Mathematical Feelings of Space: Schedule and Abstracts

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October 10 at FRUMAM

9:00 Accueil/Reception
9:30 Edmund Harriss Introduction
10:00 Peter Davidson Sir Thomas Tresham (1541-1605) Catholic Recusant, amateur architect, and numerologist
11:00 Arnaud Chéritat Exploratory experiments at representing geometric notions virtually and/or physically
12:30  Lunch
14:00 Pierre Berger Esthetopy
14:40 Paul Prudence  TBA
15:00 Alison Martin Crafting Complex Structures
15:30 Break
16:00 Jean-Paul Allouche Local versus global in mathematical and non-mathematical spaces
16:40 David Lasnier  Various Small Spaces
17:20 End

October 11 at IMéRA

In the morning there will be short 5min presentations on a variety of topics, all participants are encouraged to present. These presentations will be filmed. In the afternoon everyone will join a small group for a discussion of a topic (the topic suggestions will be finalised on the 10th). After an hour for discussion each group will have a second hour to prepare a presentation for the whole group.

9:30 Accueil/Reception
10:00 Quick (5min) presentations
11:00 General discussion and preparation for afternoon
12:30 Lunch Buffet
13:30 Unconference groups 1: General discussions
14:30 Break
14:45 Unconference groups 2: Prepare presentation
15:45 Break
16:00 Reports from small groups to whole group
17:00 End

Abstracts

Peter Davidson: Sir Thomas Tresham (1541-1605) Catholic Recusant, amateur architect, and numerologist

Thomas Tresham was a landowner, Catholic Recusant, amateur architect, and numerologist. He laid out at least one ambitious garden at Lyveden (which is being restored) and built two high symbolic and number-based buildings, Rushton Triangular Lodge (1593) and Lyveden New Building (abandoned 1605). It is these spaces which I would like to show, and on which I would invite mathematical enlightenment.

I will explain something of the context of number as symbol in English renaissance culture in particular and in renaissance culture more generally. Tresham was clearly most interested in numbers and spaces. As a Catholic gentleman he was, after 1560, technically or actively on the wrong side of the English law. He was imprisoned for long periods of “preventive detention” during which he planned his intricate and allusive symbolic buildings. He also left still-unsolved sets of number-jottings relating to his buildings.

I don’t; think his works have ever been seriously considered by mathematicians. It may be that (given the circumstances in which they were made) his number jottings may only be mysteries for their own sake, transposition-based codes involving randomly « significant » dates, or simply renderings of letters as number. In which case we’ll know not to look further by the end of the discussion. Or there may be subtleties beyond the obvious games with 3 in the Triangular Lodge, and play with 4 and 5 at Lyveden New Building. I can show you measured drawings, estate plans and pages from his notebooks. It may all be nothing or it may be a wonderful something.

Arnaud Chéritat: Exploratory experiments at representing geometric notions virtually and/or physically
In the last few years I have been using 3D printers, 3D modelling software and 2D and 3D web browser technology to represent some geometric objects including :
  • immersed surfaces in 3D and eversions
  • 2D hyperbolic space
  • 4D polytopes

In this talk I will make a short review of these experiments together with a few comments on a selection of key aspects in implementing them.

Pierre Berger: Esthetopy
The exhibition esthetopy was presenting several artworks and installations. They were designed to offer new sensitive explorations inside (imaginary) mathematical spaces  still misunderstood. Some of these artworks was created during different collaborations with the artists Pierre-Yves Fave, Sergio Krakowski, Vincent Martial and Jimena Royo-Letelier. Others gave answers to problems of Thurston’s School at the Geometry Center. Website: http://esthetopies.ihp.fr/ and  http://espaces-imaginaires.fr/
Alison Martin: Crafting Complex Structures: Bending, folding, cutting and pasting – to make mathematically inspired shapes.
Versions of complex patterns seen in nature can be generated with weaving and iterative construction techniques using simple materials and a low-tech approach.
Deconstructing space into simplified topological constituents; working with vertices and edges and modifying their connectivity offers a visual language and insight into how patterns appear from the inside out. The slow, repetitive process of hand building physical models allows unexpected connections to be made and provides tactile understanding and practical insights into spatial concepts.
Jean-Paul Allouche: Local versus global in mathematical and non-mathematical spaces

We try to underline the opposition-convergence between local and global properties in mathematics, but also in current life where global knowledge is discouraged through a systematically (and probably non-innocently) imposed local vision.

David Lasnier: Various small spaces

Some of my art projects deal with simple, yet paradoxical notions of space.They may sound ridiculous on a local scale, but make sense on a planetary or interplanetary scale. I like the idea that you have to mentally project yourself in a huge scale to understand a small object. The first part will be just a presentation of such projects as a list.
On the second part of my speech I will focus a little longer on two ongoing, more mathematical projects, one involving self avoiding hamiltonian paths and another one geometry of paper folding.


Auteur : edmundharriss

Mathematician, Teacher, Artist, Maker at the University of Arkansas. Author of the mathematical Colouring books Patterns of the Universe (Les Formes Magiques de L’Univers en Français) and Visions of the Universe with Alex Bellos, creator of Curvahedra.

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