SFT 2026 - Lectures on Statistical Field Theories

2 Feb 2026, 11:10 → 13 Feb 2026, 18:00 Europe/Rome

GGI

The aim of the school is to bring together PhD students with interests in low-dimensional quantum field theory, conformal field theory and integrable models, and their applications to statistical mechanics and condensed matter systems, and to help them build a solid and specialized background on these topics. The school provides a range of postgraduate courses covering introductory topics as well as recent developments.

Lectures are scheduled for four hours each morning, for a total amount of forty hours, over two weeks. Presentations are given at the blackboard. The afternoon is devoted to exercises, study, and discussions with lecturers and senior participants. A desk and standard research facilities are provided to all participants.

The school can admit up to fifty participants. Accommodation for two weeks in shared rooms can be provided for a total price of approximately 500 €. Financial support for this accommodation may be granted upon request.
The admitted participants will be contacted by GGI secretariat at the end of December.
The courses can be included in the the Ph.D. curricula of Italian universities and abroad. If necessary, exams on the courses can be taken.

 

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Topics

Bernard Derrida (Collège de France): Large deviations of non-equilibrium diffusive systems
Jérôme Dubail (Université de Strasbourg): An introduction to 2d CFT for stat-phys and cond-mat students
Gregory Falkovich (Weizmann Institute of Science): Introduction to Information Theory
Paul Fendley (University of Oxford): The basics of non-invertible symmetries and dualities
Maria Vozmediano (ICM - CSIC, Madrid): Thermal transport, geometry, and anomalies

Organizers
Vincenzo Alba (University of Pisa)
Jerome Dubail (CNRS and University of Strasbourg)
Cristiane de Morais Smith (University of Utrecht)
Andrea Trombettoni (University of Trieste)


Advisory board
Denis Bernard (ENS, Paris)
Pasquale Calabrese (SISSA, Trieste)
Andrea Cappelli (INFN, Florence)
Filippo Colomo (INFN, Florence)
Fabian Essler (University of Oxford)
Giuseppe Mussardo (SISSA, Trieste)


Local organizer
Andrea Cappelli, Filippo Colomo

Contact
andrea.cappelli@fi.infn.it
filippo.colomo@fi.infn.it

poster551.pdf

Monday 2 February

Bernard Derrida (Collège de France) - Large deviations of non-equilibrium diffusive systems: Bernard Derrida - Large deviations of non-equilibrium diffusive systems

After an introduction to large deviations and Markov process [2,5,6], these lectures will try
to show, through simple examples, that non-equilibrium systems have a number of properties
which contrast with those of systems at equilibrium: phase transitions in one dimension [3],
non local free energy functional, long range correlations [1,4,5], etc. . These lectures will also
try to give a review of theoretical methods such as the matrix ansatz, the Bethe ansatz, or the
macroscopic fluctuation theory [1], developed in the theory of non-equilibrium phenomena,
which allow one to calculate the fluctuations and large deviations of the density and of the
current in non-equilibrium steady states [1,4,5] of systems like exclusion processes.

Video

1 Gong seminar

Tuesday 3 February

Bernard Derrida (Collège de France) - Large deviations of non-equilibrium diffusive systems

After an introduction to large deviations and Markov process [2,5,6], these lectures will try
to show, through simple examples, that non-equilibrium systems have a number of properties
which contrast with those of systems at equilibrium: phase transitions in one dimension [3],
non local free energy functional, long range correlations [1,4,5], etc. . These lectures will also
try to give a review of theoretical methods such as the matrix ansatz, the Bethe ansatz, or the
macroscopic fluctuation theory [1], developed in the theory of non-equilibrium phenomena,
which allow one to calculate the fluctuations and large deviations of the density and of the
current in non-equilibrium steady states [1,4,5] of systems like exclusion processes.

