Algebra Seminar, Spring 2019
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Date 
Speaker 
Title/Abstract 
125 
Paolo Mantero 
Koszul Algebras part I
In this first talk of the series, we will introduce Koszul algebras, Gquadratic algebras, LGquadratic algebras and discuss some of their properties.

21 
Paolo Mantero 
Koszul Algebras part II
In this talk we will recall a few relevant properties of Koszul algebras and provide a library of examples of commutative algebras that are Koszul. We will discuss also special classes of Koszul algebras, e.g. Gquadratic algebras, LGquadratic algebras and, if time permits, absolutely Koszul algebras.

28 
Paolo Mantero 
Koszul Algebras part III
TBA

215 
Ian Aberbach 
Syzygies of finite length modules
Let (R, m) be a local ring of dimension d greater than 0 and depth zero. De Stefani, Huneke, and NúñezBetancourt asked the following question: If M is a finitelength Rmodule of infinite projective dimension and if i greater than d+1, then must the ith syzygy have infinite length? They showed that the answer is positive when R is Buchsbaum, and also showed that in a onedimensional ring, no third syzygy of a finite length module can be finite length.
We show that there is a proof of their d=1 result that offers hope for results in higher dimensions. In fact, we are able to show that over a 2dimensional ring, no third syzygy of a finite length module can have finite length. This proof is not a straightforward generalization of the 1dimensional case. This work is joint with Parangama Sarkar.

222 
Lance Miller 
Perfectoid parc spaces
This will be a two part talk on ongoing work with A. Buium. The first talk will cover background about pderivations which are a sort of arithmetic version of derviations which appear in mixed characteristic settings in the presence of lifts of Frobenius. They have been wildly successful in applications to counting rational points. The second talk will discuss how to describe them in perfectoid settings.

31 
Lance Miller 
Perfectoid parc spaces
This will be a two part talk on ongoing work with A. Buium. The first talk will cover background about pderivations which are a sort of arithmetic version of derviations which appear in mixed characteristic settings in the presence of lifts of Frobenius. They have been wildly successful in applications to counting rational points. The second talk will discuss how to describe them in perfectoid settings.

38 
Jesse Keyton 
Homogeneous Liaison and the Sequentially Bounded Licci Condition
In CILiaison, significant effort has been made to study ideals that are in the linkage class of a complete intersection, which are called licci ideals. When the ring is a polynomial ring, recently E. Chong defined a "sequentially bounded" condition on the degrees of the forms generating the regular sequences of the links, and used this condition to find a large class of licci ideals satisfying the EisenbudGreenHarris Conjecture (among them, grade 3 homogeneous Gorenstein ideals in a polynomial ring). He raised the question of whether all homogeneous licci ideals are sequentially bounded licci. In this talk we construct a class of examples that are homogeneous and licci, but not sequentially bounded licci, thus answering his question in the negative. The structure of certain minimal graded free resolutions plays a central role in our proof.

412 
Tai Ha 
TBA
TBA

419 
Liana Sega 
TBA
TBA
