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Entry requirements:
Research supervisor:
Alexander Perepechko
PhD
Supervisor’s research interests:
Affine algebraic varieties over algebraically closed fields represent a classical topic of algebraic geometry. Their automorphism groups are a rich domain of research that includes combinatorial representations of reductive group actions and birational self-maps. I am interested in topic of transitivity, additive actions, infinite-dimensional subgroups (called ind-groups), toric and T-varieties, and integer-point orbits on varieties corresponding to Diophantine equations.
Research highlights:
Supervisor’s specific requirements:
Main publications:
- Master’s degree / equivalent in a related field
- B2 level of English
- Good track record of publications related to the topic of the intended research
- Strong research proposal 1,500 - 3,500 words
Research supervisor:
Alexander Perepechko
PhD
Supervisor’s research interests:
Affine algebraic varieties over algebraically closed fields represent a classical topic of algebraic geometry. Their automorphism groups are a rich domain of research that includes combinatorial representations of reductive group actions and birational self-maps. I am interested in topic of transitivity, additive actions, infinite-dimensional subgroups (called ind-groups), toric and T-varieties, and integer-point orbits on varieties corresponding to Diophantine equations.
Research highlights:
- This research program involves international
- collaboration with research groups in the UK,
- Germany, and France.
Supervisor’s specific requirements:
- Background in basic algebraic geometry.
- Acquaintance with algebraic groups.
- Python3 knowledge is preferable.
Main publications:
- (with Ivan Arzhantsev and Hendrik Süß) Infinite transitivity on universal torsors, Journal of the London Mathematical Society 89 (2014), no. 3, 762‑778.
- (with Sergei Kovalenko and Mikhail Zaidenberg) On automorphism groups of affine surfaces, Advanced Studies in Pure Mathematics 75 (2017), Algebraic Varieties and Automorphism Groups, 207–286; arXiv:1511.09051.
- (with Andriy Regeta) When is the automorphism group of an affine variety nested?, preprint, arXiv:1903.07699.
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