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Upcoming Hot Topics Workshops

  1. Hot Topics: Galois Theory of Periods and Applications

    Organizers: LEAD Francis Brown (University of Oxford), ClĂ©ment Dupont (UniversitĂ© de Montpellier), Richard Hain (Duke University), Vadim Vologodsky (University of Oregon)

    Periods are integrals of algebraic differential forms over algebraically-defined domains and are ubiquitous in mathematics and physics. A deep idea, originating with Grothendieck, is that there should be a Galois theory of periods. This general principle provides a unifying approach to several problems in the theory of motives, quantum groups and geometric group theory.  This conference will bring together leading experts around this subject and cover topics such as the theory of multiple zeta values, modular forms, and motivic fundamental groups.

    Updated on Feb 23, 2017 08:49 AM PST
  2. The Homological Conjectures: Resolved!

    Organizers: Bhargav Bhatt (University of Michigan), Srikanth Iyengar (University of Utah), Wieslawa Niziol (CNRS, ENS-Lyon), LEAD Anurag Singh (University of Utah)

    The homological conjectures in commutative algebra are a network of conjectures that have generated a tremendous amount of activity in the last 50 years. They had largely been resolved for commutative rings that contain a field, but, with the exception of some low dimensional cases, several remained open in mixed characteristic --- until recently, when Yves Andr\'e announced a proof of Hochster's Direct Summand Conjecture. The progress comes from systematically applying Scholze's theory of perfectoid spaces, which had already shown its value by solving formidable problems in number theory and representation theory. One of the goals of the workshop is to cover the ingredients going into the proofs of the Direct Summand Conjecture.

    Updated on Feb 14, 2017 02:11 PM PST