From: Calum W Spicer <cwspicer@ucsd.edu>
Date: Wed, Feb 22, 2017 at 8:35 PM
Subject: GradSWANTAG V
To: mathgrad@math.ucsd.edu


Hey everyone,
This Saturday (2/25) is the fifth Graduate Student Workshop in Algebra,
Number Theory and Algebraic Geometry.


All talks will be held in APM 7421.

The schedule for the day:
9:30 - Light Breakfast
10-11 Stephan
11-12 Robbie
1-2 Marino
2-3 Jonno

We're super stoked to hear about what our fellow graduate students are
thinking about and hope that you will join us,
Cal, Peter, Francois


The abstracts and titles are as follows:

Robbie Snellman
Title: Fitting invariants
Abstract: Depending on the ring, Fitting invariants allow one to determine
the isomorphism class certain modules. For other rings, it turns out that
Fitting invariants don't quite determine the isomorphism class of a
module, but they do classify the module up to a four-term exact sequence.
This talk will provide an introduction to Fitting invariants and give
examples illustrating how these invariants can/cannot determine the
isomorphism class of certain modules.


Stephan Weispfenning
Title: Invariant Theory of Preprojective Algebras
Abstract: Studying invariant theory of commutative polynomial rings has
motivated many developments in commutative algebra and algebraic
geometry. One important result is the Shephard-Todd-Chevalley Theorem
that gives necessary and sufficient conditions for the fixed subring
under a finite group action to be a polynomial ring. With progress being
made to extend this result to regular algebras, the noncommutative
analogue of polynomial rings, the question arises if the theory
generalizes further to non-connected noncommutative algebras. Our
objects of study will be preprojective algebras which are certain factor
algebras of path algebras corresponding to extended Dynkin diagrams of
type A, D or E. We will point out additional difficulties and where a
straightforward generalization fails.


Marino Romero
Title: Decomposing tensor powers of standard representations
Abstract: The following is a well-known result: Let $A$ be a faithful
representation
of a finite group $G$. Then for sufficiently large $r$, $A^{\otimes r}$
contains every irreducible representation of $G$. One may then ask for the
minimum tensor power which achieves this. In general, computing tensor
products of representations can be difficult. However, we will do this
explicitly for a certain defining representation of $C_k \wr S_n$, where
$C_k$ is the cyclic group of order $k$ and $S_n$ is the symmetric group on
$n$ letters.

Jonno Conder
TBA