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Academic literature on the topic 'Meromorphic correspondences'

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Published: 6 September 2023

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Journal articles on the topic "Meromorphic correspondences"

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Londhe, Mayuresh. "Recurrence in the dynamics of meromorphic correspondences and holomorphic semigroups." Indiana University Mathematics Journal 71, no. 3 (2022): 1131–54. http://dx.doi.org/10.1512/iumj.2022.71.9753.

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Negrini, Isabella. "A Shimura–Shintani correspondence for rigid analytic cocycles of higher weight." Forum Mathematicum 35, no. 2 (February 28, 2023): 549–71. http://dx.doi.org/10.1515/forum-2022-0235.

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Abstract This paper takes the first steps towards a systematic study of additive rigid meromorphic cocycles of higher weight. These were introduced by Darmon and Vonk, who focused on additive cocycles of weight two and their multiplicative lifts. After classifying certain rigid meromorphic cocycles of weight 2 ⁢ k {2k} , we construct an explicit holomorphic kernel function realizing a Shimura–Shintani style correspondence from modular forms of weight k + 1 / 2 {k+1/2} and level 4 ⁢ p 2 {4p^{2}} to rigid analytic cocycles of weight 2 ⁢ k {2k} on SL 2 ⁡ ( ℤ ⁢ [ 1 / p ] ) {\operatorname{SL}_{2}(\mathbb{Z}[1/p])} .
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Smith, Benjamin H. "Singular G-Monopoles on S1 × Σ." Canadian Journal of Mathematics 68, no. 5 (October 1, 2016): 1096–119. http://dx.doi.org/10.4153/cjm-2016-010-2.

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AbstractThis article provides an account of the functorial correspondence between irreducible singular G-monopoles on S1×Σ and stable meromorphic pairs on Σ. A theorem of B.Charbonneau and J. Hurtubise is thus generalized here from unitary to arbitrary compact, connected gauge groups. The required distinctions and similarities for unitary versus arbitrary gauge are clearly outlined, and many parallels are drawn for easy transition. Once the correspondence theorem is complete, the spectral decomposition is addressed.
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Chuang, Wu-Yen, Duiliu-Emanuel Diaconescu, Ron Donagi, Satoshi Nawata, and Tony Pantev. "Twisted spectral correspondence and torus knots." Journal of Knot Theory and Its Ramifications 29, no. 06 (May 2020): 2050040. http://dx.doi.org/10.1142/s0218216520500406.

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Cohomological invariants of twisted wild character varieties as constructed by Boalch and Yamakawa are derived from enumerative Calabi–Yau geometry and refined Chern–Simons invariants of torus knots. Generalizing the untwisted case, the present approach is based on a spectral correspondence for meromorphic Higgs bundles with fixed conjugacy classes at the marked points. This construction is carried out for twisted wild character varieties associated to [Formula: see text] torus knots, providing a colored generalization of existing results of Hausel, Mereb and Wong as well as Shende, Treumann and Zaslow.
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Kamgarpour, Masoud. "On the Notion of Conductor in the Local Geometric Langlands Correspondence." Canadian Journal of Mathematics 69, no. 1 (February 1, 2017): 107–29. http://dx.doi.org/10.4153/cjm-2016-016-1.

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AbstractUnder the local Langlands correspondence, the conductor of an irreducible representation of Gln(F) is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.
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Dinh, Tien-Cuong, and Nessim Sibony. "Upper bound for the topological entropy of a meromorphic correspondence." Israel Journal of Mathematics 163, no. 1 (January 2008): 29–44. http://dx.doi.org/10.1007/s11856-008-0002-9.

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Ngoc Diep, Do. "A Quantization Procedure of Fields Based on Geometric Langlands Correspondence." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–14. http://dx.doi.org/10.1155/2009/749631.

