### Schedule

#### 28th January, 2020 - 04:01:00 Emil Akhmedov (ITEP Moscou)

### Ultraviolet Phenomena in AdS Self-interacting Quantum Field Theory

We study the one-loop corrections to correlation functions in quantum field theories in the Anti de Sitter space-time. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are general and applicable to general non-conformal AdS field theories. We also explain why calculations in Euclidean and Lorentzian signatures should differ even at the leading order in non globaly hyperbolic manifolds.

#### 20th January, 2020 - 02:01:00 Alexander M. Polyakov (Princeton University & IHES)

### Turbulence and Quantum Field Theory

#### 26th November, 2019 - 02:11:00 Yifei He (CEA Saclay)

### Geometrical Four-Point Functions of 2d Critical Q-State Potts Model

In this talk I will describe the geometrical four-point functions (cluster connectivities) of 2d critical Q-state Potts model and its relation to minimal models four-point functions. By studying on the RSOS lattice of the ADE type, we provide a geometrical formulation of minimal models four-point functions of operators related to the Potts model and they involve the same types of cluster/loop expansions as that of the Potts model albeit with different weights. I will discuss how our results can be used to extract useful information about the Potts model from minimal models.

#### 26th September, 2019 - 02:09:00 Dmitri Bykov (MPI für Physik, München & Steklov Math. Inst., Moscow & IHES)

### Flag Manifold Sigma-Models

The talk is dedicated to flag manifold sigma-models, which are theories of generalized harmonic maps from a Riemann surface to a manifold of flags in $C^N$. These theories feature interesting geometric properties and are in certain cases examples of the so-called ‘integrable’ models. I will review some of these facts.

#### 16th September, 2019 - 02:09:00 Jens Hoppe (IHES)

### U(1)-invariant minimal 3-manifolds

#### 10th July, 2019 - 11:07:00 Guillaume Bossard (Centre de Physique Théorique, CNRS, Ecole Polytechnique, IP Paris)

### On Supersymmetric E11 Exceptional Field Theory

We shall review how supergravity theories can emerge from an exceptional field theory based on the Kac-Moody group E11 (i.e. E8+++) with gauge symmetry a set of `generalised diffeomorphisms' acting on the fundamental module while preserving E11. The construction relies on a super-algebra T that extends E11 and provides a differential complex for the exceptional fields. A twisted self-duality equation underlying the dynamics can be shown to be invariant under generalised diffeomorphisms provided a certain algebraic identity holds for structure coefficients of the super-algebra T. The fermions of the theory belong to an unfaithful representation of the double cover of a maximal Lorentzian subgroup K(E11). We conjecture that certain tensor products of unfaithful representations are homomorphic to the quotient of specific indecomposable modules of E11. Using these conjectures, we can write a linearised Rarita-Schwinger equation and show that the E11 twisted self-duality equations are supercovariant. The conjectures are checked through computations in level decompositions with respect to maximal parabolic subgroups.

#### 9th July, 2019 - 02:07:00 Eliezer Rabinovici (Hebrew University of Jerusalem & IHES)

### On the Time Dependence of Complexities

The emergence of very long time scales on the gravity side of the AdS/CFT correspondence has led to the introduction of the notion of complexity in the research of quantum gravity. Various notions of complexity have been studied in the area of Quantum Information as well as in Quantum Field Theory. I will discuss, in this context, complexities and the time scales of their evolution following in the various definitions. The physics involved will be stressed where it is understood.

