Commutative Algebra seminar
Speaker: Kabeer Manali Rahul (Australian National University)
Host: Ananthnarayan Hariharan
Title: Metric techniques for triangulated categories
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, July 16
Venue: Ramanujan Hall
Abstract: Neeman has recently introduced certain techniques for triangulated categories which are analogous to notions related to a metric space. These techniques have been used to prove many interesting results in algebraic geometry, including settling several conjectures. In this talk, I will try to give some motivation, and an overview of these techniques. If time permits, I will also talk about some new representability theorems which have been proven using them.

Mathematics Colloquium
Speaker: Amalendu Krishna (Department of Mathematics, UCSB)
Host: Preeti Raman
Title: Some remarks on Kato's ramification theory and applications
Time, day and date: 4:00:00 PM - 5:00:00 PM, Friday, July 18
Venue: Ramanujan Hall
Abstract: Kazuya Kato developed a theory of ramification for henselian discrete valuation fields with arbitrary residue fields which extended the classical ramification theory with perfect residue fields. Kato's definition of his ramification filtration is in general complicated and is often difficult to work with. In a joint work with Subhadip Mazumder, I recently provided a new description of this filtration using sheaf theory. This description has several applications. In this talk, I shall explain this description and show some applications to Brauer groups.