

Institute of Mathematics 


Founder & Director 

Aims 

The Charter  Fundamental Research in Mathematics and its Applications.

Endowment 

The Endowed Chair  Ashay Dharwadker is the Distinguished Professor of Mathematics and Natural Sciences with $1,000,000 placed in an endowment that provides the annual funds in perpetuity.

Endowment Lecture at the Institute of Mathematics


Members 

Ashay
Dharwadker  Founder & Director, Institute of Mathematics, Gurgaon. Mathematics and its
applications, algebra, combinatorics, topology, graph theory, algorithms, computer science and the foundations of physics.

JohnTagore Tevet
 Structure Semiotics Research Group S.E.R.R., Euroacademy, Tallinn.
Graph theory and its applications.

Jonathan D.H. Smith
 Department of Mathematics, Iowa State University , Ames.
Algebra, representation theory, combinatorics and topology.

Jüri
Martin  Member of the Estonian Academy of Sciences and Rector of Euroacademy,
Tallinn. Graph theory and its applications.

Robert
Lee Muñoz  Gallery Muñoz, Oro Valley, Arizona. Mathematics
and its applications. Geometry and the visual arts.

Shariefuddin
Pirzada  Department of Mathematics, University of Kashmir, Srinagar.
Mathematics and its applications, combinatorics and graph theory.

Vinay
Dharwadker  College of Letters and Science, University
of Wisconsin, Madison. Mathematics and its applications, particle physics and cosmology.

Vladimir
Khachatryan  Department of Physics and Astronomy, State University
of New York, Stony Brook. Mathematics and its applications, particle physics and cosmology.

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 polynomialtime algorithm for finding minimal
vertex covers in a graph, 2006.

The
Independent Set Algorithm  A polynomialtime algorithm for finding
maximal independent sets in a graph with new bounds on Ramsey numbers,
2006.

The Clique
Algorithm  A polynomialtime algorithm for finding maximal cliques
in a graph with new bounds on Ramsey numbers, 2006.

The
Vertex Coloring Algorithm  A polynomialtime 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
sevenyear 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.
Ashay Dharwadker and JohnTagore Tevet

The
Graph Isomorphism Algorithm  A polynomialtime algorithm for determining
whether two graphs are isomorphic, showing that the Graph Isomorphism Problem
is in
P, 2009.
Ashay Dharwadker and Jonathan D.H. Smith
Ashay Dharwadker and Robert Lee Muñoz
Ashay Dharwadker and Shariefuddin Pirzada

Applications
of Graph Theory  Graph theoretic proofs of the CantorSchröderBernstein
theorem, Fermat's little theorem and the NielsonSchreier theorem. Applications
of graph theory to DNA sequencing, computer network security, scheduling
and GSM mobile phone networks, 2007.
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.
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 M_{H}^{0} = 125.992 ~ 126 GeV, as a direct consequence of our theory, 2009.

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 JohnTagore
Tevet at Euroacademy in 2009.

Graph Isomorphism is in P, GurgaonTallinn,
2009


Journal 
Baltic Horizons  No.14 (111), 2010  Special issue dedicated to Fundamental Research in Mathematics and Applications of Graph Theory by Euroacademy in collaboration with the Institute of Mathematics, Gurgaon.
Editorial Board: Jüri Martin (Chief Editor), Peeter Karing, JohnTagore Tevet, Aune Altmets (Assistant Editor)
Guest Editors: Ashay Dharwadker (Institute of Mathematics, Gurgaon), Vinay Dharwadker (University of WisconsinMadison)

Books 
Graph Theory
Ashay Dharwadker and Shariefuddin Pirzada
This text offers the most comprehensive and uptodate presentation available on the fundamental topics in graph theory. It develops a thorough understanding of the structure of graphs, the techniques used to analyze problems in graph theory and the uses of graph theoretical algorithms in mathematics, engineering and computer science. The climax of the book is a new proof of the famous four colour theorem.

Orient Longman and Universities Press of India, Amazon Books, 2008


Lectures 
Today's
Lecture at the Institute of Mathematics 

Copyright © Institute of Mathematics 2000 
