Mathematical Harmony and the Quantum World

# Mathematical Harmony and the Quantum World

## Practical information

The conference will take place in Salle Dussane at the Ecole Normale Supérieure (45 rue d'Ulm, 75005 Paris). The Salle Dussane is room number 9 on this map of the ground floor of 45 rue d'Ulm. The easiest way to get in would be through the corner entry at La Rotonde (room 6), but for security reasons we are not sure if this entry will be open. Alternatively get in from rue d'Ulm via the Accueil (room 3), then enter the main building at the stairs (arrow between 7 and 8), turn left and walk to the end of the aile (dark gray), and finally access Salle Dussane (room 9) from the aile (between 9 and 16).
We can arrange for the accommodation of speakers. Please reply to the email that you have received from the conference secretary.

## Timetable

Time Thursday 14 Oct Time Friday 15 Oct Time Saturday 16 Oct
9:20-9:40 J.-B. Zuber 9:20-9:40 B. Doyon 9:20-9:40 L. Cantini
9:45-10:15 G. Felder 9:45-10:15 M. Bauer 9:45-10:15 F. Smirnov
10:20-10:50 A. Kupiainen 10:20-10:50 B. Derrida 10:20-10:50 P. Di Francesco
10:55-11:15 Coffee break 10:55-11:15 Coffee break 10:55-11:15 Coffee break
11:15-11:35 V. Pasquier 11:15-11:35 L. Cugliandolo 11:15-11:35 O. Castro-Alvaredo
11:40-12:05 A. Cappelli 11:40-12:05 V. Vargas 11:40-12:05 J. De Nardis
12:10-12:30 T. Jin 12:10-12:30 A. Tilloy 12:10-12:30 A. De Luca
12:35-14:00 Lunch 12:35-14:00 Lunch 12:35-13:05 A. LeClair
14:00-14:20 R. Rhodes 14:00-14:20 T. Benoist 14:00-23:59 Discussion time
14:25-14:45 J. Viti 14:25-14:45 H. Orland
14:50-15:10 G. Sierra 14:50-15:20 G. Falkovich
15:15-15:35 P. Le Doussal 15:25-15:55 J. Thierry-Mieg
15:40-16:00 Coffee break 16:00-16:30 P. Wiegmann
16:05-16:25 S. Majumdar 16:35-16:55 Coffee break
16:30-16:50 K. Kytölä 17:00-17:30 Surprise
16:55-17:15 H. Saleur
20:00-23:59 Banquet dinner

## Remote speakers join via this Zoom link!

Topic: Mathematical Harmony and the Quantum World
Meeting ID: 845 8252 5861
Passcode: Br0TZr

## Titles and abstracts

### Michel Bauer: A quantum $0-\infty$ alternative

We present a quantum recreational mathematics result related to a classical puzzle. If time permits, we'll explain the (distant) original physical motivations.

### Tristan Benoist: Purification and stationary distrubution(s) of states for quantum trajectories

Quantum trajectories are random evolutions describing quantum system subject to repeated indirect measurements. I will present the relationship between purification of the trajectory state and the stationary distribution(s) of states for these dynamics.

### Andrea Cappelli: Fermions from elsewhere

Topological phases of matter possess both fermionic and bosonic descriptions. As such, they provide insights on bosonization in any dimension. I discuss how relativistic fermions in $(2+1)$ dimensions can be expressed in terms of gauge fields.

### Olalla Castro-Alvaredo: Twist fields and entanglement

In this short talk I will give an overview of how different types of symmetry fields or twist fields emerge in the context of entanglement measures.

### Leticia Cugliandolo: Two dimensional melting of passive and active matter

Long-range translational order is forbidden in low dimensional systems with short-range interactions: solid phases only have quasi long-range translational order. A mechanism for the transition from solid to liquid led by the dissociation of dislocation pairs was proposed by Kosterlitz & Thouless in their 1972 & 1973 Nobel prize papers. Knowing that long-range orientational order is possible in two dimensions, Nelson, Halperin and Young argued that the transition actually occurs in two steps, the second one being triggered by the unbinding of disclinations. In this picture the intermediate phase keeps quasi long-range orientational order, and the two transitions are of infinite order. Based on simulations of hard disks performed with advanced numerical methods, the latter picture was recently questioned. In this talk I will review the current understanding of melting in two dimensions and I will extend its analysis to systems made of self-propelled particles, the constituents of active matter, a new kind of soft matter relevant to describe numerous biological problems.

### Bernard Derrida: Large deviation functions of the density and of the current for diffusive systems

After a short review of the different approaches used to determine the large deviation functions of diffusive systems in their steady state, the talk will present a few recent results:
1. How these large deviations functions are modified by weak contacts with the boundaries
2. What is the influence of conditioning these large deviation functions on the current

Derrida, Hirschberg, Sadhu, (2021). Large deviations in the symmetric simple exclusion process with slow boundaries. Journal of Statistical Physics, 182, 1-13.
Derrida, Sadhu, (2019). Large deviations conditioned on large deviations I: Markov chain and Langevin equation. Journal of Statistical Physics, 176, 773-805.
Derrida, Sadhu, (2019). Large deviations conditioned on large deviations II: fluctuating hydrodynamics. Journal of Statistical Physics, 177, 151-182.

### Philippe Di Francesco: Dualities in Macdonald/Toda theory and quantum $Q$-systems

We show how one can use dualities in the theory of Macdonald operators and polynomials to prove the Macdonald-Cluster algebra conjecture, stating that for almost all (affine, twisted) types, Macdonald operators at infinite t are cluster variables in the quantum cluster algebra of the corresponding $Q$-system.

### Gregory Falkovich: Fibonacci turbulence

I shall describe a family of one-dimensional models which bridge wave and vortical turbulence. That family may present our so far best shot to develop dynamical renormalization group approach to turbulence.

### Satya Majumdar: Effective Langevin equation for constraint stochastic processes

In this talk, I will discuss how to derive an exact effective Langevin equation for a stochastic process subject to either geometric or dynamical constraints. After describing a few single particle examples, I'll generalise our method to a multiparticle process with interaction, namely the "nonintersecting Brownian bridges" and discuss its connection to random matrix theory.

### Vincent Pasquier: On discrete time lattice models

I shall describe some temporal discretizations of lattice models which preserve integrability: BBS, discretized Toda and Landau Lifschitz equation.

### Hubert Saleur: The CFT of the two-dimensional loop gas

I will give a short and qualitative summary of our recent determination of four-point functions in the 2D conformal loop ensemble

### Jean Thierry-Mieg: Superalgebraic $SU(2|1)$ model of leptons and quarks

I'll outline recent progress towards a QFT of the electroweak interactions displaying an internal SU(2/1) structure, based on the new concept of a superalgebra valued superselfdual connection polyform which unifies scalars, vectors and Avdeev-Chizhov tensors.

### Jacopo Viti: CFTs on genus two Riemann surfaces and applications to entanglement negativity

I'll show how CFT partition functions on $Z_3$ symmetric Riemann surfaces can be computed by a fastly convergent series expansion. I'll discuss applications to entanglement negativity in rational conformal theories with $c<1$.

### Jean-Bernard Zuber: Foreword

Four words on Denis' trajectory

## COVID-19 measures

For the safety of all participants, all mandatory sanitary restrictions related to the ongoing Covid-19 epidemics will be implemented throughout the duration of the conference. In particular, participants might be required to wear masks inside the conference venue.