#### 22nd May, 2019 - 03:05:00 Anatoly Dymarsky (University of Kentucky & IHES)

### Quantum KdV Hierarchy in 2nd CFTs

Infinite-dimensional conformal symmetry in two dimensions renders conformal field theories integrable with an infinite hierarchy of quantum KdV charges being in involution. These charges govern the structure of Virasoro descendant states and provide correct formulation for the Eigenstate Thermalization in 2d theories. After covering recent results on Eigenstate Thermalization, I will talk about an ongoing progress of calculating the spectrum of quantum KdV charges and generalized partition function of two dimensional theories in the limit of large central charge. The talk is based onhttps://arxiv.org/abs/1903.03559as well ashttps://arxiv.org/abs/1812.05108and https://arxiv.org/abs/1810.11025

#### 13th May, 2019 - 02:05:00 Pierpaolo Mastrolia (Universita degli Studi di Padova)

### Feynman Integrals and Intersection Theory

I will show that Intersection Theory (for twisted de Rham cohomology) rules the algebra of Feynman integrals. In particular I will address the problem of the direct decomposition of Feynman integrals into a basis of master integrals, showing that it can by achieved by projection, using intersection numbers for differential forms. After introducing a few basic concepts of intersection theory, I will show the application of this novel method, first, to special mathematical functions, and, later, to Feynman integrals on the maximal cuts, also explaining how differential equations and dimensional recurrence relations for master Feynman integrals can be directly built by means of intersection numbers. The presented method exposes the geometric structure beneath Feynman integrals, and offers the computational advantage of bypassing the system-solving strategy characterizing the standard reduction algorithms, which are based on integration-by-parts identities. Examples of applications to multi-loop graphs contributing to multiparticle scattering, involving both massless and massive particles are presented.

#### 26th April, 2019 - 02:04:00 Apratim Kaviraj & Emilio Trevisani (ENS, Paris & IHES)

### Supersymmetry and Dimensional Reduction in Random Field Models

In this talk we will discuss an ongoing work on random field models. First we will review a work by Parisi and Sourlas. They conjectured that the infrared fixed point of such random field models should be described by a supersymmetric conformal field theory (CFT). From this they argued that the disordered CFT admits a description in terms of a CFT in two less spacetime dimensions but without the disorder. We will explain how the dimensional reduction is realized. Finally we will discuss when and how the RG flow of the random field theory reaches the SUSY fixed point.

#### 25th April, 2019 - 02:04:00 Fidel Schaposnik Massolo (IHES)

### On Phases of Melonic Quantum Mechanics

We explore in detail the properties of two melonic quantum mechanical theories which can be formulated either as fermionic matrix quantum mechanics in the new large D limit, or as disordered models. Both models have a mass parameter m and the transition from the perturbative large m region to the strongly coupled "black-hole" small m region is associated with several interesting phenomena. One model, with U(n)^2 symmetry and equivalent to complex SYK, has a line of first-order phase transitions terminating, for a strictly positive temperature, at a critical point having non-trivial, non-mean-field critical exponents for standard thermodynamical quantities. Quasi-normal frequencies, as well as Lyapunov exponents associated with out-of-time-ordered four-point functions, are also singular at the critical point, leading to interesting new critical exponents. The other model, with reduced U(n) symmetry, has a quantum critical point at strictly zero temperature and positive critical mass m*. For 0<m<m*, it flows to a new gapless IR fixed point, for which the standard scale invariance is spontaneously broken by the appearance of distinct scaling dimensions Δ+ and Δ- for the Euclidean two-point function when t→ +∞ and t→ -∞

#### 24th April, 2019 - 02:04:00 Stefanos Kousvos (Université de Crète & IHES)

### Three Dimensional Cubic Symmetric CFTs in the Bootstrap and their Applications

I will discuss results of recent numerical bootstrap work performed for systems with cubic symmetry. Under certain assumptions, we find an isolated region in parameter space, which given prior intuition with the numerical bootstrap, indicates the existence of a CFT in this region. We find critical exponents for the conjectured CFT which are in discrepancy with the epsilon expansion (but in good agreement with experiments for structural phase transitions). The disagreement of critical exponents for structural phase transitions calculated in the epsilon expansion with those measured in experiments is something that was noticed since the 70s. I will briefly discuss some resolutions proposed at the time.

