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Summary: PROJECT DESCRIPTION: GROUP ACTIONS AND
COMBINATORICS IN ALGEBRAIC GEOMETRY
DAVID E. ANDERSON
How many lines meet four fixed lines in projective 3-space? What is the
dimension of the space of SL2-invariant tensors in C2
C2
C2
C2
? Both
questions can be answered in terms of the number of solutions to a combinato-
rial puzzle, and it is this interplay between algebraic geometry, representation
theory, and combinatorics that drives the principal investigator's research in-
terests.
One of the PI's goals is to understand, as concretely as possible, the coho-
mology rings of certain algebraic varieties. Specific problems include interpret-
ing the cohomology classes of subvarieties as polynomials, computing structure
constants for cup product with respect to geometrically meaningful bases, and
extracting cohomological information from polytopes associated to the varieties.
1. Background
The proposed work deals with interactions with topology, geometry, repre-
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