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We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry groupGL. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundles with connection over the space dual to the Lie algebra of the symmetry groupGL. After that we quantize the vector bundles with connection over the coadjoint orbits of the symmetry groupGL. Use the electric-magnetic duality to pass to the Langlands dual Lie groupG. Therefore, we have some affine Kac-Moody loop algebra of meromorphic functions with values in Lie algebra=Lie(G). Use the construction of Fock space reprsentations to have representations of such affine loop algebra. And finally, we have the automorphic representations of the corresponding Langlands-dual Lie groupsG.
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Dinh, Tien-Cuong, and Hao Wu. "Regularity of the equilibrium measure for meromorphic correspondences." Analysis and Mathematical Physics 13, no. 3 (May 27, 2023). http://dx.doi.org/10.1007/s13324-023-00815-9.

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Khudhur, Peshawa M. "Complete Classification of Degree 7 for Genus 1." Iraqi Journal of Science, February 27, 2021, 594–603. http://dx.doi.org/10.24996/ijs.2021.62.2.25.

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Assume that is a meromorphic fuction of degree n where X is compact Riemann surface of genus g. The meromorphic function gives a branched cover of the compact Riemann surface X. Classes of such covers are in one to one correspondence with conjugacy classes of r-tuples ( of permutations in the symmetric group , in which and s generate a transitive subgroup G of This work is a contribution to the classification of all primitive groups of degree 7, where X is of genus one.
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Ferrari, Andrea E. V., and Lionel Mason. "Meromorphic Painlevé III transcendents and the Joukowski correspondence." Journal of Integrable Systems 4, no. 1 (January 1, 2019). http://dx.doi.org/10.1093/integr/xyz001.

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Dissertations / Theses on the topic "Meromorphic correspondences"

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Mahadeo, Londhe Mayuresh. "On certain invariant measures for correspondences, their analysis, and an application to recurrence." Thesis, 2021. https://etd.iisc.ac.in/handle/2005/5522.

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The aim of this dissertation is to analyse a certain class of dynamically interesting mea- sures arising in holomorphic dynamics that goes beyond the classical framework of maps. We study measures associated with semigroups and, more generally, with meromorphic correspondences. The results presented herein are of two different flavours. The first type of results deal with potential-theoretic properties of the measures associated with certain polynomial semigroups, while the second type of results are about recurrence phenomena in the dynamics of meromorphic correspondences. The unifying features of these results are the use of the formalism of correspondences in their proofs, and the fact that the measures that we consider are measures that give the asymptotic distribution of the iterated inverse images of any generic point. The first class of results involve giving a description of a natural invariant measure associated with a finitely generated polynomial semigroup (which we shall call the Dinh–Sibony measure) in terms of potential theory. This requires the theory of logarithmic potentials in the presence of an external field, which we can describe explicitly given a choice of a set of generators. In particular, we generalize the classical result of Brolin to certain finitely generated polynomial semigroups. To do so, we establish the continuity of the logarithmic potential for the Dinh–Sibony measure, which might also be of independent interest. Thereafter, we use the F -functional of Mhaskar and Saff to discuss bounds on the capacity and diameter of the Julia sets of such semigroups. The second class of results involves meromorphic correspondences. These are, loosely speaking, multi-valued analogues of meromorphic maps. We prove an analogue of the Poincare recurrence theorem with respect to the measures alluded to above. Meromorphic correspondences present a significant measure-theoretic obstacle: the image of a Borel set under a meromorphic correspondence need not be Borel. We manage this issue using the Measurable Projection Theorem, which is an aspect of descriptive set theory. We also prove a result on the invariance properties of the supports of the measures mentioned, and, as a corollary, give a geometric description of the support of such a measure.
National Board for Higher Mathematics (Ref. No. 2/39(2)/2016/NBHM/R&D-II/11411)
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Books on the topic "Meromorphic correspondences"

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Milnor, John W. Dynamical systems (1984-2012). Edited by Bonifant Araceli 1963-. Providence, Rhode Island: American Mathematical Society, 2014.

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Book chapters on the topic "Meromorphic correspondences"

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Sabbah, Claude. "Good Meromorphic Connections (Analytic Theory) and the Riemann–Hilbert Correspondence." In Lecture Notes in Mathematics, 177–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31695-1_12.

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Sabbah, Claude. "The Riemann–Hilbert Correspondence for Good Meromorphic Connections (Case of a Smooth Divisor)." In Lecture Notes in Mathematics, 147–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31695-1_10.

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