ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAF
1
MondayTuesdayWednesdayThursdayFriday
2
3
10:00--10:30Welcome and coffee09:30--11:00Garban 209:30--11:00Peltola 209:30--11:00Kahle 309:30--11:00Kahle 4
4
10:30--12:00Garban 111:00--11:30Coffee break11:00--11:30Coffee break11:00--11:30Coffee break11:00--11:30Coffee Break
5
11:30--13:00Kahle 211:30--13:00Garban 311:30--13:00Peltola 311:30--13:00Peltola 4
6
7
afternooncontributed talks
(20' talk + 5' questions)
8
13:30--15:00Kahle 114:30--14:55DewanTitle: Gaussian first passage percolation


Abstract: The model of percolation given by sub-level sets of continuous Gaussian fields on R^d with fast decorrelation features many analogous properties with Bernoulli percolation on Z^d, including a sharp phase transition. The extent of these analogies is the subject of many recent investigations. One natural direction is to try and extend the comparison to the random pseudometric model of first passage percolation (FPP). In the lattice model, it consists in assigning independently a non-negative random variable of same law to each edge, and defining the distance T(x,y) between two vertices x and y as the least sum of these random variables among all edge paths between x and y.
We will explain how a natural counterpart of such a model can be defined in the setting of continuous Gaussian fields. We will then show how, just like in the lattice case, the important factor in the behaviour of the model is whether or not the zero-distance clusters percolate.		Free Afternoon
9
15:00--15:30Coffee break14:55--15:20AbuzaidTitle: On the thermodynamic limit of self-avoiding random walk

Abstract: A self-avoiding random walk is a uniformly sampled injective path of N steps in an infinite (square) lattice started from a fixed vertex. One of the main open problems is the existence of a unique weak limit of the random paths as N tends to infinity. I will share my on-going attempts at understanding the limiting object by reducing the analysis to so called initial box patterns and their properties.
10
15:30--17:00Peltola 115:20--15:45JaverzatTitle: Evidences of conformal invariance in 2D rigidity percolation

Abstract: It is a very remarkable and yet not understood fact that critical phenomena have conformally invariant
statistical properties. Although it is implied by scale invariance for systems with local interactions,
there is no reason to expect so when the degrees of freedom are non local, as for instance in percolation
phenomena. Nevertheless, it seems that conformal invariance emerges also in these latter cases, and
examples of scale but not conformal systems remain extremely rare.
Here, we reveal the existence of such symmetry for two-dimensional rigidity percolation that belongs
to a different universality class than connectivity percolation, and for which the question of conformal
invariance had not been addressed so far. The rigidity transition occurs at higher filling fraction than
connectivity percolation, when percolating clusters become able to transmit and ensure mechanical
stability to the overall disordered network. We show that i) these clusters are conformally invariant
random fractals and ii) we use conformal field theory to predict the form of universal finite size effects.
Our findings open a new avenue for the application of conformal field theories in physical and
biological systems exhibiting such a mechanical transition.		14:30--16Garban 4
11
15:45--16:15Coffee break
12
16:15--16:40LippolisTitle: Topology and statistics of noisy chaos

Abstract: It is well known that the phase space of a chaotic system has a self-similar (fractal) structure of infinite resolution. In reality, every system experiences noise, coming from experimental uncertainties, neglected degrees of freedom, or roundoff errors, for example. No matter how weak, noise smoothens out fractals, giving the system a finite resolution. The consequences are dramatic for the computation of long-time dynamical averages, such as diffusion coefficients or escape rates, since infinite-dimensional operators describing the evolution of the system (such as Fokker-Planck) effectively become finite matrices. In this setting, we solve the problem of statistical mechanics by studying the topology (partitioning and symbolic dynamics) of the noisy phase space, and describe the dynamics via Markov graphs, whose determinants yield the expectation values of the desired observables.
13
16:40--17:05RoldanTitle: Topology of random 2-dimensional cubical complexes

Abstract: We study a natural model of random 2-dimensional cubical complexes which are subcomplexes of an n-dimensional cube, and where every possible square (2-face) is included independently with probability p. Our main result exhibits a sharp threshold p=1/2 for homology vanishing as the dimension n goes to infinity. This is a 2-dimensional analogue of the Burtin and Erdős-Spencer theorems characterizing the connectivity threshold for random graphs on the 1-skeleton of the n-dimensional cube. Our main result can also be seen as a cubical counterpart to the Linial-Meshulam theorem for random 2-dimensional simplicial complexes. However, the models exhibit strikingly different behaviors. We show that if p > 1 - √1/2 ≈ 0.2929, then with high probability the fundamental group is a free group with one generator for every maximal 1-dimensional face. As a corollary, homology vanishing and simple connectivity have the same threshold. This is joint work with Matthew Kahle and Elliot Paquette.
14
17:05--17:30MaibachTitle: From the Weyl Anomaly Formula to the Virasoro Algebra

Abstract: In Euclidean two-dimensional conformal field theory, the Weyl anomaly formula gives the factor by which correlation functions change under local rescaling of the metric.

The "Liouville action" in this factor can be written as an anti-symmetric pairing on conformally equivalent metrics. Properties of this pairing allow the definition of a real determinant line - a real one-dimensional vector space associated to the surface, which captures the Weyl anomaly.

These determinant lines form a vector bundles over moduli spaces of Riemann surfaces.
Here I will focus on the moduli space of cylinders, which forms a semigroup under the gluing of cylinders along their boundary components.
The determinant lines together with the gluing operation induce a central extension of the diffeomorphism group of the circle. I explicitly compute that the associated Lie algebra is the Virasoro algebra - the algebra of symmetries in conformal field theory.

Related topics include modular functors, Virasoro uniformization and Malliavin-Kontsevich-Suhov loop measures.
15
17:30--17:55Adame-CarrilloTitle: The Virasoro representation of double-dimers

Abstract: We consider a discretization of the action of symplectic fermions —a CFT at c=-2 in the Physics literature— that combinatorically encodes uniform double-dimers, which is also conjectured to be described by a CFT at c=-2. Using techniques of discrete complex analysis, we construct a representation of the c=-2 Virasoro algebra on a subspace of random variables of the model of double-dimers.
16
17
20:00Social dinner
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100