|Thursday 4 March 2021|
|Events for day: Thursday 11 February 2021|
| 11:00 - 13:00 Commutative Algebra Webinar|
Hilbert Series and Poincare Series of Graded Algebras
We begin with proving a formula relating the Hilbert series of a graded algebra $A$ and the Poincare series
for $A$ in two variables using the existence of a graded minimal resolution of the field $k$ over $A$. This gives
the Froberg formula in the case where the bigraded $Tor^A(k,k)$ is concentrated on the diagonal, which we take as definition
of $A$ being ``Koszul". We look at a resolution in the commutative case obtained from the Koszul complex in the ``trivially Golod" case,
which means that there are cycles that represent the homo-logy of the Koszul complex and multiply to zero.
The algebra structur ...
11:00 - 12:00 Weekly Webinar
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