A new frontier has emerged at the interface between probability, geometry, and analysis, with a central target to produce a coherent theory of the geometry of random structures. The principal question is the following: within a given structure, what is the interplay between randomness and geometry? More precisely, does the geometry appear to be random at every scale (i.e. fractal), or do fluctuations "average out" at sufficiently large scales? Can the global geometry be described by taking a suitable scaling limit that allows for concrete computations?
Spectacular progress has been made over the last ten years in this domain. The goal of the programme is to gather experts from probability, geometry, analysis and other connected areas, in order to study aspects of this question in some paradigmatic situations. Topics of particular relevance include the Gaussian Free Field, random planar maps and Liouville quantum gravity, in connection with conformally invariant scaling limits; spin glass models and branching random walks; percolation and random graphs; and random walks on graphs and groups in the case where the geometry is determined by some algebraic ambient structure.
Click here to download the programme's final scientific report
Title | Year | Programme | |
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One-dimensional scaling limits in a planar Laplacian random growth modelAuthors: Fredrik Viklund, Alan Solar, Amanda Turner |
2014 | RGM | 20 February 2019 |
Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map I: cone timesAuthors: E Gwynne, C Mao, X Sun |
2014 | RGM | 21 October 2016 |
On the stability of geodesics in the Brownian mapAuthors: O Angel, B Kolesnik, G Miermont |
2014 | RGM | 21 October 2016 |
The front location in BBM with decay of massAuthors: L Addario-berry |
2014 | RGM | 21 October 2016 |
Joint convergence of random quadrangulations and their coresAuthors: L Addario-berry, Y Wen |
2014 | RGM | 21 October 2016 |
A probabilistic approach to block sizes in random mapsAuthors: L Addario-berry |
2014 | RGM | 21 October 2016 |
Diameter and stationary distributions of random $\it r$-out digraphsAuthors: L Addario-berry, B Balle, G Perarnau |
2014 | RGM | 21 October 2016 |
Scaling limits for the critical Fortuin-Kastelyn model on a random planar map II: local estimates and empty reduced word exponentAuthors: E Gwynne, X Sun |
2014 | RGM | 21 October 2016 |
Logarithmic coefficients and generalized multifractality of whole-plane SLEAuthors: B Duplantier, H Ho, B Le, M Zinsmeister |
2014 | RGM | 21 October 2016 |
A Hamiltonian crycle in the square of a 2-connected graph in linear timeAuthors: S Alstrup, A Georgakopolous, E Rotenberg, C Thomassen |
2014 | RGM | 21 October 2016 |
Hyperbolicity vs. amenability for planar graphsAuthors: B Federici, A Georgakopoulos |
2014 | RGM | 21 October 2016 |
9 July 2018 to 20 July 2018
The Organisers would like to thank the following sponsors for their generous support of the event:
Monday 26th January 2015 | |||
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11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
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14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 |
Aperiodic hierarchical conformal tilings: random at the ends? |
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17:00 to 18:00 | No Room Required |
Tuesday 27th January 2015 | |||
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09:00 to 10:00 |
Parafermionic observables and order of the phase transition in planar random-cluster models |
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10:00 to 11:00 | Room 1 | |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
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14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 |
Conformal invariance of boundary touching loops of FK Ising model |
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Wednesday 28th January 2015 | |||
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09:00 to 10:00 | Room 1 | |
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10:00 to 11:00 | Room 1 | |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
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14:30 to 15:00 | No Room Required | ||
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19:30 to 22:00 |
Conference Dinner at Cambridge Union Society hosted by Cambridge Dining Co. |
No Room Required |
Thursday 29th January 2015 | |||
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09:00 to 10:00 | Room 1 | |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 |
Some scaling limit results for critical Fortuin-Kastelyn random planar map model |
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Friday 30th January 2015 | |||
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09:00 to 10:00 |
Scaling limits of critical Ising correlation functions in planar domains |
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10:00 to 11:00 |
Renormalization Approach to the 2-Dimensional Uniform Spanning Tree |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
Monday 2nd February 2015 | |||
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16:00 to 17:00 |
Rothschild Distinguished Visiting Fellow Lecture: Random maps and random 2-dimensional geometries |
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17:00 to 18:00 | No Room Required |
Thursday 26th February 2015 | |||
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10:00 to 12:00 | Room 2 |
Friday 27th February 2015 | |||
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14:00 to 15:00 | Room 2 |
Tuesday 17th March 2015 | |||
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10:00 to 11:00 | Room 1 | |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Delocalization of two-dimensional random surfaces with hard-core constraints |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 |
Small-particle limits in a regularized Laplacian random growth model |
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15:00 to 15:30 | No Room Required | ||
15:30 to 16:30 | Room 1 | |
Wednesday 18th March 2015 | |||
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10:00 to 11:00 |
Branching Brownian motion, the Brownian net and selection in spatially structured populations |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 |
Genealogies with recombination in spatial population genetics |
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15:00 to 15:30 | No Room Required | ||
