23rd January 2015
Queen Mary University of London
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09:00 10:00 MTH102 |
Coffee in the Mathematics Common Room |
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10:00 11:00 ArtsTwo,
Room 3.20 |
Dr Bernd Schulze (University of Lancaster) Title: Combinatorial characterisations of rigid frameworks (slides) Abstract: Rigidity Theory is concerned
with the study of bar-joint frameworks and related constraint systems of geometric objects. This area has a rich history
which can be traced back to classical work of Euler, Cauchy and Maxwell on
the rigidity of polyhedra and skeletal frames. The combinatorial side of the theory for
generic structures began with Maxwell's counting conditions from 1864, and in
1970 Laman obtained the fundamental result that
these necessary conditions are also sufficient for generic rigidity in the
Euclidean plane. Combinatorial characterisations of generically rigid graphs
in dimension 3 or higher have not yet been found. However, there exist
significant partial results for the special classes of body-bar, body-hinge
and molecular frameworks. In the first part of this talk I will give a survey
of these key results in Combinatorial Rigidity Theory. In the second part of the talk we will
consider the impact of symmetry on the rigidity properties of frameworks. In
particular, we present combinatorial characterisations of rigid symmetric
frameworks (of various types) which are as generic as possible subject to the
given symmetry constraints. This relatively new research area draws on the combinatorics of group-labeled
quotient graphs and their associated matroids,
symmetry-adapted Maxwell counting, and methods from group representation
theory. |
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11:00 11:30 |
Coffee break |
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11:30 12:30 ArtsTwo,
Room 3.20 |
Dr Vitaliy Kurlin (Durham University and Microsoft Research, Cambridge) Title: Topological Data Analysis. Applications to Computer Vision (slides) Abstract: We briefly review
Topological Data Analysis defining basic concepts and explaining the stability of persistence under noise.
Then we describe 3 applications to Computer Vision. (1) Given only a noisy
n-point sample C of a 2D shape, we count topological persistent holes of C in time O(n log n). The output
coincides with the true number of holes in the original shape for any dense enough sample. (2) For a noisy sample C of
unknown closed contours in the plane, we provably reconstruct the unknown contours with
the same running time O(n log n) without using any extra input parameters except the sample C. (3) We introduce a
homologically persistent skeleton that depends only on a point cloud C, optimally extends a minimum
spanning tree of C and provably approximates a good enough graph represented by the
cloud C. |
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12:30 14:00 |
Lunch break |
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14:00 15:00 Laws, Room 1.12 |
Problem Session |
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15:30 16:30 Laws, Room 1.12 |
Dr Piotr Beben (University of Southampton) Title: Configuration Spaces and Polyhedral Products (slides) Abstract: We use configuration space
models for spaces of maps into certain subcomplexes
of product spaces (including polyhedral
products) to obtain a single suspension splitting for the loop space of certain polyhedral products,
and show that the summands in these splittings have a very direct bearing on the topology
of polyhedral products, and moment-angle complexes in particular. |
1. Bernd Schulze, Lancaster
2. Jacek Brodzki,
Southampton
3. Jon Selig, London South Bank
4. Mark Jerrum,
QMUL
5. Vitaliy Kurlin, Durham and Microsoft
6. Dirk Schόtz,
Durham
7. Armindo Costa, QMUL
8. Michael Farber, QMUL
9. Matthew Burfitt,
Southampton
10. Larry So, Southampton
11. Mark Grant, Aberdeen
12. Conor Smyth, Southampton
13. Hakan Guler,
QMUL
14. Katie Clinch, QMUL
15. Bill Jackson, QMUL
16. Alex Fink, QMUL
17. Hugo Maruri,
QMUL
18. Jelena Grbic, Southampton
19. Piotr Beben,
Southampton
20. Ingrid Membrillo,
Southampton