http://www.pims.math.ca/scientific-event/160718-ssscm

Summer School on Surgery and the Classification of Manifolds

Start Date: 07/18/2016
End Date: 07/22/2016
Location: University of Calgary

Description: 
The summer school is aimed at graduate students and postdocs, although all are 
welcome. It is being sponsored by the Pacific Institute of Mathematical Sciences 
(PIMS) Collaborative Research Group (CRG) in Applied, Algebraic, and Geometric 
Topology.

Scientific Plan:
The goal is for participants to learn about the classification of manifolds, up to 
homeomorphism and diffeomorphism within a fixed homotopy type, using the 
technique of surgery. This technique uses the close relations between algebraic 
and geometric topology, passing between homology and homotopy groups via 
the Hurewicz theorem and between handles in a manifold and cells in a CW 
complex through Morse theory. The classification techniques are most effective 
for manifolds of dimension four or greater, although there are be applications to 
and interactions with low-dimensional topology.

This mathematics interacts with algebraic topology, geometric topology, 
differential topology, geometric group theory, and geometric functional analysis. 
The capstone speaker will be Guoliang Yu, who will discuss connections of 
surgery theory with index theory, with the Dirac operator and the existence of 
metrics of positive scalar curvature, and with the Novikov and Baum-Connes 
conjectures.

Format: There will be four hours of lectures given by the organizers each day. In 
addition, there will be minilectures given by participants on topics suggested by 
the organizers in advance. There will also be exercise sessions and question 
sessions, promoting a good deal of interactions between the participants and the 
organizers.

Prerequisites: We hope to draw participants from multiple backgrounds, 
including geometric topology, algebraic topology, geometric group theory, 
geometry, and geometric functional analysis. But in order to effectively 
participate in the summer school, participants should come to the summer 
school with a working knowledge of smooth manifolds, vector bundles, 
transversality, the cohomology ring, the Hurewicz Theorem, and the statement 
of Poincaré duality. Familiarity with bordism theory and generalized 
(co)homology theory, classifying spaces for vector bundles, characteristic classes 
and Morse Theory would also be helpful.

Downloads (see website above)

Scientific Committee:
Diarmuid Crowley (co-chair)
James Davis (co-chair)
Qayum Khan
Guoliang Yu

Organizing Committee:
Kristine Bauer
Donald Stanley

Other Information: 
Accommodation:  
Accommodation will be provided for participants at the
University of Calgary's student residences.  
Calgary is in the foothills of the beautiful Canadian Rockies, and,
immediately prior to the summer school is the famous Calgary Stampede.  
Registration Process:  
Registration for the summer school is a two-step process:

Step 1: Application Request: Individuals interested in participating in the 
Summer School should send an email to [log in to unmask] The email 
should contain the following:
**Applicant's first, last name and gender
**Applicant's email address and institution
**Applicant's referee name and email address
**Applicant's CV (as a pdf attachment)
**A brief (less than 250 word) statement on your current research interests and 
how the summer school will benefit.
**Indication of whether you would like to present at the summer school, and 
your area of interest. 
**Indication of whether you will be able to attend without or with travel support.   
Application deadline: April 29th, 2016.

Step 2: Registration: You will be notified via email once your application has 
been accepted and will be directed to the Summer School registration page.   
There will be a $50CAD registration fee.

Collaborative Research Group:
This event is hosted by the PIMS Collaborative Research Group on Applied, 
Algebraic and Geometric Topology.

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