Founder & Director
ASHAY DHARWADKER

H-501 PALAM VIHAR
DISTRICT GURGAON
HARYANA 1 2 2 0 1 7
INDIA

Phone: + 9971107640
ashay@dharwadker.org
http://www.dharwadker.org
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Aims  
  The Charter - Fundamental Research in Mathematics and its Applications.
Endowment  
  The Endowed Chair - Distinguished Professor of Mathematics and Natural Sciences.
Members  
 
  • Ashay Dharwadker - Institute of Mathematics, Gurgaon and Euroacademy, Tallinn. Mathematics and its applications, algebra, topology, graph theory, computer science and the foundations of physics.
  • John-Tagore Tevet - Structure Semiotics Research Group S.E.R.R., Euroacademy, Tallinn. Graph theory and its semiotic interpretations.
  • Jüri Martin - Member of the Estonian Academy of Sciences and Rector of Euroacademy, Tallinn. Ecology and environmental research using mathematical methods.
  • Robert Lee Muñoz - Gallery Muñoz, Oro Valley, Arizona. Geometry and its relationship with art and aesthetics.
  • Sanjay Dharwadker - Institute of Mathematics, Gurgaon. Mathematics and its applications, combinatorics and computer science.
  • Shariefuddin Pirzada - Department of Mathematics, University of Kashmir, Srinagar. Mathematics and its applications, combinatorics and graph theory.
  • Suryaprakash Rao - Institute of Mathematics, Gurgaon. Mathematics and its applications, combinatorics and graph theory.
  • Vinay Dharwadker - College of Letters and Science, University of Wisconsin, Madison. Physics, mathematics and semiotics.
  • Vladimir Khachatryan - Department of Physics and Astronomy, State University of New York, Stony Brook. Mathematics, physics and nuclear theory.
Publications  
 
Proceedings of the Institute of Mathematics  •  Amazon Books  •  2000 -    
 
Research  
  Ashay Dharwadker
  • A New Proof of the Four Colour Theorem - A new proof of the famous four color theorem using group theory and Steiner systems, 2000.
  • The Witt Design - The Steiner system S(5, 8, 24) explicitly computed, 2001. 
  • Riemann Surfaces - Geometrical models of Riemann surfaces, 2002.
  • Heptahedron and Roman Surface - Construction of the Roman surface from Hilbert's heptahedron, 2003.
  • Hamiltonian Circuit Algorithm - A new algorithm for finding Hamiltonian circuits with a constructive proof of Dirac's theorem and applications to finding Knight's Tours, 2004.
  • Common Systems of Coset Representatives - Proof of existence of a common system of representatives for the left and right cosets of a finite subgroup of a group, 2005.
  • The Vertex Cover Algorithm - A polynomial-time algorithm for finding minimal vertex covers in a graph, 2006.
  • The Independent Set Algorithm - A polynomial-time algorithm for finding maximal independent sets in a graph with new bounds on Ramsey numbers, 2006.
  • The Clique Algorithm - A polynomial-time algorithm for finding maximal cliques in a graph with new bounds on Ramsey numbers, 2006.
  • The Vertex Coloring Algorithm - A polynomial-time algorithm for coloring the vertices of a graph with a new constructive proof of Brooks' theorem, 2006.
  • Grand Unification of the Standard Model with Quantum Gravity - 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, 2008.
  • The Cosmological Constant - We 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, 2011.
Shariefuddin Pirzada and Ashay Dharwadker
  • Applications of Graph Theory - Graph theoretic proofs of the Cantor-Schröder-Bernstein theorem, Fermat's little theorem and the Nielson-Schreier theorem. Applications of graph theory to DNA sequencing, computer network security, scheduling and GSM mobile phone networks, 2007.
Ashay Dharwadker and John-Tagore Tevet
  • The Graph Isomorphism Algorithm - A polynomial-time algorithm for determining whether two graphs are isomorphic, showing that the Graph Isomorphism Problem is in P, 2009.
John-Tagore Tevet Vladimir Khachatryan Ashay Dharwadker and Vladimir Khachatryan
  • Higgs Boson Mass predicted by the Four Color Theorem - Based on the proof of the four color theorem and the grand unification of the standard model with quantum gravity, we show how to derive the values of the famous Cabibbo angle and CKM matrix, in excellent agreement with experimental observations. We make a precise prediction for the elusive Higgs boson mass MH0 = 125.992 ~ 126 GeV, as a direct consequence of our theory, 2009.
Ashay Dharwadker and Vinay Dharwadker
  • Space, Time and Matter - We show how the grand unified theory based on the proof of the four color theorem, can be obtained entirely in terms of the Poincaré group of isometries of space and time. Electric and gauge charges of all the particles of the standard model can now be interpreted as elements of the Poincaré group. We define the space and time chiralities of all spin 1/2 fermions in agreement with Dirac's relativistic wave equation. All the particles of the standard model now correspond to irreducible representations of the Poincaré group according to Wigner's classification. Finally, we construct the Steiner system of fermions and show how the Mathieu group acts as the group of symmetries of the fundamental building blocks of matter , 2010.
Seminars  
 
Celebrating 270 Years of Graph Theory, Tallinn, 2006
  • Graph Isomorphism is in P - A special S.E.R.R. seminar to announce that the famous Graph Isomorphism Problem is in P, organized by John-Tagore Tevet at Euroacademy in 2009.
Graph Isomorphism is in P, Gurgaon-Tallinn, 2009
Journal  
Baltic Horizons - No.14 (111) - Euroacademy issue in collaboration with the Institute of Mathematics, 2010.
Books  
  Ashay Dharwadker and Shariefuddin Pirzada
  • Graph Theory - Proc. Institute of Mathematics, Amazon Books, 2008. 
John-Tagore Tevet Jüri Martin and John-Tagore Tevet Jüri Martin
Lectures  
Today's Lecture at the Institute of Mathematics
Copyright © Institute of Mathematics 2000-