Ananth Shankar
Northwestern University, IL·Mathematics & Statistics·Early-career
Some geometric shapes can be described exactly by polynomial equations, and the number system you allow for the coefficients changes what you can learn. Shimura varieties are such shapes, defined by polynomial equations whose coefficients are rational numbers (ordinary fractions).
- Fields
Mathematics & Statistics
- Topics
Shimura varieties
arithmetic geometry
number theory
- Grants
- 1 known grant, through Jun 2029
What they work on
- Construct and study integral models of exceptional Shimura varieties, that is, descriptions by polynomial equations with whole-number coefficients for the varieties attached to exceptional symmetry groups.
- Investigate the p-adic geometry of Shimura varieties, where distance is measured by divisibility by a prime, and pursue questions of p-adic transcendence in that setting.
- Establish a p-adic analogue of Borel's algebraicity theorem, which forces certain maps into Shimura varieties to be given by polynomials, and address related p-adic bi-algebraicity questions.
- Run a workshop that equips early-stage graduate students with the background needed to begin research problems in arithmetic geometry, and supervise undergraduate projects and graduate theses.
More about the research
They sit at a crossroads of geometry and number theory and have been essential in resolving long-standing conjectures, among them the Mordell Conjecture about rational solutions to equations.
Why it matters
This is pure mathematics: the work would deepen understanding of Shimura varieties, geometric objects that have already been the key to settling major conjectures in number theory. Constructing integral models and establishing p-adic analogues of algebraicity results could supply tools that other researchers use on open problems in number theory and arithmetic geometry.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Laura DeMarco
Harvard University, MA·Mathematics & Statistics
Characterize the special subvarieties — geometric pieces preserved by the map — that arise in families of dynamical systems built from endomorphisms of algebraic varieties, aiming at a general classification within a unifying conjectural framework.
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.
Christopher Rogers
University of Nevada-Reno, NV·Mathematics & Statistics
Gather evidence for the Alekseev-Torossian conjecture that the Kashiwara-Vergne group (KRV) equals the Grothendieck-Teichmueller group (GRT), by studying how both act on explicit geometric and topological objects.
The school
Northwestern University: 71 labs on PI Pages, $1.3B a year on research, 536 research doctorates a year.
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