Dear colleagues, It is with great sadness that we announce the passing of Dito Pataraia on December 15, 2011. He was 48. Dito was an indispensable source of inspiration. At seminars he generously shared his uniquely original insights on several important topics in category theory, mathematical logic and algebraic topology, but he was reluctant to publish or pursue a scientific degree. His major achievements remain unpublished and unknown to the general mathematical community. However, his brilliant ability to effortlessly present complex and deep mathematical insights with incredible simplicity and clarity would leave an unforgettable impression on those few who were lucky enough to hear him talk during a seminar. At the same time, Dito's infinite kindness, unfailing humor and sharp, but open and unassuming mind made him the heart of a company, a kind of person that makes one better by simply being around. It is an inconsolable grief that he is no longer with us. It has been a privilege to know him. The brilliant sparkle he managed to light up in our hearts will be cherished forever. The following is a characteristic illustration of his style - one of the very few things that he decided to make publicly available: http://www.emis.de/journals/GMJ/vol4/v4n6-4.pdf [1] There are (maybe too) many approaches to the universal characterization of the fundamental group, in various flavors and degrees of generality. Dito's version is not just another one. It is totally unexpected, completely against the mainstream thought on this topic, and yet ever so natural. Quite probably it opens up a new and absolutely unexplored field of study. Most of Dito's work was only known in fragments to his close friends from many long discussions. Once Mamuka Jibladze returned from one of the PSSLs, where he learned about two interesting open questions. One was whether the Witt fixed point theorem for dcpo's is constructively valid; the second - the question of Andy Pitts - whether any Heyting algebra can occur as the poset of all subobjects of some object in an elementary topos. After three days Dito came to the seminar with positive answers to both of these questions. He never published these results. The proof of the first question is relatively simple, so his talk at another PSSL (in Aarhus) was sufficient for others to reconstruct and reproduce it in the literature (you have probably seen in a paper, book or online the combination Bourbaki-Witt-Pataraia). The proof of the second question is much more complicated. Dito's proof consisted of two parts - the construction, from a Heyting algebra, of some intermediate structure which he called Higher Order Cylindric Heyting Algebra (hocha for short), and then the construction of a topos from any hocha. This second part was more or less similar to several known constructions (a hocha is sort of a (powerset, product) reduct of a topos, so an equalizer completion of a hocha is a topos). That part was more transparent and even partly written down. In fact, after Dito and Mamuka described it to Peter Johnstone, Martin Hyland, and Andy Pitts among others at Cambridge, Peter came up with yet another transparent and elegant construction of this second part based on allegories. However the first part - constructing a hocha from a Heyting algebra - is much more involved. It seems to force one into a completely unexplored territory. The proof that Dito had was stuffed with completely unexpected new ideas and constructions. As Marek Zawadowski put it after listening to Dito in Tbilisi, it was like witnessing a magician pulling rabbit after rabbit out of his hat. However the proof, if written down, would be about forty pages long and did not satisfy Dito at all. The proof that Dito had was truly stuffed with completely unexpected new ideas and constructions - as Marek Zawadowski put it after listening to Dito in Tbilisi, it was like witnessing a magician pulling rabbit after rabbit from a top hat. However the proof, if written down, would be about forty pages long and did not satisfy Dito at all. He spent a week in Utrecht, where Jaap van Oosten kindly followed the exposition every day, and came up with an extremely important simplification (Jaap discovered that the substitution operators may be expressed from the rest of the hocha structure). Still the proof remained too involved for Dito's taste, and he kept returning to it. As we mentioned, he never cared about publishing anything, his only priority was to make things as clear as possible. So Dito just took his time, having occasional opportunities to discuss it with Marek Zawadowski, Silvio Ghilardi and others. Just about a month before his death, some new idea occurred to him, which would help to organize the proof into something much more manageable. Unfortunately, there was not enough time for Dito to write it down in detail, but luckily he did share his new idea at the seminar. Dito worked on many other exciting questions in several fields, ranging from philosophy to arithmetic. Some of you might be aware of Dito's several unpublished works - an analysis-free proof of total disconnectedness of compact Hausdorff Boolean algebras, a description of the PROP of Hopf algebras, and a completely novel approach to Hopf-algebraic knot invariants. It is now our duty to make as much of his work available to the general mathematical community as possible. Dito's Georgian friends and colleagues. Links: ------ [1] http://www.emis.de/journals/GMJ/vol4/v4n6-4.pdf [For admin and other information see: http://www.mta.ca/~cat-dist/ ]