Hannah Larson
University of California-Berkeley, CA·Mathematics & Statistics·Early-career
Polynomial equations, built by adding and multiplying variables, are among the most basic objects in mathematics. Algebraic geometry tries to classify the shapes they define.
- Fields
Mathematics & Statistics
- Topics
algebraic geometry
moduli spaces
moduli of curves
- Grants
- 1 known grant, through Aug 2031
What they work on
- Develop new intersection-theory methods for moduli spaces of low-genus algebraic curves, spaces whose points each represent a curve, and connect them to closely related moduli spaces.
- Apply intersection theory to compute the cohomology of moduli spaces of curves, an algebraic measure of their shape, and to count their points over finite fields.
- Extend Brill-Noether theory, which describes the ways a curve can map into other spaces, to special curves where the general theory fails, building on earlier results for curves of low gonality.
More about the research
The one-dimensional shapes are called algebraic curves, and they appear in cryptography and string theory. Since Riemann's work in the 1850s, mathematicians have studied curves through their moduli space. This is a space in which each point stands for a different curve, and curves that share a geometric property form a subset of it. To see how different properties relate, one must understand how these subsets intersect. That is the job of intersection theory, and this project aims to develop new tools in it.
Why it matters
This is basic mathematics. It aims to deepen understanding of how families of algebraic curves are organized and how their geometric properties interact. Algebraic curves are used in cryptography and string theory, so new tools for studying them could eventually inform those areas. The grant itself names no direct applications.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Claudio Gonzales
Carleton College, MN·Mathematics & Statistics
Advance the framework of "special points" using polar cones, geometric objects encoding convexity data, to sharpen bounds on the resolvent degree of finite groups and address related arithmetic questions.
Jeremy Miller
Purdue University, IN·Mathematics & Statistics
Prove homological stability and its variants, meaning that the hole-counting homology settles down as spaces grow, for classifying spaces of arithmetic groups, using tools such as locally symmetric spaces and homological algebra.
Nicholas Salter
University of Notre Dame, IN·Mathematics & Statistics·Early-career
Establish asphericality, the absence of higher-dimensional holes, for special strata of Abelian differentials using the PI's Abel-Jacobi flow method, as progress toward the Kontsevich–Zorich conjecture.
The school
University of California-Berkeley: 46 labs on PI Pages, $1.1B a year on research, 825 research doctorates a year.
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