Workshop

Macaulay2 day

February 03, 2009

Registration Deadline:	February 03, 2009 almost 16 years ago
To apply for Funding you must register by:	November 03, 2008 about 16 years ago

Parent Program:	--

Organizers

Ravi Vakil (Stanford University), Gregory G. Smith (Queen's University) , Mike Stillman (Cornell University)

Description

Using Macaulay 2 in your research The goal of the workshop is to help the participants use the Macaulay 2 software in their research. The first presentation will focus on installation, set-up, and basic functions. Participants are encourage to bring their laptops to this session to get assistance with the software installation. The other independent talks will focus on different problems in algebraic geometry; likely topics include computing sheaf cohomology, intersection theory, and enumerative geometry. Each of these talks will also demonstrate the use of Macaulay 2. Registration Cut-Off Date 2/3/2009 "Conference webpage"

Keywords and Mathematics Subject Classification (MSC)

Primary Mathematics Subject Classification No Primary AMS MSC

Secondary Mathematics Subject Classification No Secondary AMS MSC

Schedule, Notes/Handouts & Videos

Show Schedule, Notes/Handouts & Videos

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Feb 03, 2009
Tuesday

09:00 AM - 10:00 AM		Grayson, Stillman and Smith: Installation and basic commands
Location -- Video -- Abstract We will demonstrate how to install Macaulay 2 and how to use some of the basic commands. No prior knowledge will be assumed; bring your laptops to try Macaulay 2 and get help. Supplements -- Show Detail
10:00 AM - 11:00 AM		Break
Location -- Video -- Abstract -- Supplements -- Show Detail
11:00 AM - 12:00 PM		Mike Stillman: Investigating the geometry of curves and surfaces
Location -- Video -- Abstract We show how to use Macaulay 2 to help investigate projective curves and surfaces. We will start out with a "mystery" curve: a curve given by equations in projective space. We then get to work understanding the curve. Along the way, we find the canonical embedding, and see how to compute sheaf cohomology in Macaulay 2. For the second example, we start with equations defining a surface, and once again, we try to understand the surface. We show how to compute invariants, intersection numbers, adjunction maps, exceptional lines, etc. Supplements -- Show Detail
12:00 PM - 02:00 PM		Lunch
Location -- Video -- Abstract -- Supplements -- Show Detail
02:00 PM - 03:00 PM		Stephanie Yang : Intersection numbers on Mg,n
Location -- Video -- Abstract We introduce a Macaulay 2 package which calculates top intersection numbers among tautological classes on Mg,n. As an application, we show that the tautological ring for the moduli space of genus three curves whose dual graph has at most one loop is not Gorenstein. Supplements -- Show Detail
03:00 PM - 04:00 PM		Tea
Location -- Video -- Abstract -- Supplements -- Show Detail
04:00 PM - 05:00 PM		Dan Grayson: Computation in intersection rings of flag bundles
Location -- Video -- Abstract We will describe the Macaulay 2 package Schubert 2, written with Michael Stillman, and the mathematics behind it. It incorporates the approach of Katz and Strømme for computing Chern classes intersection numbers of interest in algebraic geometry and in physics, together with algorithmic improvements afforded by using Macaulay 2 rather than Maple as the base system. Supplements -- Show Detail