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Extra Form
강연자 황준호
소속 서울대학교
date 2021-09-02

 

A fundamental result in number theory is that, under certain linear actions of arithmetic groups on homogeneous varieties, the integral points of the varieties decompose into finitely many orbits.

For a classical example, the set of integral binary quadratic forms of fixed nonzero discriminant consists of finitely many orbits under action of the modular group SL2(Z).

In this talk, we discuss certain classes of algebraic varieties with inherently nonlinear group actions, for which analogous finite generation results for integral points can be established or conjectured.

These varieties arise as various moduli spaces (of local systems on surfaces, Stokes matrices, etc.) in geometry and topology of manifolds, allowing application of external tools to the study of Diophantine problems; the latter will be emphasized in the talk.

 
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첨부 '1'
  1. Conformal field theory in mathematics

  2. Congruences between modular forms

  3. Connectedness of a zero-level set as a geometric estimate for parabolic PDEs

  4. Connes's Embedding Conjecture and its equivalent

  5. Conservation laws and differential geometry

  6. Contact Homology and Constructions of Contact Manifolds

  7. Contact instantons and entanglement of Legendrian links

  8. Contact topology of singularities and symplectic fillings

  9. Convex and non-convex optimization methods in image processing

  10. Counting circles in Apollonian circle packings and beyond

  11. Counting number fields and its applications

  12. Creation of concepts for prediction models and quantitative trading

  13. Deformation spaces of Kleinian groups and beyond

  14. Descent in derived algebraic geometry

  15. 17Oct
    by 김수현
    in 수학강연회

    Diophantine equations and moduli spaces with nonlinear symmetry

  16. Elliptic equations with singular drifts in critical spaces

  17. Entropies on covers of compact manifolds

  18. Entropy of symplectic automorphisms

  19. Equations defining algebraic curves and their tangent and secant varieties

  20. Essential dimension of simple algebras

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