#### 23rd April, 2019 - 02:04:00 Pierre Toledano (Université de Picardie Jules Verne, Amiens & IHES)

### Introduction to Structural Phase Transitions

#### 19th April, 2019 - 02:04:00 Miguel Paulos (Ecole Normale Supérieure)

### A Functional Approach to the Numerical Conformal Bootstrap

We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, truncations of the crossing equation with even a handful of components can lead to extremely accurate results, in opposition to hundreds of components in the usual approach. We explain how this is a consequence of the functional basis correctly capturing the asymptotics of bound-saturating extremal solutions to crossing. We discuss how these methods can and should be implemented in higher dimensional applications.

#### 18th April, 2019 - 02:04:00 Mikhail Isachenkov (IHES)

### Solving Large N Double-Scaled SYK

I will review a method to evaluate correlation functions of certain statistical systems via chord diagrams and apply it to compute correlators in the double-scaled version of SYK model, in particular in its large N limit. The results are exact at all energies and allow to extract corrections to the maximal Lyapunov exponent. Time permitting, I will comment on the suggested relation of this model to a Hamiltonian reduction of quantum particle moving on the non-compact quantum group SU_q(1,1).

#### 17th April, 2019 - 02:04:00 Volker Schomerus (DESY Hamburg & IHES)

### The Casimir Equation for 4D Superconformal Blocks

Applications of the bootstrap to superconformal field theories require the construction of superconformal blocks for four-point functions of arbitrary supermultiplets. Up until recently, only sporadic results had been obtained. In my talk I explain the key ingredients of a new systematic construction that apply to a large class of superconformal field theories, including 4-dimensional models with any number N of supersymmetries. It hinges on a universal construction of the relevant Casimir differential equations. In order to find these equations, we model superconformal blocks as functions on the supergroup and pick a distinguished set of coordinates. The latter are chosen so that the superconformal Casimir operator can be written as a perturbation of the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent) term. Solutions to the associated eigenvalue problem can be obtained through a quantum mechanical perturbation theory that truncates at some finite order so that all results are exact.

#### 20th March, 2019 - 02:03:00 Stefan Hollands (Univ. Leipzig)

### Modular Flows in Quantum Field Theory

The reduced density matrix of a subsystem induces an intrinsic internal dynamics called the ``modular flow''. The flow depends on the subsystem and the given state of the total system. It has been subject to much attention in theoretical physics in recent times because it is closely related to information theoretic aspects of quantum field theory. In mathematics, the flow has played an important role in the study of operator algebras through the work of Connes and others.

It is known that the flow has a geometric nature (boosts resp. special conformal transformations) in case the subsystem is defined by a spacetime region with a simple shape. For more complicated regions, important progress was recently made by Casini et al. who were able to determine the flow for multi-component regions for free massless fermions or bosons in 1+1 dimensions.

In this introductory lecture, I describe the physical and mathematical backgrounds underlying this research area. Then I describe a new approach which is not limited to free theories, based in an essential way on two principles: The so-called ``KMS-condition'' and the exchange relations between primaries (braid relations) in rational CFTs in 1+1 dimensions. A combination of these ideas and methods from operator algebras establish that finding the modular flow of a multi-component region is equivalent to a certain matrix Riemann-Hilbert problem. One can therefore apply known methods for this classic problem to find or at least characterize the modular flow.

#### 31st January, 2019 - 02:01:00 Sergiu Klainerman (Princeton University & IHES)

### On the Nonlinear Stability of Black Holes

#### 5th December, 2018 - 02:12:00 Pierre Cartier (IHES)

### Some remarks on the energy-momentum tensor in general relativity

Following the method outlined b Emmy Noether in her famous 1918 paper, we propose a version of the momentum-energy tensor in general relativity which is geometric and suitably covariant, giving conservation laws .

This conssuction appears to be novel in a field well explored.

#### 3rd December, 2018 - 11:12:00 Miguel Paulos (LPT ENS)

### A more functional bootstrap

The conformal bootstrap aims to systematically constraint CFTs based on crossing symmetry and unitarity.

