Ashay DharwadkerInstitute of Mathematics
http://www.dharwadker.org/
Four Colour TheoremA new proof of the four color theorem by Ashay Dharwadker that uses group theory and Steiner systems, 2000
http://www.dharwadker.org/
The Witt DesignThe Steiner system S(5,8,24) explicitly computed by Ashay Dharwadker, 2001
http://www.dharwadker.org/witt.html
Riemann SurfacesGeometrical models of Riemann surfaces by Ashay Dharwadker, 2002
http://www.dharwadker.org/riemann/
Heptahedron and Roman SurfaceConstruction of the Roman surface from a heptahedron by Ashay Dharwadker, 2003
http://www.dharwadker.org/hilbert/
Hamiltonian Circuit AlgorithmA 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/
Common Systems of Coset RepresentativesProof 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
The Vertex Cover AlgorithmA polynomial-time algorithm for finding minimal vertex covers in a graph by Ashay Dharwadker, 2006
http://www.dharwadker.org/vertex_cover/
The Independent Set AlgorithmA 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/
The Clique AlgorithmA 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/
The Vertex Coloring AlgorithmA 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/
Applications of Graph TheoryJournal of the Korean Society for Industrial and Applied Mathematics, Vol. 11, No. 4, 2007
http://www.dharwadker.org/pirzada/applications/
Grand Unification of the Standard Model with Quantum GravityWe 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/
The Graph Isomorphism AlgorithmA 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/
Higgs Boson Mass predicted by the Four Color TheoremUsing 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/
Space, Time and MatterWe 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/
The Cosmological ConstantWe show how to calculate Einstein's cosmological constant using the Grand Unified Theory. Using the topological properties of the gauge, we calculate the exact percentages of ordinary baryonic matter, dark matter and dark energy in the universe. These values are in perfect agreement with the seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations. Thus dark matter, dark energy and the cosmological constant are intrinsic properties of the gauge in the Grand Unified Theory. Ashay Dharwadker, 2011.
http://www.dharwadker.org/cosmology/
Ashay Dharwadker's ProfileLatest research in algebra, topology, graph theory and theoretical computer science
http://www.dharwadker.org/profile.html
Today's Lecture by Ashay DharwadkerDaily lectures in mathematics and computer science
http://www.dharwadker.org/lecture.html
My Students DatabaseProf. Ashay Dharwadker's students database
http://dharwadker.freehostia.com/
Calculus 1.0Software for Windows
http://www.dharwadker.org/calculus.html
Statistics 1.0Software for Windows
http://www.dharwadker.org/statistics.html
Contact Ashay DharwadkerGet in touch...
http://www.dharwadker.org/contact.html
Institute of MathematicsAims, Members, Research, Seminars, Books and Lectures
http://www.dharwadker.org/iom/