Topological dynamics in the physical and biological sciences

Programme theme

The programme is intended to stimulate interaction between applied mathematicians, biologists and physicists who frequently encounter dynamical problems that have some explicit or implicit topological content. We use the term 'topological' to convey the idea of structures, e.g. knots, links or braids in 3D, that exhibit some measure of invariance under continuous deformation. Dynamical evolution is then subject to the topological constraints that express this invariance. A basic common problem is to determine minimum energy structures (and routes towards these structures) permitted by such constraints; and to explore mechanisms, e.g.diffusive, by which such constraints may be broken.

When formulated in terms of the mathematical objects and issues, the current view of the common topological denominator is summarised below. We expect to add to this list during the Programme.

Tubes in R3

Surfaces in R3

Lines in R3

Lines on manifolds

Singularities

Knotted flux tubes in MHD (helicity, minimisation problems, topological aspects of dynamo theory)
Knots on vortex tubes (analogies and differences with MHD, dynamical implications of knottedness)
Knotted molecules (DNA, proteins, minimisation of drag on a knotted tubular structure)
Dynamics of protein folding, coiling and supercoiling (folding of knotted proteins)
Spectrum of knots and links under different minimisation principles
Biological membranes (minimisation problems, implications of topology for phase transitions)
Fermi surfaces (electron trajectories on Fermi surfaces, topological phase transitions)
Knots and links and braids in streamlines and magnetic field lines (decay of topological invariants in the ideal medium limit)
Quantum vortices in super bundles, topological implications on statistical mechanics)
Quantum implications of classical topological constrains
Application of knot theory to statistical mechanics
Electron trajectories on Fermi surfaces of complex topology
Formation of singularities in the Navier-Stokes and Euler equations
Topological changes in parametric evolution of magnetic fields (singularity formation under footpoint shuffling)

The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:

The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Topological dynamics in the physical and biological sciences, where work on this paper was undertaken. This work was supported by EPSRC grant EP/F005431/1 and EP/I016392/1.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme	Publication Date
Finite type invariants of magnetic lines Authors: Petr Akhmet'ev Download PDF	2012	TOD	2 March 2017
Relativistic helicity and link in Minkowski space-time Authors: Y. Kawazura, T. Yokoyama, Zensho Yoshida Download PDF	2012	TOD	2 March 2017
The symplectic geometry of closed equilateral random walks in 3-Space Authors: Jason Cantarella, Clayton Shonkwiler Download PDF	2012	TOD	21 October 2016
Reconnection of skewed vortices Authors: Yoshifumi Kimura, Keith Moffatt Download PDF	2012	TOD	21 October 2016
Topological constraints and their breakdown in dynamical evolution Authors: RE Goldstein, Keith Moffatt, Adriana Pesci Download PDF	2012	TOD	21 October 2016
The expected total curvature of random polygons Authors: Jason Cantarella, AY Grosberg, Rob Kusner, Clayton Shonkwiler Download PDF	2012	TOD	21 October 2016
The fluid dynamics of James Clerk Maxwell Authors: Keith Moffatt Download PDF	2012	TOD	21 October 2016
The tight knot spectrum in QCD Authors: R V Buniy, Jason Cantarella, T W Kephart, Eric Rawdon Download PDF	2012	TOD	21 October 2016
Applications of Lagrangian reduction to condensed matter Authors: F Gay-balmaz, Michael Monastyrsky, Tudor Ratiu Download PDF	2012	TOD	21 October 2016
Helical organization of tropical cyclones Authors: Galina Levina Download PDF	2012	TOD	21 October 2016
Generalized helicity and Beltrami fields Authors: Roman Buniy, Thomas Kephart Download PDF	2012	TOD	21 October 2016
Discrete groups and internal symmetries of icosahedral viral capsids Authors: Richard Kerner Download PDF	2012	TOD	21 October 2016

Workshops

TODW01

Topological fluid dynamics (IUTAM symposium)