In this talk I will introduce a new approach to extract information from the crossing symmetry sum rules, based on the construction of linear functionals with certain positivity properties. I show these functionals allow us to derive optimal bounds on CFT data. Furthemore I will argue that special extremal solutions to crossing form a basis for the crossing equation, with the functionals living in the dual space. As an application we reconstruct physics of QFTs in AdS2 from the properties of 1d CFTs.

#### 29th November, 2018 - 02:11:00 Georgios Papadopoulos (Kings College London & IHES)

### Robinson Structures and the Double Copy

#### 22nd November, 2018 - 02:11:00 Frank Verstraete (University of Ghent & IHES)

### Tensor networks for describing correlated quantum systems

Quantum tensor networks provide a new language for describing many body systems. They model the entanglement structure of many body wavefunctions, and give a precise description of symmetries such as arising in systems exhibiting topological quantum order. In this talk, an overview will be given of the challenges, prospects and limitations of this approach.

#### 20th November, 2018 - 02:11:00 Anatoly Dymarsky (University of Kentucky & IHES)

### Timescale of ergodicity: when many-body quantum systems can be described by Random Matrix Theory?

In this talk I will argue that after certain timescale (which scales with the system size as L^{d+2}) dynamics of a local observable becomes universal and it can be described by a random matrix.

This talks is based on https://arxiv.org/abs/1804.08626 and other recent works.

#### 8th November, 2018 - 02:11:00 Junya Yagi (Perimeter Institute for Theoretical Physics & IHES)

### Unification of integrability in supersymmetric gauge theories

The 8-vertex model and the XYZ spin chain have been found to emerge from gauge theories in various ways, such as 4d and 2d Nekrasov-Shatashvili correspondences, the action of surface operators on the supersymmetric indices of class-Sk theories, and correlators of line operators in 4d Chern-Simons theory. I will explain how string theory unifies these phenomena.

This is based on my work with Kevin Costello [arXiv:1810.01970].

#### 9th May, 2018 - 11:05:00 Gordon Slade (University of British Columbia & IHES)

### Critical exponents for long-range O(n) models

Séminaire de Probabilités et de Physique Théorique

We present results on the critical behaviour of long-range models of multi-component ferromagnetic spins and weakly self-avoiding walk in dimensions 1, 2, and 3. The range of the interaction is adjusted so that the models are below their upper critical dimension. Critical exponents are computed for the susceptibility, specific heat, and critical two-point function, using a renormalisation group method to perturb around a non-Gaussian fixed point. This provides a mathematically rigorous version of the epsilon expansion.

#### 8th March, 2018 - 11:03:00 Sandipan Kundu (Johns Hopkins University & IHES)

### Three Lectures on Causality in Conformal Field Theory (3/3)

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In these pedagogical lectures, I will explore causality constraints on conformal field theory. First, I will show how causality is encoded in crossing symmetry and reflection positivity of Euclidean correlators, and derive constraints on the interactions of low-lying operators directly from the conformal bootstrap. Then, I will explain the connection between these causality constraints and the averaged null energy condition. Finally, I will use causality to show that the averaged null energy is positive in interacting quantum field theory in flat spacetime. Based on arXiv:1509.00014, arXiv:1601.07904, arXiv:1610.05308.

#### 7th March, 2018 - 11:03:00 Sandipan Kundu (Johns Hopkins University & IHES)

### Three Lectures on Causality in Conformal Field Theory (2/3)

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In these pedagogical lectures, I will explore causality constraints on conformal field theory. First, I will show how causality is encoded in crossing symmetry and reflection positivity of Euclidean correlators, and derive constraints on the interactions of low-lying operators directly from the conformal bootstrap. Then, I will explain the connection between these causality constraints and the averaged null energy condition. Finally, I will use causality to show that the averaged null energy is positive in interacting quantum field theory in flat spacetime. Based on arXiv:1509.00014, arXiv:1601.07904, arXiv:1610.05308.

