However, our planet has been devastated in the past by antimatter asteroids, as it is the case of the celebrated 1908 Tunguska explosion in Siberia that was the equivalent of one thousand Hiroshima atomic bombs, yet no solid or liquid residue was ever located in the ground [7]. The antimatter origin of the episode is established by the fact that the entire Earth atmosphere remained excited for days to such an extent that people could read the newspaper at midnight in Sydney, Australia, without the need for any additional light. Such a large scale excitation of all molecules and atoms of our atmosphere can only be explained via a very large radiation source that, in turn, can only originate from matter-antimatter annihilation (Figure 1). Additional evidence on the existence of antimatter in the large scale structure ofthe universe is given by indications antimatter cosmic rays [8] and large explosions detected in our upper atmosphere that cannot be caused by matter asteroids (see the websites of NASA, FERMILAB and other laboratories).

Figure 1. A view of the devastation caused by the 1908 Tunguska explosion in Siberia. The flattened trees can be xplained via an ice comet exploding in our atmosphere. However, this interpretation is excluded by the fact that the entire Earth atmosphere remained illuminated at night for days, which excitation can only beexplained by matter-antimatter annihilation.

The Italian-American physicist Ruggero Maria Santilli initiated his studies on antimatter since his graduate school at the university of Torino, Italy, in the mid 1960s with the specific intent of ascertaining, in due time, whether a far away galaxy is made up of matter or of antimatter, He soon discovered that 20th century knowledge was inapplicable for such a problem since the sole available conjugation from matter to antimatter was that of a charge on Hilbert space over a numeric field,while the study of possible antimatter galaxies must be done at the classical level and antimatter galaxies must be assumed to be neutral. In this way, Santilli confirmed the teaching of scientific history according to which the protracted lack of solution of basic physical problems is generally due to use of insufficient or inadequate mathematics. Therefore, Santilli initiated his search for a new mathematics specifically built for the classical characterization of neutral or charge antimatter bodies.

ISODUAL MATHEMATICS
In this way, Santilli initiated a fifty years old scientific journey which is hereinoutlined. Since charge conjugation on a Hilbert space over the field of complex numbers

Cψ(r) = - ψ⁺(r)

is anti-Hermitean, Santilli searched for years to locate a mathematics which is an anti-Hermitean (or, more generally, anti-isomorphic) image of 20th century mathematics, none was found, thus mandating the construction of the needed new mathematics as a condition to conduct serious research in the classical representation of antimatter.

Santilli was soon faced with huge technical difficulties in the construction of the needed new mathematics. Being a physicist, he knew that, to have physical value, a theory has to be formulated over a numeric field as an evident condition to conduct consistent experimental measurements. The only known fields of the time were the real, complex and quaternionic fields. Therefore, any theory formulated on them could not possibly be anti-Hermitean or anti-isomorphic to 20th century mathematics, and the impasse was total.

Finally, when at the Department of Mathematics of Harvard University in the early 1980s under DOE support, Santilli decided to build the needed new mathematics by embedding the anti-isomorphic character in the most fundamental mathematical notion, the multiplicative unit, and assumed the following negative-definite unit he called isodual unit denoted with the superscript "d"

1^d = - 1,

and then build the entire needed mathematics via a step-by-step image of 20th century mathematics in such a way to admit -1, rather than +1, as the correct left and right unit at all levels. This led to decades of research for the construction of isodual numbers, isodual functions, isodual differential calculus, isodual metric spaces, isodual Lie theory, isodual Euclidean, Minkowskian and Riemannian geometries, etc. and other isodualities (see monograph [9] for a general presentation up to 2006 and vast prior literature quoted therein, and Refs. [11-21] for subsequent studies).

An important aim of this workshop is to further develop the ensuing isodual mathematics as well as the broader isodual isomathematics and isodual hypermathematics via the isodualities of the mathematics studied in the preceding Fifth International Workshop on Iso-, Geno-, and Hyper-Mathematics
http://www.santilli-foundation.org/Iso-Geno-Hyper-Math-2014.php

All the mathematics can be constructed via Santilli's isodual map

Q(t, r, p, ψ, ...) → Q^d(t^d, r^d, p^d, ψ^d) = -Q⁺(-t⁺, -r⁺, -p⁺, - ψ^d+, ...),

applied to the totalities of quantities Q and the totality of operations of the selected original mathematics used for matter. In the event only one quantity or operation is not mapped under isoduality, there are insidious inconsistencies that generally remain undetected by non-experts in the field.