Video

Gregory Falkovich (Weizmann Institute of Science) - Introduction to Information Theory

This is an informal and nontechnical introduction for physicists. It is panoramic to let you see how
many problems in physics, mathematics, engineering, biology, brain science, economics, and linguistics could be solved by physicists who know what entropy and free energy are. Will also include basics of quantum information and black hole entropy.
Based on the recently published textbook
https://press.princeton.edu/books/hardcover/9780691266534/the-physical-nature-of-informatio

Video

Wednesday 4 February

Gregory Falkovich (Weizmann Institute of Science) - Introduction to Information Theory

This is an informal and nontechnical introduction for physicists. It is panoramic to let you see how
many problems in physics, mathematics, engineering, biology, brain science, economics, and linguistics could be solved by physicists who know what entropy and free energy are. Will also include basics of quantum information and black hole entropy.
Based on the recently published textbook
https://press.princeton.edu/books/hardcover/9780691266534/the-physical-nature-of-informatio

Video

Bernard Derrida (Collège de France) - Large deviations of non-equilibrium diffusive systems

After an introduction to large deviations and Markov process [2,5,6], these lectures will try
to show, through simple examples, that non-equilibrium systems have a number of properties
which contrast with those of systems at equilibrium: phase transitions in one dimension [3],
non local free energy functional, long range correlations [1,4,5], etc. . These lectures will also
try to give a review of theoretical methods such as the matrix ansatz, the Bethe ansatz, or the
macroscopic fluctuation theory [1], developed in the theory of non-equilibrium phenomena,
which allow one to calculate the fluctuations and large deviations of the density and of the
current in non-equilibrium steady states [1,4,5] of systems like exclusion processes.

Video

Healthy Minds for Masterminds & Discussion

Thursday 5 February

Bernard Derrida (Collège de France) - Large deviations of non-equilibrium diffusive systems

After an introduction to large deviations and Markov process [2,5,6], these lectures will try
to show, through simple examples, that non-equilibrium systems have a number of properties
which contrast with those of systems at equilibrium: phase transitions in one dimension [3],
non local free energy functional, long range correlations [1,4,5], etc. . These lectures will also
try to give a review of theoretical methods such as the matrix ansatz, the Bethe ansatz, or the
macroscopic fluctuation theory [1], developed in the theory of non-equilibrium phenomena,
which allow one to calculate the fluctuations and large deviations of the density and of the
current in non-equilibrium steady states [1,4,5] of systems like exclusion processes.

Video

Gregory Falkovich (Weizmann Institute of Science) - Introduction to Information Theory

This is an informal and nontechnical introduction for physicists. It is panoramic to let you see how
many problems in physics, mathematics, engineering, biology, brain science, economics, and linguistics could be solved by physicists who know what entropy and free energy are. Will also include basics of quantum information and black hole entropy.
Based on the recently published textbook
https://press.princeton.edu/books/hardcover/9780691266534/the-physical-nature-of-informatio

Video

Jérôme Dubail (Université de Strasbourg) - Introduction to 2d CFT for stat-phys and cond-mat students

I intend to give an introductory course on basic concepts of 2d CFT, with a focus on how to derive
simple universal results in problems from statistical physics and condensed matter. If time permits, I
would like to cover:
1. Conformal mapping
2. How to calculate with the Gaussian free field
3. Basic structures of CFT (stress-tensor and central charge, OPEs, Hilbert space of a 2d CFT)
4. Phase diagrams of 2d stat-mech models and matching with CFT. Glimpse of random geometric
phenomena (critical percolation)
5. Universality in 1d quantum critical systems. Luttinger liquids, entanglement entropy, heat capacity, etc.

Video playlist

Friday 6 February

Jérôme Dubail (Université de Strasbourg) - Introduction to 2d CFT for stat-phys and cond-mat students

I intend to give an introductory course on basic concepts of 2d CFT, with a focus on how to derive
simple universal results in problems from statistical physics and condensed matter. If time permits, I
would like to cover:
1. Conformal mapping
2. How to calculate with the Gaussian free field
3. Basic structures of CFT (stress-tensor and central charge, OPEs, Hilbert space of a 2d CFT)
4. Phase diagrams of 2d stat-mech models and matching with CFT. Glimpse of random geometric
phenomena (critical percolation)
5. Universality in 1d quantum critical systems. Luttinger liquids, entanglement entropy, heat capacity, etc.