#### 22nd February, 2018 - 11:02:00 Sandipan Kundu (Johns Hopkins University & IHES)

### Three Lectures on Causality in Conformal Field Theory (1/3)

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In these pedagogical lectures, I will explore causality constraints on conformal field theory. First, I will show how causality is encoded in crossing symmetry and reflection positivity of Euclidean correlators, and derive constraints on the interactions of low-lying operators directly from the conformal bootstrap. Then, I will explain the connection between these causality constraints and the averaged null energy condition. Finally, I will use causality to show that the averaged null energy is positive in interacting quantum field theory in flat spacetime. Based on arXiv:1509.00014, arXiv:1601.07904, arXiv:1610.05308.

#### 21st February, 2018 - 11:02:00 Marco Meineri (EPFL & IHES)

### Universality at Large Transverse Spin in Defect CFT

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large *s*, *s* being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE and is analytic in *s*, analogous to the Caron-Huot formula for the four-point function. Some important assumptions are made in deriving this result: we comment on them.

#### 30th January, 2018 - 02:01:00 Pavel Saponov (HSE & IHES)

### Cayley-Hamilton Identity and Drinfeld-Sokolov Reduction in Quantum Algebras

Different forms of the matrix Cayley-Hamilton identity in some quantum algebras will be presented. In particular, I plan consider the so-called braided Yangian -- some generalization of Drinfeld Yangian -- recently introduced in my joint work with D.Gurevich. A quantum counterpart of the Drinfeld-Sokolov reduction based on the Cayley-Hamilton identity will be discussed as well.

#### 21st December, 2017 - 02:12:00 Mikhail Isachenkov (Weizmann Institute of Science & IHES)

### Conformal Blocks and Integrability

I will discuss a relation between conformal blocks, describing kinematics of a CFT, and integrable models of quantum-mechanical particles. I will show how the dependence of blocks on cross-ratios is encoded in equations of motion of a Calogero-Sutherland model and their dependence on conformal dimension and spin of the exchanged operator - in those of a relativistic Calogero-Sutherland model. Both are simultaneously controlled by an integrable connection generalizing 2d Knizhnik-Zamolodchikov equations. I will review how this connection, associated to representations of degenerate double affine Hecke algebra, comes from a q-deformed bispectrally symmetric setting.

#### 19th December, 2017 - 02:12:00 Emil Akhmedov (ITEP)

### Surprises of quantization in de Sitter space

I will talk about loop infrared effects in de Sitter QFT. Namely about their types, physical meaning and origin and also about their resumation and physical consequences. The talk is based on arXiv:1701.07226.

#### 5th December, 2017 - 02:12:00 Fidel I. Schaposnik Massolo (Seoul National University & IHES)

### Phase Diagram of Planar Matrix Quantum Mechanics, Tensor and SYK Models (arXiv: 1707.03431)

In this talk I present the phase diagram of a U(N)^2 x O(D) invariant fermionic planar matrix quantum mechanics (equivalently tensor or complex SYK models) in the new large D limit dominated by melonic graphs. The Schwinger-Dyson equations can have two solutions describing either a "large" black hole phase a la SYK or a "small" black hole with trivial IR behavior. In the strongly coupled region of the mass-temperature plane, there is a line of first order phase transitions between the small and large black hole phases. This line terminates at a new critical point which can be studied numerically in detail. The critical exponents are non-mean-field and different on the two sides of the transition. If time allows, I will compare this to purely bosonic unstable and stable melonic models.

#### 6th October, 2017 - 02:10:00 Bruno Le Floch (Princeton)

### Surface defects and instanton-vortex moduli spaces

Instantons on R^{4}, namely anti-self-dual Yang-Mills connections, are in bijection with framed locally free sheaves on CP^{2}. Ramified instantons have an imposed singularity along R^{2} in R^{4} that translates to a parabolic structure along a CP^{1} divisor, or equivalently to a cyclic orbifold. Such a singularity (Gukov-Witten defect) can be obtained in 4d N=2 supersymmetric Yang-Mills theory by adding 2d N=(2,2) degrees of freedom on R^{2}, and gauging a global symmetry of the 2d theory using the R^{2} restriction of the 4d gauge connection. The moduli space of ramified instantons should thus be related to a moduli space of instanton-vortex configurations of the 4d-2d pair of gauge theories. I propose an incomplete definition of the latter moduli space by fibering (over the instanton moduli space) a recent description of the vortex moduli space as based maps to the Higgs branch stack. As evidence I compare Nekrasov partition functions, namely equivariant integrals over these moduli spaces. The equality relies on Jeffrey-Kirwan technology, applicable thanks to the ADHM construction of the moduli spaces as Kähler quotients.

