### Schedule

#### 14th February, 2024 - 04:02:00 Yin-Chen He (Perimeter Institute & IHES)

### Physics Meets Geometry: a Fuzzy Sphere Odyssey in Critical Phenomena

Historically, the synergy between physics and geometry, from the times of Archimedes and Newton to the era of Einstein, has repeatedly been the catalyst for pivotal breakthroughs in physics and mathematics. In this talk, I will introduce a new narrative demonstrating how physics and geometry intertwine, leading to unexpected and significant results in critical phenomena in physics. Specifically, I will elucidate how non-commutative geometry—a mathematical framework born from the insights of physicists—offers fresh perspectives on conformal field theory, a subject with profound applications across various physics domains, from condensed matter to quantum gravity, and string theory.

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#### 7th December, 2023 - 02:12:00 Matthew Yu (Oxford University & IHES)

### U-duality Anomaly Cancelation

Theories of quantum gravity are believed to have no global symmetries. We will check this conjecture for the U-duality symmetry in 4d N=8 supergravity. Since this theory arises from string theory, the 't Hooft anomaly for this symmetry ought to vanish. We then perform a bordism computation to classify the anomaly of U-duality and notice an interesting fact about the particular Thom spectrum that we use for the computation. Finally we show that evaluating the anomaly for our particular theory on the generating manifold of the bordism group leads to it vanishing.

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#### 5th December, 2023 - 02:12:00 Anatoly Konechny (Heriot-Watt University & IHES)

### Conformal Boundary Conditions, Cardy's Variational Ansatz and Phase Structure of 2D QFTs

We will consider perturbations of 2D CFTs by multiple relevant operators. The massive phases of such perturbations can be labeled by conformal boundary conditions. Cardy's variational ansatz approximates the vacuum state of the perturbed theory by a smeared conformal boundary state. In this talk we will discuss the limitations and propose generalisations of this ansatz using both analytic and numerical insights based on TCSA. In particular we analyse the stability of Cardy's ansatz states with respect to boundary relevant perturbations using bulk-boundary OPE coefficients. We show that certain transitions between the massive phases arise from a pair of boundary RG flows. The RG flows start from the conformal boundary on the transition surface and end on those that lie on the two sides of it. As an example we work out the details of the phase diagram for the Ising field theory and for the tricritical Ising model perturbed by the leading thermal and magnetic fields. Based on arXiv:2306.13719.

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#### 16th November, 2023 - 02:11:00 Junchen Rong (IHES)

### From O(3) to Cubic CFT: Conformal Perturbation and the Large Charge Sector

The Cubic CFT can be understood as the O(3) invariant CFT perturbed by a slightly relevant operator. In this paper, we use conformal perturbation theory together with the conformal data of the O(3) vector model to compute the anomalous dimension of scalar bilinear operators of the Cubic CFT. When the Z2 symmetry that flips the signs of φi is gauged, the Cubic model describes a certain phase transition of a quantum dimer model. The scalar bilinear operators are the order parameters of this phase transition. Based on the conformal data of the O(3) CFT, we determine the correction to the critical exponent as η_Cubic-η_O(3)≈ -0.0215(49). The O(3) data is obtained using the numerical conformal bootstrap method to study all four-point correlators involving the four operators: v=φ_i, s=∑_i φ_iφ_i and the leading scalar operators with O(3) isospin j=2 and 4. According to large charge effective theory, the leading operator with charge Q has scaling dimension Δ_Q=c_3/2 * Q^{^3}/2+c_1/2 * Q1^/2. We find a good match with this prediction up to isospin j=6 for spin 0 and 2 and measured the coefficients c_3/2 and c_1/2.

