## Geometric and Cohomological Methods in Algebra: 2016-2019

### Overview

Universities in Western Canada have been traditionally strong in algebra, in particular in representation theory and the theory of Lie algebras. More recently, the algebra community in Western Canada was solidified and strengthened by the highly successful PIMS CRG in 2005-08, which helped junior researchers and recent arrivals integrate into preexisting networks. The algebraists in Western Canada are at the forefront of developments in algebra, which have been influenced by an infusion of new techniques from algebraic geometry and algebraic topology.

The community of algebraists at PIMS universities has been strengthened since 2008 and collectively, we now have a strong regional group of researchers in algebra. The five CRG organizers work in overlapping research areas of central interest in algebra: Lie algebras, quadratic forms, central simple algebras, modular representation theory, algebraic groups, homogeneous spaces, Galois cohomology, and motives.

Our impact and productivity will be amplified through scientific exchanges, joint seminars and workshops, sharing postdocs and distinguished visitors, and creating new research and training opportunities for our students.

### Research Interests:

• Applications of Galois cohomology to the study of infinite-dimensional Lie algebras

• Essential and canonical dimension

• Representation theory and support varieties

### Organizers:

• Vladimir Chernousov (UAlberta)

• Nikita Karpenko (UAlberta)

• Julia Pevstova (UWashington)

• Arturo Pianzola (UAlberta)

• Zinovy Reichstein (UBC)

### Planned Activities:

**2016 Activities:**

• Fall 2016: ABC Workshop at UAlberta

• April 24- May 18 : Distinguished Visitor, Mathieu Florence (University of Paris VI) at UAlberta and UBC

• June 24 - Aug 6: Distinguished Visitor, David Benson (University of Aberdeen) at UBC and UWashington

• Post Doctoral Fellows: Taiki Shibata at UAlberta

**2017 Activities:**

• August 14- 18: Western Summer School in Algebra at UAlberta

• August 21- 25: Conference on Lie Theory, Cohomology and Geometry in Alberta

• Fall 2017: ABC Workshop, Location TBC

• Post Doctoral Fellows (beginning Fall 2017):

* Stephen Scully at UAlberta

* Fei Hu at UBC

**2018 Activities:**

• June 11-15: 2018 Summer School on Geometry and Topology at UChicago.

• November 10 - 11: ABC Algebra Workshop at UWashington.

**2019 Activities:**

• February 19-21: Workshop on Braids, Resolvent Degree and Hilbert's 13th Problem, at IPAM

• Jan - Aug 31: Postoctoral visits between PIMS sites.

• July 8, 2019: Algebraic Geometry Seminar Series .