#### 26th September, 2017 - 02:09:00 Carlangelo Liverani (Universita' di Roma Tor Vergata & IHES)

### The Lorentz Gas : New Results and Open Problems

I will make a quick review of old and new results concerning the Lorentz gas; discuss new directions in which I’d like to proceed (e.g. non periodic obstacles, interacting particles, …) and some (very) partial results toward such directions.

#### 28th June, 2017 - 02:06:00 Ali CHAMSEDDINE (American University of Beirut & IHES)

### Resolving Space-Time Singularities in Mimetic Gravity

#### 21st June, 2017 - 02:06:00 Ali CHAMSEDDINE (American University of Beirut & IHES)

### Beyond the Standard Model in Noncommutative Geometry and Mimetic Dark Matter

#### 16th June, 2017 - 11:06:00 Raymond GOLDSTEIN (University of Cambridge & IHES)

### Dynamic Interconversions of Minimal Surfaces

A classical problem in mathematics is the determination of the minimal surface that spans a given contour, which can be realized in the laboratory as a soap film supported by a wire frame. In the early 1940s Richard Courant pointed out nontrivial situations in which a small deformation of certain frames can render unstable the supported surface, leading by a rapid dynamical process to a new minimal surface. For example, a soap film Möbius strip can transition to a disc. Despite the enormous body of work on the mathematics of minimal surfaces themselves, the understanding of these dynamical problems is at a very early stage. In this talk I will summarize our recent experimental and theoretical work on problems of this type, in which a combination of high-speed imaging and stability theory has revealed new insights. (Work done in collaboration with A.I. Pesci, H.K. Moffatt, T. Machon and G.P. Alexander)

#### 18th April, 2017 - 02:04:00 Nikita SOPENKO (ITEP & IHES)

### Surface defects and instanton-vortex interaction

#### 15th March, 2017 - 02:03:00 Brian WILLIAMS (Northwestern University & IHES)

### Higher chiral differential operators

#### 1st March, 2017 - 02:03:00 Philsang YOO (Northwestern University & IHES)

### Physics of Langlands Dualities

#### 22nd February, 2017 - 02:02:00 Yegor ZENKEVICH (ITEP and INR RAS & IHES)

### Ding-Iohara-Miki algebra and gauge theories

#### 20th February, 2017 - 02:02:00 Pavel SAFRONOV (Université de Genève & IHES)

### A q-deformation of the geometric Langlands correspondence

#### 10th February, 2017 - 11:02:00 Jürg FRÖHLICH (ETH Zurich, Suisse & IHES)

### The Classical XY Model – Vortex- and Random Walk Representations

A review of results concerning the classical XY model in various dimensions is presented.

I start by showing that the XY model does not exhibit any phase transitions in a non-vanishing external magnetic field, and that connected spin-correlations have exponential decay. These results can be derived from the Lee-Yang theorem.

Subsequently, I study the XY model in zero magnetic field: The McBryan-Spencer upper bound on spin-spin correlations in two dimensions is derived. The XY model is then reformulated as a gas of vortices of integer vorticity (Kramers-Wannier duality). This representation is used to explain some essential ideas underlying the proof of existence of the Kosterlitz-Thouless transition in the two-dimensional XY model. Remarks on the existence of phase transitions accompanied by continuous symmetry breaking and the appearance of Goldstone modes in dimension three or higher come next.

