A self-oscillator generates and maintains a periodic motion at the expense of an energy source with no corresponding periodicity. Small perturbations about equilibrium are amplified. Non-linearity accounts for steady-state oscillations and for the ability of coupled self-oscillators to exhibit both spontaneous synchronisation (“entrainment”) and chaos. The theory of self-oscillators has achieved its greatest sophistication in mathematical control theory and in the study of ordinary differential equations. I shall explain in this talk how an understanding better suited to physicists can be founded on considerations of energy, efficiency, and thermodynamic irreversibility. After reviewing the key differences between forced a parametric resonances on the one hand and self-oscillators on the other, I will comment on how a physical approach to the theory of self-oscillators throws new light on flow instabilities. I will close by describing mechanical and hydrodynamic analogs of the Zel’dovich superradiance of rotating black holes, a subject of considerable interest in high-energy physics today.

It is usually hard to compute entanglement entropy and mutual information for conformal field theories (CFT). Ryu-Takayanagi proposals allows us to find the same quantities using calculations in gravity. In this talk I will show how to find holographic entanglement entropy and scrambling time for BTZ black hole perturbed by a heavy (backreacting) particle. Holographic bulk description improves on the shock-wave approximation in 3d bulk dimensions. I will also discuss my work to generalize this calculation to the rotating BTZ black hole.

Symbolic summation started with Abramov's telescoping algorithm for rational functions (1971), was pushed further by Gosper's algorithm for hypergeometric expressions (1978) and reached its first peak level with Zeilberger's creative telescoping algorithm (1990) and Petkovsek's recurrence solver (1992) to treat definite hypergeometric sums. In this talk we focus on the difference ring approach which covers all these algorithms as special cases. Its foundation was lead by Karr's summation algorithm (1981) and has been pushed forward significantly within the last 18 years. In a long term project with DESY (Deutsches Elektronen-Synchrotron) the produced algorithms have been playing a central role to evaluate several hundred thousands of 2-loop and 3-loop massive Feynman integrals. In this talk we will elaborate by concrete examples how our advanced difference ring theory and the underlying algorithms encoded within the summation package Sigma are used to attack these highly complicated Feynman integrals.

In the first part of the talk I give an introduction to the computational tool called "Hilbert Series" (HS). I analyze how it can be employed for the characterization of the moduli space of vacua of a QFT and of the moduli space of instantons. Then, in the second part of the talk, I discuss the moduli space of (framed) self-dual instantons on CP^2. These are described by an ADHM-like construction which allows to compute the Hilbert Series of the moduli space. The latter has been found to be blind to certain compact directions. I probe these directions, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover I discuss the ADHM-like construction of instantons on CP^2/Z_n as well as compute its Hilbert series. As in the unorbifolded case, these turn out to coincide with those for instantons on C^2/Z_n. This talk is mainly based on https://arxiv.org/abs/1502.07876 .

Inspired by the recent success of the numerical approach to the conformal bootstrap, we revisit the S-matrix bootstrap program. We shall explain how to obtain analytic bounds on the interaction strength in 1+1 QFT. In higher dimensions, we propose a numerical algorithm that seems to converge to optimal bounds.

PhD Lecture 4: Black hole microstates and exotic branes: We will discuss supergravity representations of black hole microstates and the possible role played by exotic branes.

PhD Lecture 3: Exotic branes: We will see that duality predicts various low-codimension objects called exotic branes, and discuss their peculiar properties.

T-duality is known to generate exotic objects, which cannot be consistently described in terms of conventional supergravity. In the focus of this talk are backgrounds of DFT carrying Q or R fluxes, which are non-commutative and non-associative in the conventional description. We show that the Berman-Rudolph's DFT-monopole solution which unifies the backgrounds of NS5-brane and KK-monopole also describes these exotic backgrounds upon a choice of section condition. The resulting Q- and R-monopoles no longer have non-trivial monodromies and the only sign of non-geometry is a non-trivial dependence of the fields on dual (winding) coordinates. based on 1607.05450

PhD Lecture 2: Supergravity solutions: We will discuss the supergravity solutions representing various brane configurations and see how the duality transformations are manifested in them.

