UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

April 07, 2015

939 Evans Hall


3:45PM: Hollow, Solid, and Regular Log Schemes

Arthur Ogus

Logarithmic geometry is a framework for studying compactification and degeneration in algebraic geometry. In particular, smooth log schemes over C behave very much like manifolds with boundary. In an arithmetic setting, one needs to replace the relative notion of “smoothness” with the absolute notion of “regularity,” as defined by K. Kato. I will explain a new approach to log regularity, based on the concept of “solidity” of a log structure, and, if time permits, how this approach elucidates the nature of the regular locus.

5:00PM: Algebraic systems biology

Elizabeth Gross

Systems biology focuses on modeling complex biological systems, such as metabolic and cell signaling networks. These biological networks are modeled with polynomial dynamical systems. Analyzing these systems at steady-state results in algebraic varieties that live in high-dimensional spaces. By understanding these varieties, we can provide insight into the behavior of the models. Furthermore, this algebro-geometric framework yields techniques for model selection and parameter estimation that can circumvent challenges such as limited or noisy data. In this talk, we will introduce biochemical reaction networks and their resulting steady-state varieties. In addition, we will discuss the questions asked by modelers and their corresponding geometric interpretation, particularly in regards to model selection and parameter estimation. This talk will be based on a a couple of joint works, the first with Heather Harrington, Zvi Rosen, and Bernd Sturmfels, and the second with Daniel Bates, Brent Davis, Heather Harrington, and Kenneth Ho.

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