Institute of Space Sciences Cosmology and Zeta Functions: XXV years Trento-Barcelona colab*
Emilio Elizalde
Trento, June 2017 *To Sergio Zerbini, a wonderful physicist and a generous friend
Name or Title or Xtra Institute of Space Sciences
Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences
Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences
Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences MY FIRST TIME IN TRENTO Jacob Bekenstein: All black holes have a finite, non-zero entropy and temperature
Stephen Hawking: All Schwarzschild black holes of mass M emit electro- magnetic radiation like a black body with a temperature
Hawking's result improved and dramatically extended the conjecture and BH entropy formula by Jacob Bekenstein. It was a bombshell: How on Earth could a BH radiate ??? SW Hawking, Particle creation by black holes, Comm. Math. Phys. 43, 199 (1975); Black hole explosions? Nature 248, 30 (1974) JD Bekenstein, Black holes and entropy, Phys. Rev. D7, 2333 (1973) Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences Some scholars tried very hard to disprove his marvelous universal expression “I distinctly remember that year, 1975, attending as a graduate student my first international school at Schladming (Austria); after a wonderful trip by car, with a couple of colleagues from Barcelona, through the spectacular North-Italian lakes and the Brenner pass in the Alps. What a magnificent meeting was this!” Julian Schwinger lectured as the star there, but the excitement about Hawking's result kept growing every day during the sessions. No wonder that Hawking's article has got a record number of over 9,000 cits Participants in the Schladming school all worked with a preprint version of Hawking's paper E Elizalde, “On how the Cyberspace arose to fulfill theoretical physicists' needs and eventually changed the World”, in Cyberspace, Springer Verlag (2017) to appear; arXiv:1701.04765
Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences LAST MINUTE ADD 1: EMOOCs Conference 2017 FIFTH EUROPEAN MOOCS STAKEHOLDERS SUMMIT Digital Education: Out to the world and back to the campus http://emoocs.eu/ Massive Open Online Courses (MOOCs) have marked a milestone in the use of technology for education MOOCs are free courses However, if you want a certificate you must negotiate with the implicated Universities or Centers that extend them
Harvard Online Learning CaltechX Free online courses from Caltech Oxford University Online and distance courses online learning The Open University Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences LAST MINUTE ADD 2: IMU Newsletter, May 31, 2017 EDITORIAL: GRAID: A NEW IMU PROGRAM FOR GRADUATE ASSISTANTSHIPS IN DEVELOPING COUNTRIES Mathematicians from developing countries who chose to return to their home country after obtaining a promising Ph.D. degree at a high quality research institution, used to find that it was virtually impossible to keep up with their field - their isolation from new directions, the lack of libraries, the high cost of travel to conferences or possible collaborators … Internet and its embrace by researchers have changed all that … … findings online, before they are published, to share with the whole research community In short, it is now possible for cohorts of graduate students in developing countries to reach mathematical levels achieved only rarely outside major research centers This has potentially far-reaching consequences: as shown at the MENAO symposium: http://www.mathunion.org/cdc/menao/ Opportunity recognized by several organizations, which have responded with initiatives that make graduate studies and research possible for talented students in many parts of the world Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences ON OUR COLLABORATION OF XXV YEARS
Started in 1992, “go betweens” Andrei Bytsenko and Sergei Odintsov Later, Klaus Kirsten Our works are pioneering and have got international recognition in some domains of fundamental physics, cosmology and mathematical physics top international level One fundamental achievement concerns the development and uses in Physics of the Zeta Function Regularization procedure Other key achievements have to do with modified gravity theories, in particular f(R) models and variations of them (GB, torsion, etc.)
Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue, E Elizalde, L Vanzo, S Zerbini
Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem, G Cognola, E Elizalde, S Nojiri, SD Odintsov, S Zerbini
Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences SOME SEMINAL BOOKS & PAPERS E . Elizalde, S.D. Odintsov, A. Romeo, A.A. Bytsenko and S.Zerbini, Zeta regularization techniques with Applications (World Sci., Singapore, 1994). ISBN 9810214413. - Cit 860 G Cognola, E Elizalde, S Nojiri, SD Odintsov, S Zerbini, Dark energy in modified Gauss- Bonnet gravity: Late-time acceleration and the hierarchy problem, Phys Rev D73, 084007 (2006) - Cit 402 G Cognola, E Elizalde, S Nojiri, SD Odintsov, L Sebastiani, S Zerbini, Class of viable modified f (R) gravities describing inflation and the onset of accelerated expansion, Phys Rev D77, 046009 (2008) - Cit 389 G Cognola, E Elizalde, S Nojiri, SD Odintsov, S Zerbini, One-loop f (R) gravity in de Sitter universe, J Cosmol Astrop Phys 2005, 010 (2005) - Cit 311 G Cognola, E Elizalde, S Nojiri, SD Odintsov, S Zerbini, String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy, Phys Rev D75, 086002 (2007) - Cit 147 E Elizalde, L Vanzo, S Zerbini, Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue, Commun Math Phys 194, 613-630 (1998) - Cit 125
Name or Title or Xtra EE, Sergio Zerbini’s Fest Institute of Space Sciences
Sergio, ti auguro una vita lunga e felice in seguito, con Lucia, e Livio, e Giulia, e …
Name or Title or Xtra EE, Sergio Zerbini’s Fest