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#### 14th November, 2023 - 02:11:00 Martin Hasenbusch (Universität Heidelberg & IHES)

### Precise Monte Carlo Estimates of Universal Quantities: Improved Lattice Models and Finite Size Scaling

I discuss improved lattice models in three dimensions. Improved means that either one or two parameters of the model are tuned such that the leading or the leading and the next to leading correction to scaling have, at least approximately, a vanishing amplitude. This is achieved by using a finite size scaling analysis of dimensionless quantities. Based on these results, accurate estimates of universal quantities such as critical exponents are obtained. I summarize results that have been obtained for the Ising, the XY, the Heisenberg and the cubic universality classes and compare them with those obtained by other methods, in particular precise estimates obtained recently by using the conformal bootstrap method.

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#### 23rd October, 2023 - 02:10:00 John Cardy (All Souls College & IHES)

### Bulk Renormalization Group Flows and Boundary States in Conformal Field Theories

We propose using smeared boundary states as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT.

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#### 9th October, 2023 - 02:10:00 Balt van Rees (École polytechnique)

### Perturbative RG Flows in AdS

We discuss general properties of perturbative RG flows in AdS with a focus on the treatment of boundary conditions and infrared divergences. In contrast with flat-space boundary QFT, general covariance in AdS implies the absence of independent boundary flows. We illustrate how boundary correlation functions remain conformally covariant even if the bulk QFT has a scale. We apply our general discussion to the RG flow between consecutive unitary diagonal minimal models which is triggered by the φ(1,3) operator. For these theories we conjecture a flow diagram whose form is significantly simpler than that in flat-space boundary QFT.

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#### 3rd October, 2023 - 02:10:00 Thomas Scaffidi (University of California Irvine)

### Complex CFT in the O(n) Loop Model: Numerical Evidence for Loss of Conformality in the Large-n Limit

The presence of nearby complex conformal field theories (CCFTs) hidden in the complex plane of the tuning parameter was recently proposed as an elegant explanation for the ubiquity of "weakly first-order" transitions in condensed matter and high-energy systems. Recently, we have numerically confirmed the presence of such a CCFT in a loop model which derives from a high-temperature formulation of the O(n) model. Surprisingly, we found that the CCFT only survives until n=12.34, beyond which the transfer matrix acquires a gap. In this talk, I will discuss ongoing work in trying to explain this loss of complex conformality at large n, using a mapping to a hard hexagon model for n going to infinity. I will also discuss the connection between the original O(n) model and its loop version and the consequences for CCFTs in these models.

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#### 20th June, 2023 - 02:06:00 Yuto Moriwaki (RIKEN & IHES)

### Bootstrap Hypothesis – From Algebraic Point of View

**ANNULÉ ET REPORTÉ**

In this talk we will revisit the bootstrap hypothesis in the two-dimensional case from a mathematical perspective. The bootstrap equations is a consistency for the CFT four-point correlation functions. Therefore, the following question is not mathematically clear: (Math Question) If the four-point correlation functions satisfy the bootstrap equations, can we define a multi-point correlation functions? (Is it convergent and consistent?) After introducing the notion of a full vertex algebra, which is equivalent to the fact that the four-point correlation functions satisfy the bootstrap equations, we will explain that all n-point correlation functions converge and are consistent when the full vertex algebra satisfies certain finiteness. An crucial step in the proof is to show that the operad of configuration spaces acts on representations of the full vertex algebra (under the finiteness assumption). We will explain this idea in detail.

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#### 13th June, 2023 - 02:06:00 Clément Delcamp (Univ. Gent & IHES)

### Higher Categorical Symmetries on the Lattice

Higher categorical symmetries have received widespread attention in recent years, generalising in various ways the usual notion of symmetry. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging ordinary symmetries. Specialising to certain finite group generalisations of the (2+1)d transverse-field Ising model, I will explain what it means for a quantum lattice model to have such a symmetry structure.

