Talks
Combinatorial Approaches to Monomial Ideals
Location: MGO Colloquium, Syracuse University, February 2022
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Abstract: In this talk we will discuss two combinatorial objects which can be built from monomial ideals, namely the Buchberger Graph and Scarf Complex. Both of these can be used to get resolutions of the ideal. We will discuss how to get the resolutions, when and if the resolutions are minimal, and how the two approaches relate to each other.
Finding Resolutions of Monomial Ideals
Location: MGO Colloquium, Syracuse University, November 2020
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Abstract: Given a monomial ideal I and a polynomial ring S we are often interested in finding resolutions of S/I over S. Particularly it is useful to have a minimal free resolution. In this talk we will discuss how to use the structure of the ideal to get a specific type of graph, how this graph gives us a resolution, and under what conditions this resolution is the minimal free resolution.
Diffsequences for Fibonacci and Related Sequences
Location: AGNT Talks, Clemson University, November 2015
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Joint work with Harry Choi and Leanna O’Brien
Papers
Abstract: In this paper we present two different combinatorial approaches to finding resolutions of polynomial ideals. Their goal is to get resolutions that are as small as possible while still preserving the structure of the zeroth syzygy module. Then we present the idea of a differential graded algebra and discuss when the minimal resolutions of a polynomial ideals admits such a structure.
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