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[4:00pm] Department Colloquium
 Description:
 Department Colloquium
Speaker: Dhruv Ranganathan
Time & Date: 4pm Wednesday, September 19
Venue : Room 215
Title and abstract:
The space of equations for an algebraic curve
The geometry of a Riemann surface is captured by the ways in which it can
manifest as a projective variety, or more precisely, by the geometry of
spaces parameterizing embeddings of the curve into projective space. These
“BrillNoether varieties” of a curve are well understood in two cases. On
one end, work of Clifford gives a complete understanding of hyperelliptic
curves. On the other end, a curve that is general in moduli exhibits
expected behaviour. In recent joint work with Dave Jensen, building on
previous work of Nathan Pflueger, we determine formulas for the dimensions
of the BrillNoether varieties for the intermediate cases, i.e. general
curves of a fixed gonality. Our methods blend the combinatorics of the
sandpile model on graphs with methods from nonarchimedean analysis and
deformation theory. I will give an overview of ideas surrounding the
theorem and its proof, and try to give a sense of the link between
algebraic and combinatorial geometry.


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