23 July 2012 to 27 July 2012

TODW02

Topological aspects of DNA function and protein folding

3 September 2012 to 7 September 2012

Satellite

TODW03

Seminars

Thursday 19th July 2012
11:30 to 12:30	Phil Boyland University of Florida Some topological tools in two-dimensional dynamics	Room 1

Thursday 2nd August 2012
11:30 to 12:30	John Gibbon Imperial College London Higher norms of vorticity applied to the intermittency and blow-up problems in the 3D Navier-Stokes and Euler equations	Room 2

Tuesday 7th August 2012
11:30 to 12:30	Konrad Bajer Uniwersytet Warszawski Development of singularities in relaxing magnetic fields	Room 1

Thursday 9th August 2012
11:30 to 12:30	Andrzej Herczynski Boston College Pollockian Mechanics: Painting with Viscous Jets	Room 1

Tuesday 14th August 2012
11:30 to 12:30	Gunnar Hornig University of Dundee Magnetic braids, Hamiltonian action and selective decay	Room 1

Wednesday 15th August 2012
12:00 to 17:00	Informal discussion	Discussion Room

Thursday 16th August 2012
11:30 to 12:30	Roman Buniy Chapman University An algebraic classification of entangled states	Room 2

Tuesday 21st August 2012
11:30 to 12:30	Piotr Szymczak Uniwersytet Warszawski Reactive-infiltration instabilities in fractures and porous rock	Room 1

Thursday 23rd August 2012
11:30 to 12:30	Giovanni Dietler Centre de Physique Théorique de l’Ecole Polytechnique (CPHT) Knots: from the sailing boat down to the cell's nucleus illustrated by means of simple experiments	Room 2

Tuesday 28th August 2012
11:30 to 12:30	Alexander Shnirelman Concordia University On the 2-point problem for the Lagrange-Euler equation	Room 1

Thursday 30th August 2012
11:30 to 12:30	Tomasz Lipniacki Polish Academy of Sciences Stochastic travelling waves in bistable biochemical system: Numerical and mathematical analysis	Room 1

Tuesday 11th September 2012
11:30 to 12:30	William Irvine University of Chicago Knots in light and fluids	Room 2

Thursday 13th September 2012
11:30 to 12:30	Marek Cieplak Polish Academy of Sciences Nanoindentation of virus capsids	Room 2

Tuesday 18th September 2012
14:30 to 15:00	Open for Business: Registration and Welcome	No Room Required
15:00 to 15:30	Dorothy Buck Imperial College London DNA topology: where maths meets molecular biology	Room 1
15:30 to 16:00	Lynn Zechiedrich Baylor College of Medicine A new non-viral, non-toxic DNA minivector for basic and clinical research: how basic DNA topology research opened doors for gene therapy	Room 1
16:00 to 16:30	Open for Business: Tea Break	No Room Required
16:30 to 17:05	New approaches to understanding and treating neurodegenerative diseases	Room 1
17:05 to 17:15	Calcium hypothesis of Alzheimer's disease	Room 1
17:15 to 18:00	The business of science; building therapeutic drugs based on proteins	Room 1
18:00 to 19:00	Open for Business: Wine Reception	No Room Required

Thursday 20th September 2012
11:30 to 12:30	Jason Cantarella University of Georgia The geometry and topology of random polygons	Room 2

Tuesday 25th September 2012
11:30 to 12:30	Shigeo Kida Kyoto University On bright pattern of flakes in flow visualization	Room 2

Wednesday 26th September 2012
11:30 to 12:30	Tony Leonard CALTECH (California Institute of Technology) A study of structures with intense vorticity in isotropic turbulence	Room 2

Thursday 27th September 2012
11:30 to 12:30	Kenneth Millett University of California, Santa Barbara The average geometric and topological properties of open and closed equilateral polygonal chains	Room 2

Tuesday 2nd October 2012
11:30 to 12:30	Clayton Shonkwiler University of Georgia Homotopy, link homotopy and (higher?) helicity	Room 1

Thursday 4th October 2012
11:30 to 12:30	Clare Parnell University of St Andrews On the topology of complex magnetic fields of the Sun and the magnetosphere	Room 1

