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An overview of the mathematics of Loop Quantum Gravity

Área: Física-matemática

Thursday, September 7th, 2017

Alejandro Corichi

Centro de Ciencias Matemáticas, UNAM, Morelia, Michoacán, México.

Abstract: In this talk we shall provide an overview of the main ideas and the mathematics involved the construction of Loop Quantum Gravity, one of the paths in the quest trying to reconcile the Quantum Theory (that describes very accurately the world at small scales) with General Relativity (that so far it has been proved itself a good description for the large scales). In this approach, we don't assume more than 4 dimensions (the ones we are used to), and the core principles of General Relativity and Quantum Theory. With these ingredients, in the last 30 years we have been able, as a community, to produced a robust candidate for a Quantum Theory of Gravity: Loop Quantum Gravity. This task involves quite some mathematics, to define the Hilbert space, the algebra of the operators among other particularities in a consistent and systematic way since so far we do not have guidance from the experiment.

Alejandro Corichi obtained his bachelor’s degree at the Faculty of Science in UNAM. He pursued graduate studies at the Physics Department of the University of Syracuse (master’s) and at the Physics Department of Penn State University (PhD), under the supervision of Professor Abhay Ashtekar. He has been researcher at ICN, UNAM, the Department of Physics and Astronomy at the University of Mississippi, at the Institute of Mathematics of UNAM, at the institute of Cosmos and Gravitation at Penn State University, and currently at the Center of Mathematical Sciences of UNAM in Morelia. He has published 78 papers in peer-reviewed journals, and has supervised 6 PhD theses. He has taken part in several outreach activities. For instance, he was script co-writer and scientific co-advisor on the TV shows: 'El Nuevo Universo: Cómo la Física cambió al mundo' (TV-UNAM),  'Los 5 secretos del Oficinista' (Canal 22). He has been member of the editorial board of the journals Classical and Quantum Gravity and International Journal of Mathematical Sciences. He has been referee for Physical Review Letters, Classical and Quantum Gravity, International Journal of Modern Physics D, Physical Review D and A, General Relativity and Gravitation, Modern Physics Letters A, and Revista Mexicana de Física. He has received the following awards: Medalla Gabino Barreda (UNAM), Collegiate Scholastic All American (United States Achievement Academy), Who's who in Science and Enginering 2001, Who's Who in the World 2003, Gran Premio Bachiller Alvaro Galvez y Fuentes (muestra Iberoamericana 2007 de Televisión y video educativo), Premio Prisma de Bronce a la Divulgación (Coruña, España), Selección Oficial of the science category at the XXV Certamen Unicaja de Cine científico (Ronda, España), Mentes Quo+Discovery Channel 2010, first place in the science category at the XXVI Certamen Bienal Unicaja  de Cine Científico (Ronda, España) 2010, Mejor Documental Mexicano para Televisión (Festival de cine documental de la Ciudad de México 2010), Mejor Divulgación Científica y Tecnológica and Mejor Animación at Festival de Cristal 2010 of Cineteca Nacional.