Video playlist

Bernard Derrida (Collège de France) - Large deviations of non-equilibrium diffusive systems

After an introduction to large deviations and Markov process [2,5,6], these lectures will try
to show, through simple examples, that non-equilibrium systems have a number of properties
which contrast with those of systems at equilibrium: phase transitions in one dimension [3],
non local free energy functional, long range correlations [1,4,5], etc. . These lectures will also
try to give a review of theoretical methods such as the matrix ansatz, the Bethe ansatz, or the
macroscopic fluctuation theory [1], developed in the theory of non-equilibrium phenomena,
which allow one to calculate the fluctuations and large deviations of the density and of the
current in non-equilibrium steady states [1,4,5] of systems like exclusion processes.

Video

2 Discussion

Monday 9 February

Jérôme Dubail (Université de Strasbourg) - Introduction to 2d CFT for stat-phys and cond-mat students

I intend to give an introductory course on basic concepts of 2d CFT, with a focus on how to derive
simple universal results in problems from statistical physics and condensed matter. If time permits, I
would like to cover:
1. Conformal mapping
2. How to calculate with the Gaussian free field
3. Basic structures of CFT (stress-tensor and central charge, OPEs, Hilbert space of a 2d CFT)
4. Phase diagrams of 2d stat-mech models and matching with CFT. Glimpse of random geometric
phenomena (critical percolation)
5. Universality in 1d quantum critical systems. Luttinger liquids, entanglement entropy, heat capacity, etc.

Video playlist

Maria Vozmediano (ICM-CSIC, Madrid) - Thermal transport, geometry, and anomalies

The aim of this course is to introduce students to the ideas and techniques that, originating in
so-called `high-energy’ physics, have become standard tools in statistical physics and
condensed matter physics in the 21st century. In particular, we will revisit effective actions,
introduce quantum anomalies and anomaly-related transport, and the relationship between
thermal transport and general relativity. The course is motivated by some of the new
developments in condensed matter physics in the 21st century that have led to a new grand
unification of high- and low-energy physics.

Video playlist

3 Spritz of Science - Paul Fendley - Two cultures separated by a common language

Abstract:
athematics and physics have different cultures and are practiced by different tribes. Much invective has been designed to instil tribal loyalty, with pronouncements ranging from “Mathematics is the handmaiden of physics” to “Throughout mathematics, inspiration and the hard work of completing proofs are necessary. No guide from physics can help.” Nonetheless, quality research bridging the two is easy to find. Mathematics is at the core of physics, and time and time again, results in physics have proved essential to mathematics. I’ll argue that there’s no meaningful dividing line between the two disciplines, and that both cultures would be better off if we stopped worrying about maintaining purity.

Tuesday 10 February

Maria Vozmediano (ICM-CSIC, Madrid) - Thermal transport, geometry, and anomalies

The aim of this course is to introduce students to the ideas and techniques that, originating in
so-called `high-energy’ physics, have become standard tools in statistical physics and
condensed matter physics in the 21st century. In particular, we will revisit effective actions,
introduce quantum anomalies and anomaly-related transport, and the relationship between
thermal transport and general relativity. The course is motivated by some of the new
developments in condensed matter physics in the 21st century that have led to a new grand
unification of high- and low-energy physics.

Video playlist

Jérôme Dubail (Université de Strasbourg) - Introduction to 2d CFT for stat-phys and cond-mat students

I intend to give an introductory course on basic concepts of 2d CFT, with a focus on how to derive
simple universal results in problems from statistical physics and condensed matter. If time permits, I
would like to cover:
1. Conformal mapping
2. How to calculate with the Gaussian free field
3. Basic structures of CFT (stress-tensor and central charge, OPEs, Hilbert space of a 2d CFT)
4. Phase diagrams of 2d stat-mech models and matching with CFT. Glimpse of random geometric
phenomena (critical percolation)
5. Universality in 1d quantum critical systems. Luttinger liquids, entanglement entropy, heat capacity, etc.

Video playlist

Healthy Minds for Masterminds & Discussion

Wednesday 11 February

Jérôme Dubail (Université de Strasbourg) - Introduction to 2d CFT for stat-phys and cond-mat students

I intend to give an introductory course on basic concepts of 2d CFT, with a focus on how to derive
simple universal results in problems from statistical physics and condensed matter. If time permits, I
would like to cover:
1. Conformal mapping
2. How to calculate with the Gaussian free field
3. Basic structures of CFT (stress-tensor and central charge, OPEs, Hilbert space of a 2d CFT)
4. Phase diagrams of 2d stat-mech models and matching with CFT. Glimpse of random geometric
phenomena (critical percolation)
5. Universality in 1d quantum critical systems. Luttinger liquids, entanglement entropy, heat capacity, etc.