Tuesday 9th October 2012
11:30 to 12:30	Tomoo Yokoyama Hokkaido University Word representation of streamline topologies for structurally stable vortex flows in multiply connected domains	Room 1

Wednesday 10th October 2012
11:30 to 12:30	Denis Weaire Trinity College Dublin Packing Spheres in a Cylinder	Room 1

Thursday 11th October 2012
11:30 to 12:30	Asher Yahalom Ariel University Center of Samaria Magnetohydrodynamics as a field theory: topological and group theoretical aspects	Room 1

Tuesday 23rd October 2012
11:30 to 12:30	EULAG-MHD: Simulation of the global solar dynamo	Room 1
11:45 to 13:00	Alessandra Renieri skype interview for PhD	Discussion Room

Thursday 25th October 2012
11:30 to 12:30	Jason Parsley Wake Forest University Helicity, cohomology, and configuration spaces	Room 1

Tuesday 30th October 2012
11:30 to 12:30	Francesca Maggioni Università degli studi di Bergamo Optimal kinematics of supercoiled filaments	Room 1

Wednesday 31st October 2012
14:00 to 16:00	Informal discussion	Discussion Room

Thursday 1st November 2012
11:30 to 12:30	Xin Liu University of Sydney Knot polynomial invariants in terms of helicity for tackling topology of fluid knots	Room 1

Tuesday 6th November 2012
11:30 to 12:30	Tom Kephart Vanderbilt University The tight knot spectrum in quantum chromodynamics	Room 1

Thursday 8th November 2012
11:30 to 12:30	Louis Kauffman University of Illinois at Chicago Quantum information, the Jones polynomial and the Fibonacci model	Room 1

Tuesday 13th November 2012
11:30 to 12:30	Eleni Panagiotou National Technical University of Athens A study of the entanglement in polymer melts	Room 1

Wednesday 14th November 2012
11:30 to 12:30	Efim Kats L.D.Landau Institute for Theoretical Physics, Moscow Dynamics of pore formation in membranes	Room 1
16:30 to 17:30	Victor Buchstaber Steklov Mathematical Institute, Russian Academy of Sciences Symmetric quadratic dynamical systems	Room 1

Thursday 15th November 2012
11:30 to 12:30	Richard Kerner Université Pierre et Marie Curie Paris Self-assembly of icosahedral viral capsids: the combinatorial analysis approach	Room 1

Tuesday 20th November 2012
11:30 to 12:30	Rob Kusner University of Massachusetts The space of soap bubbles	Room 1

Wednesday 21st November 2012
11:30 to 12:30	Fermi surface topology and topological numbers in conductivity of normal metals	Room 1

Thursday 22nd November 2012
11:30 to 12:30	Shahin Rouhani Sharif University of Technology Classification of rough surfaces using Schramm-Loewner evolution	Room 1

Friday 23rd November 2012
11:30 to 12:30	Some aspects of iceberg mechanics	Room 1
16:00 to 17:00	Some aspects of iceberg mechanics	Room 1

Tuesday 27th November 2012
11:30 to 12:30	Two amusing problems in geometry and topology	Room 1

Thursday 29th November 2012
11:30 to 12:30	Tudor Ratiu Centre de Physique Théorique de l’Ecole Polytechnique (CPHT) The dynamics of conservative charged molecular strands	Room 1

Tuesday 11th December 2012
11:30 to 12:30	Jens Eggers University of Bristol Generic free surface singularities	Room 1

Thursday 13th December 2012
10:00 to 11:00	Surfaces and curvature in Euler and Navier-Stokes simulations. Where next?	Discussion Room
11:30 to 12:30	Michael Proctor University of Cambridge Modern trends in dynamo theory	Room 1

Tuesday 18th December 2012
11:30 to 12:30	Mark Dennis University of Bristol Vikings in shades: navigating by skylight polarization	Room 1

Thursday 20th December 2012
11:30 to 12:30	Sergey Nazarenko University of Warwick Quadratic invariants for clusters of resonant wave triads	Room 1

