The conference "Fundamental Geometries" will be held at the SAIS–Johns Hopkins Institute at the University of Bologna, Italy, on June 22-26, 2026. Geometry plays a central role in mathematics by providing powerful ways to understand complex structures and reveal connections between different areas of science. Recent advances in geometric thinking have uncovered new relationships linking fields such as topology, algebra, combinatorics, and arithmetic geometry, opening fresh perspectives on longstanding mathematical questions. The conference will bring together researchers working in these areas to explore the fundamental geometric structures that underlie many branches of modern mathematics. By promoting the exchange of ideas and collaboration, the meeting will advance basic mathematical research while strengthening international cooperation between U.S. and European institutions. These interactions will expand opportunities for researchers based at U.S. institutions to participate in international collaborations at the forefront of modern mathematics. Support from the project will also strengthen the training pipeline in the mathematical sciences by enabling graduate students, postdoctoral researchers, and early career faculty to engage directly with leading researchers and develop new collaborations. The meeting is intended as the beginning of a continuing series of collaborative events connecting researchers at U.S. institutions with colleagues in Europe. The scientific program will explore emerging directions in modern geometry and closely related fields, highlighting how geometric methods reveal common structural principles across different mathematical frameworks. Topics represented in the meeting include geometric and categorical methods, noncommutative and arithmetic geometry, tropical and combinatorial approaches, and other perspectives that demonstrate the unifying role of geometric thinking. Approximately twenty-five invited talks, together with structu