Trends in Differential and Complex Geometry

  The interactions between geometry, topology, representation theory, and mathematical physics have transformed our understanding of geometric structures and their applications in both pure mathematics and theoretical physics. Geometry has long been at the heart of mathematical advances, with differential and complex geometry playing a fundamental role in many breakthroughs. Over the past half-century, ideas from these fields have influenced areas such as mathematical physics, topology, and number theory while also evolving through interactions with fields like gauge theory and integrability. This workshop will explore foundational developments and recent progress, focusing on how core geometric structures continue to shape modern mathematical research. Hitchin’s profound contributions — ranging from Higgs bundles and hyperkähler geometry to generalized complex geometry — have transformed the way we understand and apply geometric structures in modern mathematics. His influence can be seen across multiple areas, providing a central theme that will unify the discussions at this conference. 

Get in touch at schapos@uic.edu

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