Topological dynamics in the physical and biological sciences

Organisers

Konrad Bajer Uniwersytet Warszawski
Tom Kephart
Yoshi Kimura Nagoya University
Keith Moffatt University of Cambridge
Andrzej Stasiak Université de Lausanne

Speakers

Konrad Bajer Uniwersytet Warszawski
Phil Boyland University of Florida
Victor Buchstaber Steklov Mathematical Institute, Russian Academy of Sciences
Dorothy Buck Imperial College London
Roman Buniy Chapman University
Jason Cantarella University of Georgia
Marek Cieplak Polish Academy of Sciences
Mark Dennis University of Bristol
Giovanni Dietler Centre de Physique Théorique de l’Ecole Polytechnique (CPHT)
Jens Eggers University of Bristol
John Gibbon Imperial College London
Andrzej Herczynski Boston College
Gunnar Hornig University of Dundee
William Irvine University of Chicago
Efim Kats L.D.Landau Institute for Theoretical Physics, Moscow
Louis Kauffman University of Illinois at Chicago
Tom Kephart Vanderbilt University
Richard Kerner Université Pierre et Marie Curie Paris
Shigeo Kida Kyoto University
Rob Kusner University of Massachusetts
Tony Leonard CALTECH (California Institute of Technology)
Tomasz Lipniacki Polish Academy of Sciences
Xin Liu University of Sydney
Francesca Maggioni Università degli studi di Bergamo
Kenneth Millett University of California, Santa Barbara
Sergey Nazarenko University of Warwick
Eleni Panagiotou National Technical University of Athens
Clare Parnell University of St Andrews
Jason Parsley Wake Forest University
Michael Proctor University of Cambridge
Tudor Ratiu Centre de Physique Théorique de l’Ecole Polytechnique (CPHT)
Shahin Rouhani Sharif University of Technology
Alexander Shnirelman Concordia University
Clayton Shonkwiler University of Georgia
Piotr Szymczak Uniwersytet Warszawski
Denis Weaire Trinity College Dublin
Asher Yahalom Ariel University Center of Samaria
Tomoo Yokoyama Hokkaido University
Lynn Zechiedrich Baylor College of Medicine

Show All

Topological dynamics in the physical and biological sciences

Programme theme

Preprints

Finite type invariants of magnetic lines

Relativistic helicity and link in Minkowski space-time

The symplectic geometry of closed equilateral random walks in 3-Space

Reconnection of skewed vortices

Topological constraints and their breakdown in dynamical evolution

The expected total curvature of random polygons

The fluid dynamics of James Clerk Maxwell

The tight knot spectrum in QCD

Applications of Lagrangian reduction to condensed matter

Helical organization of tropical cyclones

Generalized helicity and Beltrami fields

Discrete groups and internal symmetries of icosahedral viral capsids

Workshops

Topological fluid dynamics (IUTAM symposium)

Topological aspects of DNA function and protein folding

Tangled magnetic fields in astro- and plasma physics

Quantised flux in tightly knotted and linked systems

Topological vorticity dynamics in the physical and biological sciences

Seminars

Organisers

Speakers

Supported By

Topological dynamics in the physical and biological sciences

Programme theme

Preprints

Finite type invariants of magnetic lines

Relativistic helicity and link in Minkowski space-time

The symplectic geometry of closed equilateral random walks in 3-Space

Reconnection of skewed vortices

Topological constraints and their breakdown in dynamical evolution

The expected total curvature of random polygons

The fluid dynamics of James Clerk Maxwell

The tight knot spectrum in QCD

Applications of Lagrangian reduction to condensed matter

Helical organization of tropical cyclones

Generalized helicity and Beltrami fields

Discrete groups and internal symmetries of icosahedral viral capsids

Workshops

Topological fluid dynamics (IUTAM symposium)

Topological aspects of DNA function and protein folding

Tangled magnetic fields in astro- and plasma physics

Quantised flux in tightly knotted and linked systems

Topological vorticity dynamics in the physical and biological sciences

Seminars

Organisers

Speakers

Supported By

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