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Katalin has vast knowledge on Combinatorial Group Theory. She has attended the Magus Group Theory Seminar (now The New York Group Theory Seminar) for decades, and studied under Gilbert Baumslag.
When I have any questions about groups given by generators and relations, she is one of the people that I ask for orientation and her advice is always fruitful. It is a tragedy that this mathematician had to spend so many years of her life teaching HUGE numbers of classes every semester, but that is the life of a great number of mathematicians, especially those that are not working in fashionable mathematical fields.
Incidentally Gerd Faltings did rather unpopular mathematics for his PhD and eventually shocked the world with his findings. The moral of the story. Don't forget unpopular mathematics.
Advisor: Prof. Paul Voyles (Materials Science and Engineering Department.)
Research: "I will be taking a combinatorial approach to the discovery of new transparent conductive oxide films for use in optoelectronic devices."
This is a set of cold-drink coasters that I modeled in Combinatorial Solid Geometry using a CAD package called BRL-CAD back in 1994. I was heavily involved in advancing their Ray Tracer to produce photorealism with the goal of using BRL-CAD as the heart of a computer-animation studio in my home. Unfortunately the technology of the time didn't support my dream, and so I had to temporarily move onto other things while waiting for the tech to catch up.
This was the best photorealism experiment I produced with BRL-CAD and includes true penumbras, a light/distance attentuation term, state-of-the-art optical shader, etc. I had lots of other directions I wanted explore, including physics-based rendering, bleeding-edge "intelligent" geometric primitives/shaders, and more; but I had to move on.
Unfortunately I saved it in GIF so someday if I can find the original geometry file I'd like to re-render it in the PNG format.
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Stuhl 1
Auf die Mitwirkung des Publikums wir nicht verzichtet.
Kombinatorischer Bastelplatz.
Wurde tatsächlich genutzt.
Einmal jedoch in wegwischender Gebärde, weil da kein Platz war, den Terminkalender auszubreiten. Der lag dann da, eine andere Art der Kombinatorik wohl. Die Pattern lagen quer, Gedränge von Eisschollen am Ufer, seltsam und glücklicherweise keins zerknickt. Was das nun wieder bedeuten soll …
Die freie Kombinatorik der Pattern kann von jedwedem betrieben werden. Kein Grund, warum allein der Künstler hier Anordnungen treffen sollte. Warum nicht überhaupt die Zufälle. Kränkend. Die Wucherungen der Musterflächen bekommen erst überindividuell individualisierend ihre virulentesten Level und Ebenen. Tja.
From a paper by Ron Graham. (1975). The largest small hexagon. *Journal of Combinatorial Theory, Series A*, *18*(2), 165-170.
Artist: John Sims
This installation presents all of the knots up to and including 8 crossings. These knots were cut and presented as rope hangings. This work was inspired by looking at the mathematics of the Hangman's noose. Also this work was dedicated to Sol LeWitt, my art mentor for his inspirational combinatorial work. The installation is sized at 12 feet high and 18 feet long.
The Art of Computer Programming: Generating All Trees--History of Combinatorial Generation; Volume 4 - By Donald Ervin Knuth
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Die Photos, Flammenbilder, negativ entwickelt, hießen Miasmen in der Installation im Mindener Fort C. Schwarze Flammen. Sie werden zu Dingen, Und das naß gewordene Papier klebt inzwischen unablöslich an den Glasscheiben, wellig, Lufteinschlüsse, … sie verändern sich. Materialgeschichte. Photo-Objekte. Die e-Zeichnungen darüber treiben weiße Striche als Abstraktionen in ein noch abstrakteres Schwarz. Ein Gegensatz.
The text is from Emmanuel Roblet's thesis. The title in English is "A combinatorial interpretation of Pade approximants". It's closely related to my own research.
Image analysis is a scientific discipline which provides theoretical foundations and methods for solving problems appearing in a range of areas as diverse as biology, medicine, physics, astronomy, geography, chemistry, robotics, and industrial manufacturing. It deals with algorithms and methods aimed at extracting meaningful information from images; obtaining quantitative measurements such as lengths, areas, and thicknesses; and deriving object elements such as contours, skeletons, and holes. The processing is done through computer systems, and the focus is therefore usually on images presented in digital form.
The reviewing and program committee consisted of 86 scientists from 29 countries, and five continents. The selection of papers was very rigorous: each paper was sent to at least four members of the program committee for a double-blind review.
The volume starts with the survey paper entitled "Current Challenges in Vision-Based Driver Assistance" by the invited speaker Reinhard Klette from the University of Auckland, New Zealand. This paper reviews current developments in the field of vision-based active safety components of cars, which aim at advanced solutions, using stereo or motion data as basic input for providing accurate lane or corridor data, for estimating ego motion, or for pedestrian detection. The fifteen contributed papers included in this volume are separated into the following three sections: Discrete, Digital and Computational Geometry and their Applications to Image Analysis; Topological and Combinatorial Models, and Grammars for Image Representation and Analysis; Segmentation, Processing, and Reconstruction of Digital Images.
MSRI conference on combinatorial game theory, MSRI (Berkeley, CA), November 2015
From left to right: Aaron Siegel, Elwyn Berlekamp, David Eisenbud, Thane Plambeck, Richard K Guy
View the large version to see all the detail. Stitched from 7 hdr images, each of which were from 3 bracketed shots.... so 21 photos in total went into making this panorama.
Trax (1997/2010)
Douglas Edric Stanley
Trax est un jeu d'écriture musicale combinatoire. S'inspirant à la fois du modélisme ferroviaire et de la composition minimaliste des années 60, Trax propose un espace de construction ludique où le joueur compose des réseaux de pistes bifurquantes qui forment au final un enchevêtrement simple mais complexe de potentiel musicale. En plaçant ensuite des notes, des trains et des sémaphores, une modulation mélodique émerge, que l'on peut qualifier plus généralement de musique algorithmique.
Trax sera présenté au festival Gamerz sous la forme d'un prototype jouable sur iPad.
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Trax is a combinatorial sound toy. Mixing model railroads and 1960's minimalist composition, Trax allows players to build up circular networks of bifurcating rails that branch out into both simple and complex combinations of musical possibility. By placing notes, “tranes”, and semaphores into this ludic rail yard, a modular melody emerges, otherwise known as algorithmic music.
Trax will be exhibited at the Festival Gamerz as a playable prototype for iPad.
I'm cleaning up a math paper for final submission to INTEGERS, an online combinatorial number theory journal. Dan Hoey drew my attention to a lot of redundant information in one table. So I started matching up pairs of symbols in the table, only one of which I need to keep in the final version of the paper. Because there were a lot more pairs than I expected to find (thanks, Dan!), I needed to get out multiple pens and colors to find them all. It was more fun to color it than to type it in (actually I dont know that, since I haven't typed it in yet)
Hardcore Combinatorial Group Theorists, Katalin Bencsath and Ben Fine (a former student of Magnus) were long time attendees of the New York Group Theory Seminar (Earlier known as the Magnus Group Theory Seminar). As a PhD student at the Graduate Center seeing them provided a sense of security and a feeling of continuity for the subject especially after Magnus was no longer in the picture.