Journal: International Mathematics Research Notices

Abbreviation

Int. Math. Res. Not.

Publisher

Oxford University Press

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ISSN

1073-7928
1687-0247

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Publications1 - 10 of 93
  • On the Grid Ramsey Problem and Related Questions
    Item type: Journal Article
    Conlon, David; Fox, Jacob; Lee, Choongbum; et al. (2015)
    International Mathematics Research Notices
  • Lower Semi-continuity of the Index in the Viscosity Method for Minimal Surfaces
    Item type: Journal Article
    Rivière, Tristan (2021)
    International Mathematics Research Notices
    The goal of the present work is two-fold. First we prove the existence of a Hilbert manifold structure on the space of immersed oriented closed surfaces with three derivatives in L2 in an arbitrary compact submanifold Mm of an Euclidian space RQ. Second, using this Hilbert manifold structure, we prove a lower semi-continuity property of the index for sequences of conformal immersions, critical points to the viscous approximation of the area satisfying a Struwe entropy estimate and a bubble tree strongly converging in W1,2 to a limiting minimal surface as the viscous parameter is going to zero.
  • The Nontrivial Zeros of Period Polynomials of Modular Forms Lie on the Unit Circle
    Item type: Journal Article
    Imamoglu, Özlem; Conrey, John Brian; Farmer, David W. (2013)
    International Mathematics Research Notices
  • Mod-Poisson Convergence in Probability and Number Theory
    Item type: Journal Article
    Kowalski, Emmanuel; Nikeghbali, Ashkan (2010)
    International Mathematics Research Notices
  • RTT Realization of Quantum Affine Superalgebras and Tensor Products
    Item type: Journal Article
    Zhang, Huafeng (2016)
    International Mathematics Research Notices
  • The Extremal Number of Cycles with All Diagonals
    Item type: Journal Article
    Bradač, Domagoj; Methuku, Abhishek; Sudakov, Benny (2024)
    International Mathematics Research Notices
  • On an elliptic equation arising from photo-acoustic imaging in inhomogeneous media
    Item type: Journal Article
    Ammari, Habib; Dong, Hongjie; Kang, Hyeonbae; et al. (2015)
    International Mathematics Research Notices
  • A desingularization of real differentiable actions of finite groups
    Item type: Journal Article
    Feichtner, Eva Maria; Kozlov, Dmitry N. (2005)
    International Mathematics Research Notices
  • Hochschild (Co)homology of the Dunkl Operator Quantization of Z₂- singularity
    Item type: Journal Article
    Ramadoss, Ajay; Tang, Xiang (2012)
    International Mathematics Research Notices
  • Two-loop Loewner potentials
    Item type: Journal Article
    Luo, Yan; Maibach, Sid (2025)
    International Mathematics Research Notices
    We study a generalization of the Schramm–Loewner evolution (SLE) loop measure to pairs of non-intersecting Jordan curves on the Riemann sphere. We introduce four equivalent definitions of two-loop Loewner potential for smooth pairs: respectively expressing it in terms of normalized Brownian loop measure, zeta-regularized determinants of the Laplacian, an integral formula generalizing universal Liouville action, and Loewner–Kufarev energy of a foliation. Moreover, we prove that the potential is an Onsager–Machlup functional for the two-loop SLE, and a variational formula involving Schwarzian derivatives. The first, third and fourth definitions are finite if and only if both loops are Weil–Petersson quasicircles. Addressing the question of minimization of the two-loop Loewner potential, we find that any such minimizers must be pairs of circles. However, the potential is not bounded, diverging to negative infinity as the circles move away from each other and to positive infinity as the circles merge, thus preventing a definition of two-loop Loewner energy for the prospective large deviations principle for the two-loop SLE. To remedy the divergence, we study a way of generalizing the two-loop Loewner potential by taking into account how conformal field theory (CFT) partition functions depend on the modulus of the annulus between the loops. This generalization is motivated by the correspondence between SLE and CFT, and it also emerges from the geometry of the real determinant line bundle as introduced by Kontsevich and Suhov.
Publications1 - 10 of 93