University of British Columbia - Department of Mathematics
Algebraic groups, Galois cohomology and related topics
The seminar meets Thursdays at 1:30 or 2pm in MATX 1102, unless noted otherwise. |
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September 11 2 pm, MATX 1102 |
Mark Macdonald (UBC) |
Introduction to Galois cohomology |
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September 18 1:30 pm, MATX 1102 |
Mark Macdonald (UBC) |
Introduction to cohomological invariants |
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September 25 1:30 pm, MATX 1102 |
Aurel Meyer (UBC) |
Introduction to cohomological invariants and essential dimension |
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October 2 2 pm, MATX 1102 |
Max Lieblich (Princeton University) |
Recent progress on the period-index problem |
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October 9 1:30 pm, MATX 1102 |
Jean Fasel (UBC) |
Introduction to Witt rings |
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October 16 1:30 pm, MATX 1102 |
Jean Fasel (UBC) |
Gersten complexes |
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October 23 2 pm, MATX 1102 |
Mark Macdonald (UBC) |
Cohomological invariants of quadratic forms |
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November 6 2 pm, MATX 1102 |
Masoud Kamgarpour (UBC) |
Understanding lower cohomology groups via monoidal categories |
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November 13 2 pm, MATX 1102 |
Masoud Kamgarpour (UBC) |
Torsors, Gerbes, and Group Extensions |
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November 20 2 pm, MATX 1102 |
Alejandro Adem (UBC) |
Elements of Finite Group Cohomology I |
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Novemeber 27 2 pm, MATX 1102 |
Alejandro Adem (UBC) |
Elements of Finite Group Cohomology II |
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Max Lieblich - Recent progress on the period-index problem The period-index problem is a classical problem on the complexity of division algebras over fields (or, via the work of Brosnan, Reichstein, and Vistoli, on the essential dimensions of certain algebraic stacks). In the case of function fields, this problem has an appealing geometric avatar which ties it to the properties of moduli spaces of sheaves on Deligne-Mumford stacks (including the stacks of roots familiar from work of Cadman). I will review some of what is known about this problem and then discuss recent progress using geometric techniques. Masoud Kamgarpour - Understanding lower cohomology groups via monoidal categories I will explain Grothendieck's dictionary relating central extensions and multiplicative torsors. This will provide us with a "new" interpretation of the second group cohomology. Time permitting, I will discuss an analogous interpretation of the third cohomology group. In a future lecture, we will apply these techniques to understand lower cohomology groups of algebraic groups. Familiarity with the notion of monoidal category will be helpful, though not necessary. Alejandro Adem - Elements of Finite Group Cohomology I&II In these two lectures we plan to present an introduction to the cohomology of finite groups, including as time permits -- basic definitions and properties -- restriction, transfers & detection -- connections to representation theory -- cohomology calculations --examples related to fields |