ISODUAL THEORY OF ANTIMATTER
Thanks, and only thanks to his isodual mathematics, Santilli was able to construct the isodual theory of antimatter which characterizes antimatter at all possible levels, from Newtonian mechanics to second quantization (see also the 2006 monograph [9] and the important recent memoir [10] and independent contributions [12-19]).

In particular, isodual mathematics permitted the first known geometrically consistent representation of the gravitational field of a neutral antimatter body via the Riemann-Santilli isodual geometry defined over isodual fields (see monograph [9] and memoir [19]).

It should be stressed that the isodual theory of antimatter requires, for consistency requirement, the conjugation of all physical quantities of matter as well as, most importantly, all their units of measurements. Consequently, antimatter evolves along a time moving backward, the t^d = - t, and has negative-definite energy E^d = - E along Dirac's original conception [6]. The historical inconsistencies are resolved via the joint conjunction of the related units, in fact, negative time and negative energy referred to negative units of time and energy are as causal as our positive time and energies referred to positive units of time and energy.

Figure 2. An important prediction of Santilli's isodual theory of antimatter is that antimatter light experiences a repulsion (called isodual bending) when in a matter gravitational field. Astrophysical research on this prediction are strongly recommended.

To the best of our knowledge, the isodual theory of antimatter verifies all available experimental data on antimatter at the classical and particle levels. In classical mechanics, all data are verified via the interplay of Newton's and the Newton-Santilli isodual equations. Experimental data on antimatter at the particle level are verified due to the equivalence of isoduality and charge conjugation.

An important function of this workshop is to verify that indeed the isodual theory of antimatter is compatible with all available experimental data.

NOVEL PREDICTIONS
Another important function of the workshop is to appraise the consistency and feasibility of the various novel predictions of the isodual theory of antimatter, among which we quote:

1. Light emitted by antimatter stars, called antimatter light for large wavelengths and isodual photons for short wavelengths, is physically different than light emitted by matter stars, or matter light according to experimentally measurable ways [20].

Figure 3. Another inevitable prediction of the isodual theory of antimatter is that antimatter light propagating in a matter medium exhibits a negative-definite isodual index of refraction. This prediction stems from any consistent conjugation matter to antimatter in the absence of a charge. It should be noted that this prediction implies that antimatter light travels at superluminal speeds when seen from our world.

2. Antimatter light experiences gravitational repulsion when passing near a matter gravitational field (Figure 2), which is a necessary consequence of the negative energy of antimatter light when in a gravitational field with positive curvature tensor [19](Figure 2);

3. Matter and antimatter bodies experience gravitational repulsion (antigravity). This prediction exists at all levels of studies, from Newtonian to Riemannian profiles. In particular, Santilli proposed in 1994 the measurement of the gravity of positrons in horizontal flight in a supervacuum and supercooled tube (see the review in Ref. [20] and independent experimental studies [13-14]).

4. Antimatter light propagating within a matter medium experiences a negative index of refraction. This is an additional necessary consequence of the fact that, in the absence of a charge, the conjugation from matter to antimatter requires the conjugation of all possible quantities, thus including the conventional index of refraction n which is mapped into the for n^d = - n (figure 3) [21];

Figure 4. Yet another important prediction of the isodual theory of antimatter is the inapplicability of Feynman's diagrams for particle-antiparticle interactions since annihilation initiates at the first contact of the wavepackets without any possibility of admitting interactions mediated by particles or antiparticles. In any case, the latter mediations violate isoselfduality [21]..

5. In particle-antiparticle annihilations, there is the production of matter and antimatter lights, or photons and isodual photons, in equal amounts [21]. This is a necessary consequence of the isoselfduality, namely, the invariance under isoselfduality, which is verified by a particle-antiparticle system such as electron-positron and, therefore, it is predicted to be equally verified by the produced photons, resulting in the predicted reaction

e^+- → γ + γ^d

which is expected to be experimentally verifiable with high sensitivity neutron interferometric easurements.

