Project Grant 2545830

CONFERENCE: INTEGRATING RESEARCH AND ILLUSTRATION IN NUMBER THEORY -THE WORKSHOP INTEGRATING RESEARCH AND ILLUSTRATION IN NUMBER THEORY WILL BE HELD MARCH 23-27, 2026 AT THE INSTITUTE HENRI POINCAR? IN PARIS, FRANCE, AS PART OF A TRIMESTER PROGRAM FOCUSING ON ILLUSTRATION AS A RESEARCH TECHNIQUE IN MATHEMATICS. IN REGARD TO THE PROGRAM, THE TERM ?ILLUSTRATION? IS USED TO ENCOMPASS ANY OF THE MANY WAYS ONE MIGHT BRING A MATHEMATICAL IDEA INTO PHYSICAL FORM OR EXPERIENCE, INCLUDING COMPUTER VISUALIZATION, 3D PRINTING, AND VIRTUAL REALITY. THE WEEK-LONG WORKSHOP WILL BRING TOGETHER MATHEMATICIANS USING ILLUSTRATION AS A RESEARCH TOOL WITH THOSE NEWLY LEARNING THESE TOOLS. THE MAIN GOALS OF THE WORKSHOP ARE TO ADVANCE RESEARCH THROUGH THE USE OF MATHEMATICAL ILLUSTRATION, DISSEMINATE THE SKILLS FOR THE CREATION OF MATHEMATICAL ILLUSTRATION AND ITS USE IN RESEARCH, AND FURTHER THE THEORY OF ILLUSTRATION AS A TOOL. BROADER IMPACTS OF THE WORKSHOP INCLUDE RAISING PUBLIC AWARENESS ABOUT ILLUSTRATION AS A SCIENTIFIC TOOL AND PROVIDING NEW CHANNELS OF COMMUNICATION IN TEACHING AND OUTREACH. AMONG THE MANY APPROACHES TO STUDYING MATHEMATICS, ILLUSTRATION HAS BEEN A COMPANION TO--AND TOOL FOR-- RESEARCH FOR AS LONG AS RESEARCH HAS TAKEN PLACE. WITH MODERN TOOLS, ILLUSTRATION CAN EVEN MAKE MATHEMATICS AN EXPERIMENTAL SCIENCE, SO THAT COMPUTATIONAL RESULTS CAN DRIVE THE CYCLE OF PROBLEM, CONJECTURE, AND PROOF. TODAY, MODERN TECHNOLOGY FOR THE FIRST TIME PLACES THE PRODUCTION OF FAR MORE COMPLICATED 3D MODELS WITHIN THE REACH OF MANY INDIVIDUAL MATHEMATICIANS. MOREOVER, THE VERY PROCESS OF ILLUSTRATION ITSELF CHALLENGES HUMAN UNDERSTANDING OF A MATHEMATICAL TOPIC AND FORCES MATHEMATICIANS TO ANSWER QUESTIONS THAT THEY MAY NOT HAVE POSED OTHERWISE. WORKSHOP SPEAKERS' MATHEMATICAL EXPERTISE INCLUDES HOMOGENEOUS DYNAMICS, CONTINUED FRACTIONS, KLEINIAN GROUPS, RANDOM MATRICES, P-ADIC ANALYSIS, MODULAR FORMS, GAUSSIAN PERIODS, ARITHMETIC GEOMETRY, AND MORE. THE STRUCTURE OF THE WORKSHOP WILL INCLUDE RESEARCH TALKS, RESEARCH IN GROUPS, LIGHTNING TALKS, AND COMMUNITY-BUILDING ACTIVITIES; IT HAS BEEN DESIGNED TO PROVIDE A WIDE VARIETY OF OPPORTUNITIES FOR PARTICIPANTS NOT JUST TO DISSEMINATE RESEARCH, BUT TO FORM NEW COLLABORATIONS AND TO LEARN NEW SKILLS. 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.