Dear Colleague,

The Alterman event is approaching and the deadlines must be remembered:

1) The reduced and student fees are only valid before the deadline of June 1st. After this date, the Conference fee will rise to 300€ and the fee for the whole event to 400€. The modular fees will not be applicable yet. The means of payment are the following: a) Bank transfer, b) Western Union c) PayPal d) In cash. You will find the details for payment of the fee at:

http://cs.unitbv.ro/~acami/registration.htm

2) Some participants who wish to submit an abstract and now have not time enough for doing so (owing to duties of ending the academic course) have requested us to postpone the deadline for abstract submission. Therefore, we have postponed this deadline to June 1st. On that date, the booklet of abstract will be published at the website of the Alterman Conference:

3) The deadline of submission of articles for the Early Proceedings is July 1st. Please be aware that there will not be much time for editing the Early Proceedings before the conference. Therefore it is unlikely that this deadline will be postponed. The Early Proceedings will be published very likely about July 15th-20th at the same website. The articles will simply be accepted or refused by the scientific committee. There will not be time enough for improving texts as usually happens in a reviewing process. Since there is only one and a half months to the deadline, authors are requested to begin now, if they have not done yet, to prepare their papers. Do not leave for the last moment the text of your talk. A reasonable suggestion is a maximum of 20 pages. The Latex and PDF templates for preparing articles can be downloaded from:

http://cs.unitbv.ro/~acami/submission.htm

Submissions must be sent to acami@unitbv.ro in PDF format. The accepted articles will be included in the Early Proceedings only if one of the authors has paid the fee.

Some participants who have requested free shared lodging have not registered or payed the fee yet. We will confirm their lodging after fee payment. If you are not registered, please fill in the registration form available at:

http://cs.unitbv.ro/~acami/registration.htm

On the other hand, if there is some change in the nights you will stay in Brasov, please fill in the form for free shared lodging again. It is available at:

http://cs.unitbv.ro/~acami/lodging.htm

In order to both motivate and do justice to proponents of alternative approaches to projective geometry, Jose G. Vargas has posted first pages of his paper “Grassmannian Algebras and Erlangen Program, with Special Emphasis on Projective Geometry”. Please find them just in the same link to his abstract in the website of the Alterman event:

http://cs.unitbv.ro/~acami/conference.htm

The author is critical of claims made by, for instance, Hestenes and Ziegler (in “Projective Geometry with Clifford Algebra”, Acta Applicandae Mathematicae 23 [1991] pp. 25-63) on how to bring projective geometry closer or into the main stream of mathematics through Clifford algebra. Others who may feel criticized by proxy (perhaps followers of Rota: see M. Barnabei, A. Brini, G.C. Rota, “On the Exterior Calculus of Invariant Theory”, J. of Algebra 96 [1985] pp. 120-160) may also like to make their case known. Here are some key points:

(1) As pointed out by Dieudonné in his paper “The Tragedy of Grassmann”, the main interest of Grassmann was geometric, not algebraic. And, as pointed out by E. Cartan in his paper “Complex Numbers”, Clifford’s work was algebraic. Geometry is not a branch of Clifford algebra or of any other algebra; they simply can and should be used in geometry, but the difference and the how to breach the gap between algebra and geometry must be clearly stated, stating with what is one’s concept of geometry and how the said concept relates to what is understood in the paradigm that geometry is.

(2) Jose makes the obvious observation that there is not a special element in affine space, where all points are equivalent. There is not, therefore, a zero element. A vector space, on the other hand, has a zero. In order to use vector spaces (and then Clifford or any other quotient algebra of the general tensor algebra constructed upon a vector space) while maintaining that equivalence, Cartan had to create frame bundles. This concept is very close to the concept of Klein geometry in the modern sense of the term (not in Klein’s original sense), and which also is due to Cartan, although he did not formulate it explicitly (but he used it everywhere). He implicitly created the new concept of Klein geometry and then replaced the role of group by the role of action on those bundles (see Dieudonné’s argument in the introduction to “The Erlangen Program”).

(3) One may be aware of (1) and (2) (as Jose knew for many years) and yet not know how to easily handle projective geometry. Here the book “Treatise of Plane Geometry through Geometric Algebra” by Ramon Gonzalez provided the missing element. It was known since 1908 (Cartan in his paper “Complex Numbers” while discussing Grassmann’s Ausdehnungslehre) that a geometry can be represented by different bundles. But this had been overlooked. Ramon connected the “canonical bundles” (generated while addressing the issue in (2)) with bundles of frames of points and bundles of frames of lines (or of hypersurfaces depending on the dimension of the space). They make projective geometry so easy!

(4) The treatment outlined in (1)-(3) helps to illustrate the subtleties (and even dangers!) involved in viewing projective geometry simply as the geometry defined by the group of matrices known as homographies. The theory of these matrices has an extensive life of their own, which not always matches what makes sense geometrically. This problem is already clear with the representation of affine transformations in n dimensions through square matrices for dimension n+1, i.e. as homographies. In this case, it is very easy to compute the inverse matrix after first organizing them into 4 blocks, one of them being of type n x n. There is a difference in the translation parameters of a homography and of its inverse, as the ones are not just the negative of the others; the translation gets entangled with the linear part of the transformation. This is but the simplest of the examples of subtleties or dangers (Call them what you want).

Looking forward to seeing you in Brasov,

With kind regards,

The organizing committee,

Jose G. Vargas, Marius Paun, Ramon Gonzalez, Panackal Harikrishnan

*Source:* Email from acami_AT_unitbv.ro, 22 May 2016