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Extra Form
Lecturer 황준호
Dept. 서울대학교
date Sep 02, 2021

 

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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  1. Existence of positive solutions for φ-Laplacian systems

  2. Essential dimension of simple algebras

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

  4. Entropy of symplectic automorphisms

  5. Entropies on covers of compact manifolds

  6. Elliptic equations with singular drifts in critical spaces

  7. 17Oct
    by 김수현
    in Math Colloquia

    Diophantine equations and moduli spaces with nonlinear symmetry

  8. Descent in derived algebraic geometry

  9. Deformation spaces of Kleinian groups and beyond

  10. Creation of concepts for prediction models and quantitative trading

  11. Counting number fields and its applications

  12. Counting circles in Apollonian circle packings and beyond

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

  14. Contact topology of singularities and symplectic fillings

  15. Contact instantons and entanglement of Legendrian links

  16. Contact Homology and Constructions of Contact Manifolds

  17. Conservation laws and differential geometry

  18. Connes's Embedding Conjecture and its equivalent

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

  20. Congruences between modular forms

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