Video playlist

Paul Fendley (University of Oxford) - The basics of non-invertible symmetries and dualities

I will explain the basic structure of non-invertible symmetries and dualities using various quantum
spin chains. I will first show how Kramers-Wannier duality provides a canonical example. The key
to finding more general analogs is to define a Hamiltonian using a fusion category; most wellknown quantum spin chains can be defined in such a fashion. Non-invertible symmetries and dualities are then built in from the start. Topological defects provide a key tool, as their action implements the symmetry/duality.
I won’t assume any prior knowledge of duality or categories. It would be useful to understand a little about the quantum Ising Hamiltonian in advance; the level of Wikipedia should be sufficient
(search “transverse-field Ising model”). Most of the material will come from the pair of papers I
wrote with Aasen and Mong (1601.07185 and 2008.08598), but I’ll be presenting it from a somewhat different starting point. Thus there’s no requirement to read them in advance, although of
course a glance wouldn’t hurt.

Video playlist

Thursday 12 February

Maria Vozmediano (ICM-CSIC, Madrid) - Thermal transport, geometry, and anomalies

The aim of this course is to introduce students to the ideas and techniques that, originating in
so-called `high-energy’ physics, have become standard tools in statistical physics and
condensed matter physics in the 21st century. In particular, we will revisit effective actions,
introduce quantum anomalies and anomaly-related transport, and the relationship between
thermal transport and general relativity. The course is motivated by some of the new
developments in condensed matter physics in the 21st century that have led to a new grand
unification of high- and low-energy physics.

Video playlist

Paul Fendley (University of Oxford) - The basics of non-invertible symmetries and dualities

I will explain the basic structure of non-invertible symmetries and dualities using various quantum
spin chains. I will first show how Kramers-Wannier duality provides a canonical example. The key
to finding more general analogs is to define a Hamiltonian using a fusion category; most wellknown quantum spin chains can be defined in such a fashion. Non-invertible symmetries and dualities are then built in from the start. Topological defects provide a key tool, as their action implements the symmetry/duality.
I won’t assume any prior knowledge of duality or categories. It would be useful to understand a little about the quantum Ising Hamiltonian in advance; the level of Wikipedia should be sufficient
(search “transverse-field Ising model”). Most of the material will come from the pair of papers I
wrote with Aasen and Mong (1601.07185 and 2008.08598), but I’ll be presenting it from a somewhat different starting point. Thus there’s no requirement to read them in advance, although of
course a glance wouldn’t hurt.

Video playlist

Discussion

Friday 13 February

Paul Fendley (University of Oxford) - The basics of non-invertible symmetries and dualities

I will explain the basic structure of non-invertible symmetries and dualities using various quantum
spin chains. I will first show how Kramers-Wannier duality provides a canonical example. The key
to finding more general analogs is to define a Hamiltonian using a fusion category; most wellknown quantum spin chains can be defined in such a fashion. Non-invertible symmetries and dualities are then built in from the start. Topological defects provide a key tool, as their action implements the symmetry/duality.
I won’t assume any prior knowledge of duality or categories. It would be useful to understand a little about the quantum Ising Hamiltonian in advance; the level of Wikipedia should be sufficient
(search “transverse-field Ising model”). Most of the material will come from the pair of papers I
wrote with Aasen and Mong (1601.07185 and 2008.08598), but I’ll be presenting it from a somewhat different starting point. Thus there’s no requirement to read them in advance, although of
course a glance wouldn’t hurt.

Video playlist

Maria Vozmediano (ICM-CSIC, Madrid) - Thermal transport, geometry, and anomalies

The aim of this course is to introduce students to the ideas and techniques that, originating in
so-called `high-energy’ physics, have become standard tools in statistical physics and
condensed matter physics in the 21st century. In particular, we will revisit effective actions,
introduce quantum anomalies and anomaly-related transport, and the relationship between
thermal transport and general relativity. The course is motivated by some of the new
developments in condensed matter physics in the 21st century that have led to a new grand
unification of high- and low-energy physics.

Video playlist

Discussion