Another important function of the workshop is to further develop the isodual theory of antimatter with new basic advances, such as:

I. Trajectory of antimatter asteroids colliding with Earth.
This is a very interesting project with particular relevance for our safety that has never been studied to date, to the best of our knowledge. Its main novelty is based on the fact that antimatter asteroids are predicted to be repelled by Earth, thus requiring a particular speed and trajectory to actually have a collision,

II. Isodual scattering theory and the particle-antiparticle scattering problem.
This is also a very interesting problem of main relevance for all quantitative studies of antimatter. The problem has been created by the expected lack of applicability of Feynman's diagrams that, while being so effective for electron scattering on matter, violate the isoselfduality symmetry when applied to particle-antiparticle scattering. It should be noted that in the latter case there the inapplicability of the very Feynman;s conception of interaction mediated by a "particle" exchange, since annihilation initiate at the very first contact of wavepackets, thus allowing no time for particles or antiparticles exchanges..

III. Isodual optics and its relationship with optics.
As it is well known, our current knowledge on the matter component of the universe is a result of systematic studies of matter light covered by the discipline known as optics. There is no doubt that similar advances on antimatter will not be possible until the corresponding optics for antimatter light, isodual optics, is sufficiently developed.

Figure 5. As indicated in Ref. [10], the biggest threat facing our planet these days is a possible collision with an antimatter asteroid due to our basic lack of knowledge on whether Sunlight is refracted on its surface or absorbed. It should be indicated that, ad established by the Tunguska explosion (Figure 1), the annihilation of an antimatter asteroids in our atmosphere will paralyze all civilian,industrial and military communications for days due to the excitation of atmospheric atoms and molecules caused by large electromagnetic radiations.

Addition darted March 3, 2014

APPARENT DETECTION OF ANTIMATTER-GALAXIES,
ANTIMATTER-ASTEROIDS, AND ANTIMATTER-COSMIC RAYS VIA
SANTILLI TELESCOPE WITH CONCAVE LENSES

We are pleased to announce the apparent first detection by R. M. santilli [23] of antimatter-galaxies, antimatter-asteroids and antimatter0-cosmic rays via a refractive telescope with concave lenses and its experimental confirmation by independent scientists [24] as illustrated in the pictures below for analysis and discussions at the workshop.

The announcement has been jointly made with the PRWeb Release
http://www.prweb.com/releases/2014/02/prweb11589410.htm

FINANCIAL SUPPORT FOR PARTICIPATION

Scientist interested in participating are suggested to apply for financial support by sending via email a one page motivation and the DSV to
The R. M. Santilli Foundation
http://www.santilli-foundation.org/
http://www.world-lecture-series.org/
Email: board(at)santilli-foundation(dot)org

Deadline for applications: August 15, 2014

REFERENCES
[1] Newton, I., Philosophia Naturalis Principia Mathematica (1687), translated by Cambridge University Press 91934).

[2] Galileo, G., Dialogus de Systemate Mundi, 1638, Reprinted by MacMillan, New York,1917.

[3] Einstein, A., Ann. Phys. (Leipzig) 1905, 17, 891.

[4] Einstein, A., Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin 1915, 844847.

[5] Dirac, P. A. M., Proceedings of the Royal Society 1928,,117, 610624.

[6] Anderson, C. D., Phys.Rev. 1933, 43, 491.

[7] Dermer ,C. D., "Gamma-Ray Bursts from Comet-Antimatter Comet Collisions in the Oort Cloud. In C. Kouveliotou, M. S. Briggs, and G. J. Fishman. 384. The Third Huntsville Symposium on Gamma-Ray Bursts, Huntsville AL, USA, October 1995, 2527, Woodbury: American Institute of Physics. pp. 744748.

[8] Rojansky, V., Cosmic Rays and Comets, Phys. Rev. 58, 1010 - 1010 (1940).

[9] Santilli, R. M., Isodual Theory of Antimatter with Applications to Antigravity, Grand Unification and Cosmology, Springer (2006).

