Institut des Hautes Etudes Scientifiques
Le Bois-Marie, 35 route de Chartres
91440 Bures-sur-Yvette
France
CFM
email: bhattacharya@ihes.fr
gourabmath@gmail.com
gourabb@ihes.fr
phone: (+33) 1 60 92 66 27
office: 0S6 (26627)
I do not consider Mathematics only as a formal language, but a way of thinking, a narrative to some abstract objects that require a certain generalised but simple explanation, that can unify a vast amount of informations in a single statement, it is similar to something like, "Be Wise Generalise", I forgot who first said the quote, but whoever that person might be, it actually describes and explains Mathematics and its nature, however, a certain level of consistency and rigour is necessary for the development of Mathematical thinking, but rigour has its limitations, it may not be absolute, it is the end product, for me, Mathematics is a part of life, like breathing. At this point of time, I am working in several topics related to the celebrated Homological Mirror Symmetry of Maxim Kontsevitch, some are directly related, some are not, also the theory of the Gravitation and corresponding Gravitational Waves attract me much due to its deeply hidden Geometric structures that need to be discovered. The Thermodynamic objects in a Strong Gravitational Field attracts my attention a lot, I have lots of unanswered questions in this field of study, hopefully one day I will get my answers to all my questions.
My main interest and the object of study now is to understand the noncommutative instantons from the noncommutative Hermitian Yang-Mills equation or the infinite dimensional Nekrasov equation, actually one can show (we showed in our work with Kontsevich) that, it is a consequence of certain M-Theory (M = Matrix ) compactification of higher dimensions on noncommutative tori (Physicists call it the IKKT and the BFSS models) of the Connes-Douglas-Schwarz type (more Mathematically), also I am interested in Fukaya Category via the Kontsevich-Soibelman Wall-Crossing structures, specifically those wall-crosiing structures coming from the Blackhole attractors in the Superstrings and Supergravity theories.
Besides that, we are hoping our future paper on the infinite diemensional King's equation will shed considerable amout of light on the q-Difference equations and the Discrete Integrable Systems coming from Geometry, Physics and, Arithmetic. I am also interested in the theories of Gravitation of various kinds (not necessarily of Einsteinian one's) , Quantum Field Theories, Conformal Field Theories, the Foundational problems in Quantum Mechanics, and, different Noncommutative Geometries.
I consider myself mainly as a "Physical Geometer". It is hard to define what a Geometry is, and, it is more difficult to define what a Physical Geometer might mean, however, I love Physics, and I extract various Geometries from Physics. What I sense and realise that our understanding of Science is very limited, for say, it is hard to say what is the general definition of Mass of an object in Classical Gravitational Theories. No one knows in what context one can understand the principle of conservation of the Mass or the Energy separately, together they form an Energy-Momentum Tensor but individually they constitute what is called a pseudo-tensor, so the energy or the mass becomes background dependent. The case for the Angular-Momentum becomes more complicated, and it is impossibly hard to have a general definition. It seems all these concepts to have any meaning in the presence of Gravity, requires a new Breakthrough.