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#### 1st June, 2023 - 02:06:00 Justin Kulp (Perimeter Institute, Waterloo & IHES)

### Self-Similar Quasicrystals and Hyperbolic Honeycombs

Most people are familiar with periodic tessellations and lattices; from the patio floor at the reception building to their favourite spin systems. In this talk, I will discuss two less familiar families of tessellations and their possible connections to high energy physics, condensed matter physics, and mathematics: hyperbolic tessellations and quasicrystals. After introducing the basics of regular hyperbolic lattices, I will survey constructions and surprising properties of quasicrystals (like the Penrose tiling), including their classically forbidden symmetries, long-range order, and self-similar structure. Inspired by the AdS/CFT correspondence, I will describe a mathematical relationship between hyperbolic lattices in (D+1)-dimensions and quasicrystals in D-dimensions, as well as the resolution of a conjecture by Bill Thurston. Based on work to appear with Latham Boyle.

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#### 9th May, 2023 - 02:05:00 Nick Jones (University of Oxford & IHES)

### Bulk boundary correspondence in long-range quantum chains

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#### 18th April, 2023 - 02:04:00 Thomas Fischbacher (Google Research, Zurich & IHES)

### A Quick Introduction to Machine Learning

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#### 23rd February, 2023 - 02:02:00 Federico Piazza (Marseille, CPT & IHES)

### Properties of Average Distances and Emergent Causality

In the presence of a (quantum or classical) statistical ensemble of metrics one can consider averages of distances between points/events, as long as a prescription is assigned for identifying such points.

These average distances, in general, are not geodesic distances of any metric because they are not *additive*, in a sense that I will specify. Deviations from additivity can be measured by a quantity that, in any coordinate expansion, starts only at forth order. In Euclidean signature average distances are always subadditive. In Lorentzian signature it proves convenient to identify the events by anchoring them to a set of free falling observers. This prescription, by no means unique, naturally conveys the point of view of these observers, whose causal relations are inevitably affected by the fluctuations of the metric field. Average Lorentzian distances portray an interesting ``average causal structure” that has no classical analogue.

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#### 15th December, 2022 - 02:12:00 Leonardo Rastelli (Stony Brook University)

### Informal Update on Bootstrapping Large N QCD

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#### 25th November, 2022 - 02:11:00 Julio Parra-Martinez (Caltech & IHES)

### Soft Theorems: Symmetry and Geometry

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#### 25th May, 2022 - 11:05:00 Anatoly Dymarski (University of Kentucky & IHES)

### Optimal Narain Theories from Codes

Connection to codes has emerged recently as a new tool to construct and study Narain CFTs with special properties. In the talk I will review this connection and argue that optimal theories, i.e. those maximizing the value of spectral gap for the given central charge, are code CFTs - meaning they can be constructed using codes. This applies to known optimal theories with c<=8 as well as to asymptotically large c. I will also discuss spinoff results, in particular construction of fake torus partition function Z(\tau, \bar \tau), which satisfies all properties of the 2d CFT torus partition function (modular invariance, discreteness and positive-definiteness of spectrum), yet can be shown not to be a partition function of any 2d theory.

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#### 15th April, 2022 - 11:04:00 Henri Epstein (IHES)

### Archeological remarks on analyticity properties in momentum space in QFT, Part II : details on the 4-point function

I will describe the proof of the crossing property for the 4-point function.

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__IHES Covid-19 regulations__:

- all the participants who will attend the event in person will have to keep their mask on indoor

and where the social distancing is not possible;

- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable without it;

- Up to 70 persons in the conference room

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#### 8th March, 2022 - 02:03:00 Massimiliano Maria Riva et Filippo Vernizzi (Institut de physique théorique, Université Paris-Saclay, CEA, CNRS)

### Worldline Approach to Gravitational Bremsstrahlung

The need to improve the analytical knowledge of the gravitational waveforms emitted by binary systems has recently sparked a fervent activity in the application of (classical and/or quantum) post-Minkowskian perturbation methods (expansion in G) to the two-body relativistic gravitational dynamics and radiation. We shall discuss how the use of a classical Effective-Field-Theory worldline approach to gravitational scattering, combined with modern Quantum-Field-Theory integration techniques, allows one to compute both the gravitational-wave amplitude and the associated radiated four-momentum.

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__IHES Covid-19 regulations__:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces

and where the social distancing is not possible;

- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable

without it;

- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass

- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will

be checked at the entrance of the conference room.

