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09:00 AM - 10:00 AM
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Grayson, Stillman and Smith: Installation and basic commands
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- Location
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- Video
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- 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
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10:00 AM - 11:00 AM
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Break
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- Location
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- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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Mike Stillman: Investigating the geometry of curves and surfaces
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- Location
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- Video
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- 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
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12:00 PM - 02:00 PM
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Lunch
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- Location
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- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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Stephanie Yang : Intersection numbers on Mg,n
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- Location
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- Video
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- 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
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03:00 PM - 04:00 PM
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Tea
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- Location
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- Video
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- Abstract
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- Supplements
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04:00 PM - 05:00 PM
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Dan Grayson: Computation in intersection rings of flag bundles
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- Location
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- Video
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- 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
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