Embedded Files
List of Speakers, Titles and Abstracts
List of Speakers, Titles and Abstracts
Dale Cutkosky, University of Missouri
Dale Cutkosky, University of Missouri
Title: Growth of filtrations
Title: Growth of filtrations
ABSTRACT: We consider the Hilbert function of the fiber cone of a graded filtration, and discuss good and bad properties of this function, especially for divisorial filtrations. We mention some open problems.
Hema Srinivasan, University of Missouri
Hema Srinivasan, University of Missouri
Title: What can we see from a Principal Matrix of a Numerical semigroup?
Title: What can we see from a Principal Matrix of a Numerical semigroup?
ABSTRACT: I will define the notion of Principal matrix from the critical binomials and survey some known results and some questions.
Bernd Ulrich, Purdue University
Bernd Ulrich, Purdue University
Title: Residual Intersection Theory
Title: Residual Intersection Theory
ABSTRACT : TBA
ABSTRACT : TBA
Le Tuan Hoa, Institute of Mathematics, Hanoi
Le Tuan Hoa, Institute of Mathematics, Hanoi
Title: Upper bounds on Hilbert coefficients
Title: Upper bounds on Hilbert coefficients
ABSTRACT: This talk is mainly based on a recent joint work with L. X. Dung and J. Elias: "Upper bounds on two Hilbert coefficients, Journal of Algebra,
633 (2023), 563 - 590". Some new upper bounds on the first and the second Hilbert coefficients of a Cohen-Macaulay module over a local ring are presented. Characterizations are provided for some upper bounds to be attained. The characterizations are given in terms of Hilbert series as well as in terms of the Castelnuovo-Mumford regularity of the associated graded module.
Claudia Polini, University of Notre Dame
Claudia Polini, University of Notre Dame
Title: Set theoretic complete intersections: a very classical problem
Title: Set theoretic complete intersections: a very classical problem
ABSTRACT: A very classical problem in algebraic geometry and commutative algebra is whether an algebraic curve in n space can be written set theoretically as the intersection of n-1 hypersurfaces. I will explain this problem and describe several approaches. The talk is suitable for graduate students.
Vaibhav Pandey, Purdue University
Vaibhav Pandey, Purdue University
Title: Comparing the algebraic properties of an ideal with its link.
Title: Comparing the algebraic properties of an ideal with its link.
ABSTRACT: The geometric link of a proper, unmixed ideal in a polynomial ring is another ideal such that their intersection is generated by a regular sequence, i.e., the union of their vanishing loci is a complete intersection. The 'most general' such link is called the generic link.
A classical research theme in linkage theory is to investigate what properties remain invariant along links. For example, height and the Cohen-Macaulay property are invariants of linkage. It is well-known that the generic link of a radical ideal is radical (even prime). This raises the question: Are either 'squarefreeness of the initial ideal' or 'F-purity' invariants of generic linkage? We answer this question in the negative.
On the other hand, under certain strong assumptions, we show that squarefreeness of the initial ideal, F-purity, and even the F-pure threshold are not only invariants of linkage but even invariants of residual intersections (a vast generalization of links).
Page updated
Report abuse