All talks take place in Lecture Hall MH 309A. Further information can be found here including a map of the campus.

Schedule:

• Monday June 10th
• 13:30 – 14:20 Dag Madsen: Hochschild homology and global dimension
  
  Abstract: In this talk I will discuss the current status of Han's conjecture. This conjecture says that a finite dimensional associative algebra whose higher Hochschild homology groups eventually vanish must be of finite global dimension.
  
  
• 14:35 – 15:25 Gunnar Fløystad: Zipping Tate resolutions over an exterior algebra to get free resolutions over a symmetric algebra
  
  Abstract: The bounded derived category of coherent sheaves on the projective space \(\mathbb{P}(W)\) is equivalent to the category of Tate resolutions over the exterior algebra \(\oplus_i \wedge^i W^*\). Given such a resolution,it may be amalgamated, "zipped", with the exterior powers \(\wedge^i V\) of a new vector space \(V\), to get a bounded complex of free modules over the polynomial ring \(\text{Sym}(V \otimes W^*)\). We describe this construction and its properties, and apply this to give explicit constructions of several notable classical and recent resolutions over polynomial rings, like the Eagon-Northcott complex, Buchsbaum-Eisenbud complexes, pure free resolutions, and the recent tensor complexes.
  
  
• 15:40 – 16:30 Henning Krause: A local-global principle for triangulated categories
  
  Abstract: One of the cornerstones of commutative algebra is the local-global principle. In my talk I discuss a version of this principle for triangulated categories. Some applications from representation theory will serve as an illustration. This is based on joint work with Dave Benson and Srikanth Iyengar.
  
  
• Tuesday June 11th
• 13:30 – 14:20 Marius Thaule: The Grothendieck group of higher triangulated categories
  
  Abstract: The Grothendieck group of a triangulated category is the free abelian group on the (set of) isomorphism classes of objects, modulo the Euler relations corresponding to the distinguished triangles. Thomason proved that the set of subgroups of the Grothendieck group classifies the dense triangulated subcategories. Namely, there is a bijective correspondence between the set of subgroups and the set of dense triangulated subcategories.
  
  In my talk I will discuss an extension of this result to the case of \(n\)-angulated categories for \(n\) odd. This is joint work with Petter Bergh.
  
  
• 14:35 – 15:25 Alexander Berglund: Duality, descent and extensions I
  
  Abstract: I will talk about joint work with Kathryn Hess on connections between homotopical notions of Koszul duality, Grothendieck descent and Hopf-Galois extensions. My talk will focus on describing a general categorical framework that allows for a comparison of the three notions. Roughly speaking, it turns out that each of the notions can be formulated as asserting that a certain morphism of corings induces a Quillen equivalence between the associated categories of comodules. This realization led us to develop what could be thought of as a homotopical version of Morita theory for model categories of comodules. Kathryn's talk will then formulate the main theorems that connect the three different notions, as well as discuss further examples and applications.
  
  
• 15:40 – 16:30 Kathryn Hess: Duality, descent and extensions II
  
  Abstract: I will present joint work with Alexander Berglund on the close relations among homotopical notions of Koszul duality, Grothendieck descent and Hopf-Galois extensions, based on the categorical framework that Alexander will describe in his talk.
  
  I will also sketch recent progress on properties of Hopf-Galois extensions of commutative differential graded algebras, due to my graduate student, Varvara Karpova.