[10] Anderson, R., Bhalekar, A. A., Davvaz, B., Muktibodh, P., Tangde, V. M., Muktibodh. A., and Vougiouklis, T. "An introduction to Santilli isodual theory of antimatter and the ensuing problem of detecting antimatter asteroids," Numta Bulletin 2012-2013, 6, 1-33
http://www.santilli-foundation.org/docs/Antimatter-2013.pdf

[11] Dunning-Davies, J., "Thermodynamics of antimatter via Santillis isodualities." Found. Phys. 1999,Vol. 12, page 593 (1999
http://www.santilli-foundation.org/docs/Isodual-therm.pdf

[12] Corda, C., Introduction to Santillis IsoNumbers, AIP Conf. Proceed. 2012, 1479, 1013
http://www.santilli-foundation.org/docs/Corda-2012.pdf

[13] Mills, A. P., Possibilities of measuring the gravitational mass of electrons and positrons in free horizontal flight, contributed paper for the Proceedings of the International Conference on Antimatter, held in Sepino, Italy, May 1996, published in the Hadronic J. 1996 19, 77-96
http://www.santilli-foundation.org/docs/Santilli-11.pdf

[14] de Haan, V., Proposal for the realization of Santilli comparative test on the gravity of electrons and positrons via a horizontal supercooled vacuum tube, Proceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes, C. Corda, Editor, Kathmandu University, 2011, pages 57-67
http://www.santilli-foundation.org/docs/deHaan-Arxiv.pdf

[15] Muktibodh, P. S., "Introduction to Isodual Mathematics and its Application to Special Relativity," American Institute of Physics Proceedings 2013
http://www.santilli- foundation.org/docs/P-Muktibodh.pdf

[16] Davvaz, B., Santilli, R. M., and Vougiouklis T., Studies of Multi-Valued Hyperstructures for the Characterization of Matter-Antimatter Systems and their Extension, in Proceedings of the 2011 International Conference on Lie-admissible Formulations for Irreversible Processes, C. Corda, editor, Kathmandu University, Nepal, 2011,
http://www.santilli-foundation.org/Hyperstructures.pdf

[17] Bhalekar, A. A., "Studies of Santilli's isotopic, genotopic and isodual four directions of time," American Institute of Physics proceedings, 1558, 697-701 (2013)
http://www.santilli-foundation.org/docs/Bhalekar-2013-I.pdf.

[18] Bhalekar A. A., "Santilli's New Mathematics for Chemists and Biologists. An Introductory Account," CACAA, 2014 (In press)
http://www.santilli-foundation.org/docs/Bhalekar-Math-2013.pdf.

[19] Santilli, R. M. "Isominkowskian Geometry for the Gravitational Treatment of Matter and its Isodual for Antimatter," Intern. J. Modern Phys. 1998, D 7, 351
http://www.santilli-foundation.org/docs/Santilli-35.pdfR.

[20] Santilli, R. M. "Does antimatter emit a new light?" Invited paper for the proceedings of the International Conference on Antimatter, held in Sepino, Italy, on May 1996, published in Hyperfine Interactions 1997, 109, 63-81
http://www.santilli-foundation.org/docs/Santilli-28.pdf

[21] Santilli, R. M. "The Mystery of Detecting Antimatter Asteroids, Stars and Galaxies," American Institute of Physics, Proceed. 2012, 1479, 1028-1032 (2012)
http://www.santilli-foundation.org/docs/antimatter-asteroids.pdf

[22] Corda, C., Introduction to Santillis IsoMathematics, AIP Conf. Proceed. 2013, 1558, 685

[23] Santilli, R. M. APPARENT DETECTION OF ANTIMATTER GALAXIES
VIA A REFRACTIVE TELESCOPE WITH CONCAVE LENSES
Clifford Analysis, Clifford Algebras and their Applications
Vol. 3, pages 1-26, 2014 (Cambridge, UK)
http://www.santilli-foundation.org/docs/Antimatter-telescope-2013-final.pdf

[24] Bhujbal, P., J. V. Kadeisvili, A. Nas, S Randall, and T. R. Shelke,
PRELIMINARY CONFIRMATIONS OF ANTIMATTER DETECTION
VIA SANTILLI TELESCOPE WITH CONCAVE LENSES
Clifford Analysis, Clifford Algebras and their Applications
Vol. 3, pages 27-39, 2014 (Cambridge, UK)
http://www.santilli-foundation.org/docs/Con-Ant-Tel-2013.pdf

**********************************