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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. Conformal field theory in mathematics

  2. 17Sep
    by 김수현
    in Math Colloquia

    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. 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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