Institute of Mathematics http://www.dharwadker.org/ A new proof of the four color theorem by Ashay Dharwadker that uses group theory and Steiner systems, 2000 http://www.dharwadker.org/ The Steiner system S(5,8,24) explicitly computed by Ashay Dharwadker, 2001 http://www.dharwadker.org/witt.html Geometrical models of Riemann surfaces by Ashay Dharwadker, 2002 http://www.eg-models.de/models/Surfaces/Riemann_Surfaces/2002.05.001/_preview.html Construction of the Roman surface from a heptahedron by Ashay Dharwadker, 2003 http://www.eg-models.de/models/Surfaces/Algebraic_Surfaces/2003.05.001/_preview.html A new algorithm for finding Hamiltonian circuits with a constructive proof of Dirac's theorem and applications to finding Knight's Tours by Ashay Dharwadker, 2004 http://www.dharwadker.org/hamilton/ Proof of existence of a common system of representatives for the left and right cosets of a finite subgroup of a group by Ashay Dharwadker, 2005 http://www.dharwadker.org/coset.html A polynomial-time algorithm for finding minimal vertex covers in a graph by Ashay Dharwadker, 2006 http://www.dharwadker.org/vertex_cover/ A polynomial-time algorithm for finding maximal independent sets in a graph with new bounds on Ramsey numbers by Ashay Dharwadker, 2006 http://www.dharwadker.org/independent_set/ A polynomial-time algorithm for finding maximal cliques in a graph with new bounds on Ramsey numbers by Ashay Dharwadker, 2006 http://www.dharwadker.org/clique/ A polynomial-time algorithm for coloring the vertices of a graph with a new constructive proof of Brooks' theorem by Ashay Dharwadker, 2006 http://www.dharwadker.org/vertex_coloring/ Journal of the Korean Society for Industrial and Applied Mathematics, Vol. 11, No. 4, 2007 http://www.dharwadker.org/pirzada/applications/ We show that the mathematical proof of the four colour theorem directly implies the existence of the standard model, together with quantum gravity, in its physical interpretation. Conversely, the experimentally observable standard model and quantum gravity show that nature applies the mathematical proof of the four colour theorem, at the most fundamental level. Ashay Dharwadker 2008 http://www.dharwadker.org/standard_model/ A polynomial-time algorithm for determining whether two graphs are isomorphic, showing that the Graph Isomorphism Problem is in P. Ashay Dharwadker and John-Tagore Tevet, S.E.R.R. Tallin 2009. http://www.dharwadker.org/tevet/isomorphism/ Using the proof of the four color theorem and the grand unified theory, we show how to calculate the Cabibbo angle, CKM matrix and present a precise prediction for the Higgs boson mass. Ashay Dharwadker and Vladimir Khachatryan, Proceedings of the IoM, 2009. http://www.dharwadker.org/khachatryan/higgs/ We show how the grand unified theory based on the proof of the four color theorem, can be obtained entirely in terms of the Poincare group of isometries of space and time. Ashay Dharwadker and Vinay Dharwadker, Baltic Horizons, 2010. http://www.dharwadker.org/space_time/ Latest research in algebra, topology, graph theory and theoretical computer science http://www.dharwadker.org/profile.html Daily lectures in mathematics and computer science http://www.dharwadker.org/lecture.html Prof. Ashay Dharwadker's students database http://dharwadker.freehostia.com/ Software for Windows http://www.dharwadker.org/calculus.html Software for Windows http://www.dharwadker.org/statistics.html Get in touch... http://www.dharwadker.org/contact.html Aims, Members, Research, Seminars, Books and Lectures http://www.dharwadker.org/iom/