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Algebraic and Arithmetic Geometry Research Group
Our Research
Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically closed field, while arithmetic geometry deals with the more subtle study of solutions lying in a number field or its rings of integers. Both these topics are central to mathematics鈥� and connect to subjects ranging from Number Theory and cryptography to mirror symmetry. Our individual research interests at 丁香园AV cover a broad spectrum, including toric geometry, linear subspaces of varieties, modular curves, and rational points on hyperelliptic curves.
The algebraic and arithmetic geometry group runs a regularly meeting research seminar. For more information, see link here...
People
Faculty
Hyperelliptic curves, rational points, Chabauty methods, covering techniques, descent, local-to-global obstructions
Algebraic number theory, arithmetic geometry, representation theory, modular varieties, automorphic forms, diophantine problems, Galois representations, elliptic curves, Q-curves, function fields
Katrina Honigs
Varieties over fields of positive characteristic, Q-rational points of varieties, derived category of coherent sheaves on a variety
Toric geometry, Fano varieties, mirror symmetry, deformation theory, linear subspaces of varieties, algebraic complexity theory
Representation theory, Schubert calculus, moduli of curves, syzygies
Geometric and analytic methods for combinatorial enumeration
Postdoctoral Fellows & Visitors
PhD Graduate Students
- Emiel Haakma
- Haggai Liu
- Sharon Robins
- Carl F Waller
MSc Graduate Students
- Zhe Xu