postdoctoral faculty at the University of Nebraska, Lincoln
PhD from UC Berkeley, advised by David Eisenbud
e-mail: lheller2@unl.edu
office: Avery 328
Department of Mathematics
University of Nebraska, Lincoln
210 Avery Hall
1144 T St
Lincoln, NE 68588
interested in commutative algebra with geometric applications
multigraded regularity, virtual resolutions, Cox rings, toric varieties
Consider the rings \(k[s^2,st]\) and \(k[s^2,t^2]\). What are their dimensions? Are they integrally closed? How do they relate to maps to projective space?
How about \(k[s^3,s^2t,st^2,t^3]\)?
Calculate a Grobner basis for for the ideal \((xz,yw,xw)\) in \(k[x,y,z,w]\).
Give the Koszul complex on the generators of this ideal. Is it a resolution?
Define the canonical curve of genus 4 and describe its ideal sheaf.
Find the Picard group of a nonsingular quadric.
Draw a picture of \(\operatorname{Spec}\mathbb{Z}[x]\).
What are the maximal ideals in the ring of smooth functions on a compact manifold?
Define the tangent space.
Given a vector field \(X\), do there exist local coordinates under which \(X\) is constant?