT ADVANCES IN THE MATHEMATICAL AREAS OF REPRESENTATION THEORY AND AUTOMORPHIC FORMS, CLOSELY CONNECTED FIELDS WHOSE INFLUENCE EXTENDS WELL BEYOND NUMBER THEORY TO TOUCH MANY OTHER AREAS OF MATHEMATICS. NUMBER THEORY STUDIES DEEP PATTERNS OF THE INTEGERS, ESPECIALLY PRIME NUMBERS, THE FUNDAMENTAL BUILDING BLOCKS OF ARITHMETIC. REPRESENTATION THEORY STUDIES ALGEBRAIC STRUCTURES BY REALIZING THEM AS LINEAR TRANSFORMATIONS OF VECTOR SPACES, ALLOWING ABSTRACT SYMMETRY TO BE ANALYZED USING THE TOOLS OF LINEAR ALGEBRA. AUTOMORPHIC FORMS ARE HIGHLY-SYMMETRIC FUNCTIONS THAT CONNECT NUMBER THEORY AND REPRESENTATION THEORY BY ENCODING ARITHMETIC INFORMATION IN FORMS THAT CAN BE STUDIED THROUGH SYMMETRY. THIS INTERACTION HAS LED TO MAJOR ADVANCES ON LONGSTANDING PROBLEMS AND REMAINS ONE OF THE CENTRAL THEMES OF MODERN MATHEMATICS. EACH TORA MEETING WILL BE DESIGNED TO FOSTER COLLABORATION AND INTERACTION AMONG MATHEMATICIANS IN THE TEXAS-OKLAHOMA REGION AND BEYOND, INCLUDING EARLY-CAREER RESEARCHERS. THE CONFERENCES WILL ALSO GIVE GRADUATE STUDENTS THE OPPORTUNITY TO SPEAK ON THEIR OWN RESEARCH. OVER THE PAST CENTURY, THE THEORIES OF AUTOMORPHIC FORMS AND REPRESENTATIONS HAVE EXPANDED DRAMATICALLY, WITH APPLICATIONS REACHING INTO NUMBER THEORY, CODING THEORY, COMBINATORICS, ALGEBRAIC GEOMETRY, TOPOLOGY, KAC-MOODY ALGEBRAS, AND QUANTUM FIELD THEORY. THE RELATIONSHIP BETWEEN AUTOMORPHIC FORMS AND REPRESENTATION THEORY HAS PROVEN ESPECIALLY PRODUCTIVE, YIELDING NUMEROUS DEEP AND UNEXPECTED RESULTS. THE TORA MEETINGS IN 2027, 2028, AND 2029 WILL CENTER ON CUTTING-EDGE DEVELOPMENTS IN THIS CONNECTION WITHIN BOTH CLASSICAL AND ADELIC SETTINGS, ALONG WITH RELEVANT PROGRESS FROM RELATED AREAS SUCH AS ANALYTIC NUMBER THEORY AND HARMONIC ANALYSIS. FURTHER DETAILS FOR THE TORA MEETING IN 2027 ARE AVAILABLE ON THE CONFERENCE WEBSITE: HTTPS://SITES.MATH.UNT.EDU/~RICHTER/TORA.HTML THIS AWARD REFLECTS NSF'S STATUTORY MISSION AND HAS BEEN DEEMED WORTHY OF SUPPORT THROUGH EVALUATION USING THE FOUNDATION'S INTELLECTUAL MERIT AND BROADER IMPACTS REVIEW CRITERIA.- SUBAWARDS ARE NOT PLANNED FOR THIS AWARD.