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A century ago, Srinivasa Ramanujan -- the great self-taught Indian genius of mathematics -- died, shortly after returning from Cambridge, UK, where he had collaborated with Godfrey Hardy. Ramanujan contributed numerous outstanding results to different branches of mathematics, like analysis and number theory, with a focus on special functions and series. Here we refer to apparently weird values which he assigned to two simple divergent series, $sum_{n geq 1} n$ and $sum_{n geq 1} n^{3}$. These values are sensible, however, as analytic continuations, which correspond to Riemanns $zeta$-function. Moreover, they have applications in physics: we discuss the vacuum energy of the photon field, from which one can derive the Casimir force, which has been experimentally measured. We further discuss its interpretation, which remains controversial. This is a simple way to illustrate the concept of renormalization, which is vital in quantum field theory.
Dedicated to the centenary of the Ioffe Institute, the article contains the shortest review of scientific achievements of the theorists of the institute during this time. We concentrate mainly on research in the field of elementary particle physics,
We survey early Indian ideas on the speed of light and the size of the universe. A context is provided for Sayanas statement (14th century)that the speed is 2,202 yojanas per half nimesha (186,000 miles per second!). It is shown how this statement ma
Indigenous peoples across the world observe the motions and positions of stars to develop seasonal calendars. Additionally, changing properties of stars, such as their brightness and colour, are also used for predicting weather. Combining archival st
Twisted, or vortex, particles refer to freely propagating non-plane-wave states with helicoidal wave fronts. In this state, the particle possesses a non-zero orbital angular momentum with respect to its average propagation direction. Twisted photons
Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high dimensional theory has emerged. In this paper these developments are surveyed