# Algebra and Number Theory Seminar Spring 2017

**April 7, 2017
No Seminar
**

**April 14, 2017
**

**Rob Carman, UCSC**

**Title: Unit Groups of Trivial Source Rings as a Biset Functor**

**Abstract: The theory of biset functors has been instrumental in studying the unit group of the Burnside ring of a finite group. I will explain a notion of tensor induction for modules of a group algebra and show how this can be used to define the biset functor structure for the unit group of the trivial source ring of a finite group.**

**April 21, 2017
**

**Markus Linckelmann, City University, London**

**Title: On Triangulated Categories in Representation Theory**

**Abstract: There are two types of triangulated categories which arise routinely in modular representation theory - derived categories, and stable module categories.
Derived categories determine many fundamental numerical invariants of algebras, such as the number of isomorphism classes of simple modules and irreducible characters.
By contrast, it is not known whether stable module categories determine any of the above mentioned numerical invariants in general. This is one of the major obstacles in modular representation theory. Unlike derived categories, stable module categories need not have any t-structures, and hence their stability spaces in the sense of Bridgeland may be empty. Still, a stable module category may have many abelian subcategories whose exact structure is compatible with the triangulated structure, and whose numerical invariants are, in some cases, those of the original algebra. We will describe a simple construction principle for abelian subcategories of stable module categories. **

**April 28, 2017
TBA
**

**May 5, 2017
TBA
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**May 12, 2017
TBA
**

**May 19, 2017
TBA
**

**May 26, 2017
TBA
**

**June** **2, 2017**

**TBA**

**June 9, 2017
TBA
**

**June 16, 2017
TBA
**

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