Preface
Every year we organize the Maurice Auslander Distinguished Lectures and In-
ternational Conference to celebrate the mathematical legacy of Maurice Auslander
who was one of the founding fathers of the representation theory of artin algebras.
These are selected notes from this event which took place April 25-30, 2012, at the
Woods Hole Oceanographic Institute, Quissett Campus in Falmouth, MA.
The International Conference was particularly successful this year; using NSF
funds we were able to invite participants from Argentina, Canada, Germany, Great
Britain, Italy, Japan, Norway, and Russia. The seven invited expository talks
were very well received and set the pace for accessible talks by others during the
conference. Long coffee breaks and lunches at the conference center were very
fruitful and enjoyable events in which participants discussed mathematics on the
balcony with a beautiful view of the ocean.
A wide variety of topics were discussed at the conference. Birge Huisgen-
Zimmermann opened the conference with an overview of the concept of fine and
course moduli spaces for representation theory. Frauke Bleher discussed an emerg-
ing interaction between number theory (based on Mazur’s theory of universal de-
formation rings) and representations of finite dimensional algebras. Otto Kerner,
considered to be the leading expert on wild hereditary algebras, gave a review of
basic theorems and latest results in this field. Aslak Buan, one of the founders
of cluster categories talked about torsion pairs in tubes, but he describes a more
complete classification in his contributed notes. Yuri Berest, with coauthors Felder
and Ramadoss, develops the theory of derived representation schemes.
There were also several inspiring talks by others during the conference. Ivo
Herzog gave a heart-felt tribute to Maurice Auslander when he explained his ideal
approximation theory and how it was motivated by his desire to understand Mau-
rice’s work from a different perspective. Kunio Yamagata gave such a nice survey
talk on Morita Theory leading up to the most recent results that we also invited
him to contribute to the proceeding of the conference. Claudia Chaio and Markus
Schmidmeier were also invited to contribute write ups of their talks since their top-
ics were deemed to be suitable for these proceedings in terms of both novelty and
accessibility. Claudia gives a very complete description of what is known about de-
grees of irreducible maps. Markus Schmidmeier gave an entertaining talk about arc
diagrams which are intuitive pictorial descriptions of representations and how they
deform. His contribution, with coauthor Justyna Kosakowska, gives new results on
this topic.
We would like to thank Bernice Auslander for her initiation and continued sup-
port of the Maurice Auslander Distinguished Lectures, around which the conference
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