Ramanujan's notebooks contain the equation 1+2+3....= - 1/12. While this seems to go against common sense, there is deep mathematics behind this assertion. I will try to explain in what sense this must be understood. Such mathematical interpretations of divergent series have had an impact in physics, leading for example to a quantitative understanding of the Casimir effect, which has been measured in the laboratory. I will try to bring out how higher mathematics meets physics.
About the Speaker: -
Joseph Samuel is at ICTS as Simons Visiting Professor. His interests include general relativity, quantum theory, optics, the geometric phase and the geometry of soft matter. He is also interested in disseminating the excitement of science and gives talks in schools, colleges and to general audiences. A unifying theme in his work is the use of differential geometry and topology in physics. He likes to be in touch with mathematics as well as experiments. He is interested in seeing analogies between different areas of physics. One example of this is exploring the relation between surface tension and the cosmological constant.