15:30 to 16:30 |
Branching processes with competition by pruning of Levy trees |
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19:30 to 22:00 | No Room Required |
Thursday 19th March 2015 | |||
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10:00 to 11:00 |
A multi-scale refinement of the second moment method Co-authors: L.P |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 |
On the complex cascade and the complex branching Brownian motion |
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15:00 to 15:30 | No Room Required | ||
15:30 to 16:30 |
Maxima of log-correlated Gaussian fields and of the Riemann Zeta function on the critical line |
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Friday 20th March 2015 | |||
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10:00 to 11:00 | Room 1 | |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Rate of convergence of the mean of sub-additive ergodic processes |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 |
Uniformity of the late points of random walk on $\mathbb{Z}_d^n$ for $d \geq 3$ |
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15:00 to 15:30 | No Room Required | ||
15:30 to 16:30 | Room 1 |
Wednesday 25th March 2015 | |||
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Wednesday 1st April 2015 | |||
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Wednesday 8th April 2015 | |||
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Friday 10th April 2015 | |||
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14:30 to 16:30 | Discussion Room |
Wednesday 15th April 2015 | |||
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10:00 to 12:00 | Room 2 |
Monday 20th April 2015 | |||
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09:00 to 09:50 | No Room Required | ||
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 |
Scaling constants and the lazy peeling of infinite Boltzmann planar maps |
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16:30 to 17:30 | No Room Required |
Tuesday 21st April 2015 | |||
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
A hidden quantum group for pure partition functions of multiple SLEs |
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12:30 to 13:30 | No Room Required | ||
14:00 to 16:00 | Room 2 | ||
14:00 to 15:00 | Room 1 | ||
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15:30 to 16:30 | Room 1 | |
Wednesday 22nd April 2015 | |||
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09:00 to 10:00 |
On the geometry of discrete and continuous random planar maps |
Room 1 | |
10:00 to 11:00 |
On classes of planar maps with $\alpha$-orientations having geometric interpretations |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Nesting statistics in the O(n) loop model on random lattices |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 | Room 1 | |
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15:00 to 15:30 | No Room Required | ||
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19:30 to 22:00 | No Room Required |
Thursday 23rd April 2015 | |||
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10:00 to 11:00 |
Characterstic polynomials of random matrices and logarithmically correlated processes |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Pinning and disorder relevance for the lattice Gaussian free field |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 | Room 1 | |
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15:30 to 16:30 | Room 1 | |
Friday 24th April 2015 | |||
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10:00 to 11:00 | Room 1 | |
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11:00 to 11:30 | No Room Required | ||
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 | Room 1 | |
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15:00 to 15:30 | No Room Required | ||
15:30 to 16:30 |
Scaling limits of random planar maps and growth-fragmentations |
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Wednesday 6th May 2015 | |||
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Wednesday 13th May 2015 | |||
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Wednesday 20th May 2015 | |||
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Wednesday 27th May 2015 | |||
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Wednesday 3rd June 2015 | |||
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Wednesday 10th June 2015 | |||
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Tuesday 16th June 2015 | |||
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09:00 to 10:00 | Room 1 | |
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10:00 to 10:10 | No Room Required | ||
10:10 to 11:10 |
On Disconnection, random walks, random interlacements, and the Gaussian free field |
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11:10 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 |
Convergence of discrete holomorphic functions on non-uniform lattices |
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15:00 to 15:30 | No Room Required | ||
15:30 to 16:30 | Room 1 | |
Wednesday 17th June 2015 | |||
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10:00 to 10:10 | No Room Required | ||
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11:10 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 | Room 1 | |
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15:00 to 15:30 | No Room Required | ||
15:30 to 16:30 |
Where Planar Simple Random Walk Loses its Rotational Symmetry |
Room 1 | |
19:30 to 22:00 | No Room Required |
Thursday 18th June 2015 | |||
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10:00 to 11:00 | Room 1 | |
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11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
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12:30 to 13:30 | No Room Required | ||
14:00 to 15:00 |
Scaling limit of the probability that loop-erased random walk uses a given edge |
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15:00 to 15:20 | No Room Required | ||
15:20 to 16:20 | Room 1 | |
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16:20 to 16:30 | No Room Required | ||
16:30 to 17:30 | Room 1 | |
Wednesday 24th June 2015 | |||
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Wednesday 1st July 2015 | |||
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10:00 to 12:00 | Room 2 |
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