Finally, I sketch the random-walk representation of the XY model and explain some consequences thereof – such as convergence to a Gaussian fixed point in the scaling limit, provided the dimension is > 4; and the behaviour of the inverse correlation length as a function of the external magnetic field.

#### 17th January, 2017 - 02:01:00 Pavel SAPONOV (Institute for High Energy Physics, Protvino, Russia & Higher School of Economics, Faculty of Mathematics, Moscow, Russia)

### Braided Yangians

#### 28th November, 2016 - 02:11:00 Vyacheslav RYCHKOV (CERN & IHES)

### State of the art of conformal bootstrap (2/2)

__MINI-COURS__

Conformal bootstrap is a mathematically well-defined framework for performing non-perturbative computations in strongly coupled conformal field theories, including theories of real physical interest like the critical point of the 3d Ising model. In these lectures I will describe the recent advances in this field and the challenges it faces.

#### 21st November, 2016 - 02:11:00 Vyacheslav RYCHKOV (CERN & IHES)

### State of the art of conformal bootstrap (1/2)

__MINI-COURS__

Conformal bootstrap is a mathematically well-defined framework for performing non-perturbative computations in strongly coupled conformal field theories, including theories of real physical interest like the critical point of the 3d Ising model. In these lectures I will describe the recent advances in this field and the challenges it faces.

#### 15th November, 2016 - 02:11:00 Bethan CROPP (Indian Institute of Science Education and Research, Trivandrum)

### Hints of quantum gravity from the horizon fluid

#### 15th November, 2016 - 11:11:00 Taro KIMURA (Department of Physics, Keio University)

### Elliptic deformation of W-algebras from 6d quiver gauge theory

#### 20th October, 2016 - 02:10:00 Michele CIRAFICI (Instituto Superior Técnico & IHES)

### Framed BPS states from framed BPS quivers

#### 14th September, 2016 - 02:09:00 Peter KOROTEEV (University of Minnesota & IHES)

### Elliptic algebras and large-N supersymmetric gauge theories

We shall address the duality between supersymmetric gauge theories in various dimensions and elliptic integrable systems such as Ruijsenaars-Schneider model and periodic intermediate long wave hydrodynamics. These models arise in instanton counting problems and are described by certain elliptic algebras. We discuss the correspondence between the two types of models by employing the large-n limit of the dual gauge theory.

#### 12th July, 2016 - 02:07:00 Artan SHESHMANI (MIT)

### Donaldson-Thomas theories and modular forms and S-duality conjecture

I will start by an introduction to Donaldson Thomas theory and some of the statements about its modularity properties, as well as its connection to S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin. I will then provide an algebraic geometric approach to prove this conjecture for DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold.

#### 18th May, 2016 - 03:05:00 Dmytro VOLIN (Trinity College Dublin & IHES)

### All unitary representations of su(p,qIm)

Classification of all unitary representations of su(p,q|m) algebra with non-zero p,q,m should have been achieved a while ago, given the current level of the representation theory development. However, to our surprise, the literature on the subject contains some incomplete or incorrect statements, save the well-understood su(2,2|N) case. We therefore decided to address the question from scratch and were able to get a complete and concise description of the unitary dual for generic su(p,q|m).

In the current talk:

- The classification statement is presented in full generality, we also mention all the other real forms of gl(p+q|m,C).

- Shortening conditions naturally arise from considering of all possible choices of the Kac-Dynkin-Vogan diagram at once.

- Schwinger oscillators are used to prove unitarity, with a novel option to work with non-integer weights by representing the oscillator algebra in a generalisation of the Fock module.

- A generalisation of Young diagrams inscribed into a T-hook [almost] bijectively labels the unitary dual. This opens interesting opportunities for new combinatorial identities.

