Northwestern’s Ben Antieau is a Principal Investigator on a major new $8 million Simons Collaboration on Perfection in Algebra, Geometry and Topology. This is a collaboration across multiple institutions, with Northwestern’s portion of the grant being $650,000. Antieau is a professor of mathematics at Northwestern’s Weinberg College of Arts and Sciences. His research focuses on Brauer groups, algebraic K-theory, and, recently, machine calculations of syntomic cohomology.
“The connection between geometry, algebra and arithmetic is at the heart of many parts of mathematics, such as arithmetic and algebraic geometry, number theory and representation theory. This interplay has been critical in some of the greatest achievements in these fields and has informed the development of key tools, including arithmetic cohomology theories and guiding visions in the Langlands program and the theory of motives. The last decade has seen remarkable new ideas and techniques emerging in mixed characteristic geometry, such as perfectoid spaces, prismatic cohomology and systematic use of derived algebraic geometry. The key new notions, unified by the theme of perfection in a very broad sense, have revolutionized a number of algebraic fields. – Simons Collaborartion on Perfection in Algebra, Geometry and Topology.
“This collaboration brings together mathematicians from a range of algebraic fields to study new ideas which have emerged over the last two decades in mixed characteristic algebraic geometry. These new ideas, which we broadly capture with the term “perfection”, include prismatic cohomology, perfectoid spaces, and the Cartier-Witt stack,” according to the the Simons Collaboration on Perfection in Algebra, Geometry, and Topology website.