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Extra Form
Lecturer 유화종
Dept. 서울대
date Sep 13, 2018

We introduce the notion of congruences (modulo a prime number) between modular forms of different levels. One of the main questions is to show the existence of a certain newform of an expected level which is congruent to a given modular form. (For instance, if a given modular form comes from an elliptic curve over the field of rational numbers, then this problem is known as "epsilon-conjecture".) We partially answer this question when a given modular form is an Eisenstein series.


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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. 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. 17Sep
    by 김수현
    in Math Colloquia

    Congruences between modular forms

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