p Adic String Amplitudes and Local Zeta Functions (Wilson Zúniga)

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p-Adic String Amplitudes and Local Zeta Functions

Plática dada por Wilson Zúñiga (Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, CINVESTAV) en el evento Algebraic Geometry in Mexico 2017 el sábado 2 de diciembre del 2017 en Puerto Escondido, Oaxaca, México

Abstract:
In this talk we will discuss the connections between p-adic string amplitudes and local zeta functions (also called Igusa´s local zeta functions). In [1], we established that p-adic Koba-Nielsen string amplitudes are essentially finite sums of Igusa´s local zeta functions, by using this fact, we showed that these amplitudes are convergent integrals admitting meromorphic continuations as rational functions. Some physicists have conjectured that in the limit p ! 1 the p-adic string amplitudes approximate the classical strings. In the ´90s, Denef and Loeser established that the limit p !1 of Igusa´s local zeta functions give rise to new objects, that they called topological zeta functions. By using Denef-Loeser´s theory of topological zeta functions, we show that limit p !1 of the tree-level p-adic open strings amplitudes give rise to a new amplitudes, which we have called topological open string amplitudes, see [2]. In [2], we showed that the Feynman amplitudes of the effective Lagrangian of the p-adic strings are precisely the topological open string amplitudes.

The talk is based in a joint work with Miriam Bocardo, Hugo García Compeán.

References
[1] Bocardo-Gaspar, Miriam, García-Compeán, H., W. A. Zúñiga-Galindo, Reg-ularization of p-adic String Amplitudes, and Multivariate Local Zeta Functions, arXiv:1611.03807 (2017).

[2] Bocardo-Gaspar, Miriam, García-Compeán, H., W. A. Zúñiga-Galindo, On p-adic string amplitudes in the limit p approaches to one. Preprint 2017.

Video de la plática
https://youtu.be/0SWKTIrJxE8

Foto de miniatura del video
https://photos.app.goo.gl/gHpex99rWaPFzwoL2

Wilson Zúñiga en:

El Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, CINVESTAV
http://www.math.cinvestav.mx/zuniga

Mathematics Genealogy Project
https://www.genealogy.math.ndsu.nodak.edu/id.php?id=53666

arXiv
https://arxiv.org/find/math/1/au:+Zuniga_Galindo_W/0/1/0/all/0/1

ResearchGate
https://www.researchgate.net/profile/W_Zuniga-Galindo2

Google Scholar
https://scholar.google.es/citations?user=RGxxO5wAAAAJ&hl=es

Youtube
https://www.youtube.com/playlist?list=PLrg-5oUhFeiqHkHumPN4Uu-4lH0CWrYR0

Otras pláticas del evento Algebraic Geometry in Mexico 2017
https://www.youtube.com/playlist?list=PLrg-5oUhFeirKNj3qs2gQlk7nms2Kx0b7

Otras pláticas del evento Algebraic Geometry in Mexico 2016
https://www.youtube.com/playlist?list=PLrg-5oUhFeioieJgNVvON2WGwIh07bh8M