#### 13th April, 2016 - 03:04:00 Sergei ALEXANDROV (Université de Montpellier & IHES)

### D-instantons, mock modular forms and BPS partition functions

I'll discuss the modular properties of D3-brane instantons appearing in Calabi-Yau string compactifications. I'll show that the D3-instanton contribution to a certain geometric potential on the hypermultiplet moduli space can be related to the elliptic genus of (0,4) SCFT. The modular properties of the potential imply that the elliptic genus associated with non-primitive divisors of Calabi-Yau is only mock modular. I'll show how to construct its modular completion and prove the modular invariance of the twistorial construction of D-instanton corrected hypermultiplet moduli space.

#### 6th April, 2016 - 10:04:00 Nicolas BOULANGER (Université de Mons & IHES)

### Spin two duality in linearised gravity around ads

#### 1st April, 2016 - 10:04:00 Anne TAORMINA (Durham University & IHES)

### Mathieu Moonshine

I shall give a brief introduction to Mathieu Moonshine, an observation made in 2010 in the context of string theory compactified on a K3 surface and whose significance in string theory remains elusive. Attempts to understand the mathematical structure behind this observation have included techniques from Number Theory, Group Theory and Geometry. I will discuss how geometry provides an interesting angle when attempting to explain the presence of the huge Mathieu 24 discrete symmetry in string theories compactified on a K3 surface.

#### 12th January, 2016 - 02:01:00 Dmitri GUREVICH ()

### Quantum matrix algebras and their applications

By quantum matrix algebras I mean these related to braidings (solutions to Quantum Yang-Baxter Equation) and in a sense similar to the classical matrix algebras. In first turn, I am interested in the so-called Reflection Equation algebra. By using it, me (in collaboration with P.Saponov) have introduced the notion of partial derivatives on the enveloping algebra U(gl(m)). This leads to a new type of Noncommutative Geometry (we call it Quantum Geometry), which is deformation of the classical one. In my talk I plan to consider a way of defining some dynamical models on U(u(2)) background.

#### 8th January, 2016 - 11:01:00 Tin SULEJMANPASIC (North Carolina State University & IHÉS)

### An inextricable link : semi-classics and complex saddles

I will discuss the use of semi-classics and instanton calculus and argue that, contrary to common wisdom, complex solutions of the equations of motion are a necessary ingredient of semi-classical expansion. In particular, I will show that without the complex solutions semi-classical expansion of supersymmetric theories cannot be reconciled with the constraints of supersymmetry. This has a natural interpretation in the Picard-Lefschetz theory.

#### 2nd December, 2015 - 02:12:00 Vasily SAZONOV (University of Graz)

### Convergent series : from lattice models to QCD

The standard perturbation theory leads to the asymptotic series because of the illegal interchange of the summation and integration. However, changing the initial approximation of the perturbation theory, one can generate the convergent series. We study the lattice \phi^{4}-model and compare observables calculated using the convergent series and Monte Carlo simulations. Then, we discuss the generalization of the same ideas for the continuum \phi^{4}-model and QCD.

#### 12th November, 2015 - 11:11:00 Seth HOPPER (Instituto Superior Técnico, Lisboa & IHÉS)

### Finding self-force quantities in a post-Newtonian expansion: Eccentric orbits on a Schwarzschild background

#### 27th October, 2015 - 02:10:00 Hovhannes M. KHUDAVERDIAN (The University of Manchester & IHÉS)

### The modular class of an odd Poisson supermanifold and second order operators on half-densities

` Second order operator $\Delta$ on half-densities can be uniquely defined by its principal symbol $E$ up to a `potential' $U$. If $\Delta$ is an odd operator such that order of operator $\Delta`^{^2}$ is less than $3$ then principal symbol $E$ of this operator defines an odd Poisson bracket. We define the modular class of an odd Poisson supermanifold in terms of $\Delta$ operator defining the odd Poisson structure. In the case of non-degenerate odd Poisson structure (odd symplectic case) the modular class vanishes, and we come to canonical odd Laplacian on half-densities, the main ingridient of Batalin-Vilkovisky
formalism. Then we consider examples of odd Poisson supermanifolds with non-trivial modular classes related with the Nijenhuis bracket.
The talk is based on the joint paper with M. Peddie: arXive: 1509.05686