==================================================================

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#### 15th December, 2021 - 11:12:00 Henri Epstein (IHES)

### Archeological Remarks on Analyticity Properties in Momentum Space in QFT

I will describe the foundations of the program of studying the analyticity properties of the n-point functions in momentum space : the primitive domain of analyticity and methods to enlarge it. If time permits, some of the results for the 4-point function will be described.

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__IHES Covid-19 regulations__:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces

and where the social distancing is not possible;

- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable

without it;

- Up to 70 persons in the conference room, every participant will be asked to be able to provide a health pass

- Over 70 persons in the conference room, every participant will be asked to provide a health pass which will

be checked at the entrance of the conference room.

==================================================================

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#### 6th December, 2021 - 10:12:00 Sylvain Ribault (CEA Saclay)

### Global Symmetry and Conformal Bootstrap in the Two-Dimensional O(n) Model

The torus partition function of the critical O(n) model, which is known since 1987, does not fully characterize the space of states. For complex n, I will conjecture a determination of that space in terms of irreducible O(n) representations and indecomposable Virasoro representations. I will then describe the interplay between O(n) symmetry and crossing symmetry in four-point correlation functions, and explain how the solutions of crossing symmetry can be counted numerically. This leads to the determination of some of the model's fusion rules.

This talk is based on the preprint https://arxiv.org/abs/2111.01106 with Linnea Grans-Samuelsson, Rongvoram Nivesvivat, Jesper Lykke Jacobsen, and Hubert Saleur.

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__IHES Covid-19 regulations__:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces

and where the social distancing is not possible;

- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable

without it;

- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass

- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will

be checked at the entrance of the conference room.

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#### 15th November, 2021 - 10:11:00 Andrei Smilga (Université de Nantes)

### Spin(7) and Generalized SO(8) Instantons in Eight Dimensions

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__IHES Covid-19 regulations__:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces

and where the social distancing is not possible;

- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable

without it;

- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass

- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will

be checked at the entrance of the conference room.

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#### 27th October, 2021 - 10:10:00 Antoine Tilloy (Mines Paris-Tech)

### Variational Method in 1+1 Dimensional Relativistic Field Theory

The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods usually break one of the 3, which translates into the need to have an IR or UV cutoff. I will explain how a relativistic modification of continuous matrix product states allows us to satisfy the 3 requirements jointly in 1+1 dimensions. Optimizing over this class of states, one can solve scalar QFT without UV cutoff and directly in the thermodynamic limit, and numerics are promising. I will try to cover both the general philosophy of the method, the basics of the computations, and mention the many open problems.

__IHES Covid-19 regulations__:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces

and where the social distancing is not possible;

- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable

without it;

- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass

- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will

be checked at the entrance of the conference room.

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#### 18th October, 2021 - 02:10:00 Ritam Sinha (Hebrew Univ. Jerusalem)

### The Bi-conical Vector Model at 1/N

We study finite N aspects of the O(m) × O(N-m) vector model with quartic interactions in general 2 ≤ d ≤ 6 spacetime dimensions. This model has recently been shown to display the phenomenon of persistent symmetry breaking at a perturbative Wilson-Fisher-like fixed point in d=4-ε dimensions. The large rank limit of the bi-conical model displays a conformal manifold and a moduli space of vacua. We find a set of three double trace scalar operators that are respectively irrelevant, relevant and marginal deformations of the conformal manifold in general d. We calculate the anomalous dimensions of the single and multi-trace scalar operators to the first sub-leading order in the large rank expansion. The anomalous dimension of the marginal operator does not vanish in general, indicating that the conformal manifold is lifted at finite N. In the case of equal ranks we are able to derive explicitly the scaling dimensions of various operators as functions of only d.

__IHES Covid-19 regulations__:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces

and where the social distancing is not possible;

- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable

without it;

- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass

- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will

be checked at the entrance of the conference room.

==================================================================

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#### 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