PhD Lecture 1: String theory and branes: We will review the extended objects in string theory and the duality transformations relating them

Higher-spin fields can play an important role in effective field theories and increasingly are of interest due to their appearance in recent studies of holography. Understanding their interactions is however often involved and searching for alternative formulations could be very useful. In this talk we will consider one such formulation, namely twistors. After giving a general introduction to the use of twistors in describing the dynamics of massless field theories, we will focus on the construction of off-shell actions directly in twistor space including a recent higher-spin generalisation of self-dual Weyl gravity. We will show how this formulation produces the expected flat space-time spectrum and linearised symmetries. In analogy with the known embedding of Einstein gravity inside Weyl gravity, we identify a ghost free sub-sector of the conformal higher-spin theory and consider its cubic couplings. Finally we describe proposed anti-self-dual interaction terms to extend the twistor action to the full conformal higher-spin theory.

The high energy behavior of physical scattering amplitudes challenged early string theory. With the discovery of gauge-string dualities the obstacle was overcome and today string theory provides precision results, in particular for the high energy limit. In my talk I will review the many facets of integrability in high energy scattering at weak, intermediate and strong coupling.

I will present a proof for a monotonicity theorem, or c-theorem, for a three-dimensional Conformal Field Theory (CFT) on a space with a boundary, and for a higher-dimensional CFT with a two-dimensional defect. The proof is applicable only to renormalization group flows that preserve locality, reflection positivity, and Euclidean invariance along the boundary or defect, and that are localized at the boundary or defect, such that the bulk theory remains conformal along the flow. The method of proof is a generalization of Komargodski’s proof of Zamolodchikov’s c-theorem. The key ingredient is an external “dilaton” field introduced to match Weyl anomalies between the ultra-violet (UV) and infra-red (IR) fixed points. Reflection positivity in the dilaton’s effective action guarantees that a certain coefficient in the boundary/defect Weyl anomaly must take a value in the UV that is larger than (or equal to) the value in the IR. This boundary/defect c-theorem may have important implications for many theoretical and experimental systems, ranging from graphene to branes in string theory and M-theory.

We will review a series of algebraic techniques to describe classically integrable systems, with an eye to their quantisation. The topics we shall attempt to cover will be: 1. General introduction to classical integrability and notion of Lax pair 2. Classical r-matrices and exchange relations 3. Belavin-Drinfeld theorems and classifications 4. Quantisation and elements of algebraic Bethe ansatz

In this talk we consider BPS states in 4D, N=2 gauge theory in the presence of defects. We give a semiclassical description of these `framed BPS states' in terms of kernels of Dirac operators on moduli spaces of singular monopoles. For both framed and ordinary BPS states we present a conjectural map between the data of the semiclassical construction and the data of the low-energy, quantum-exact Seiberg-Witten description. This map incorporates both perturbative and nonperturbative field theory corrections to the supersymmetric quantum mechanics of the monopole collective coordinates. We use it to translate recent developments in the study of N=2 theories, including wall-crossing formulae and the no-exotics theorem, into geometric statements about the Dirac kernels. The no-exotics theorem implies a broad generalization of Sen's conjecture concerning the existence of L^2 harmonic forms on monopole moduli space. This talk is based on work done in collaboration with Greg Moore and Dieter Van den Bleeken.

We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin fields. They arise from an internal structure which can be viewed as a twisted bundle over S^4, leading to a covariant noncommutative geometry. The linearized 4-dimensional Einstein equations are obtained from the classical matrix model action under certain conditions, modified by an IR cutoff. Some one-loop contributions to the effective action are computed using the formalism of string states.

One can easily be frustrated by the tremendous redundancy in possible physical description. By this I mean the freedom to choose gauge, make field redefinitions, add any amount of auxiliary spectator matter, and the such. Happily we can exploit such freedom to encourage the emergence of a new duality in gauge theories. The existence of a duality between color and kinematics exposes a hidden local double-copy structure inherent to prediction in many theories. This structure weaves its way between theories both formal and phenomenological, from QCD to Gravity, from Chiral Perturbation Theory to Born-Infeld and Volkov-Akulov, and from open to closed superstring theories. The duality is sharpest at the level of the perturbative S-matrix — so I will focus my talk there, although I will also mention some recent provocative work beyond scattering. I will mainly discuss progress and challenges to generically achieving color-dual kinematic representations at the multi-loop level. I present a path forward that introduces, at least temporarily, a redundancy of description that we can exploit to map a set of functional relations to linear ones. I will talk about this approach in terms of a geometric picture involving the graph of local graphs, discussing tradeoffs and applicability to long-standing problems.

The Cachazo-He-Yuan (CHY) formulas are a remarkable representation of tree-level massless scattering amplitudes. Similarly to the Twistor String formulas, the CHY formula presents amplitudes as an integrals over the moduli space of Riemann surfaces constrained to the solutions of a set of algebraic equations called the scattering equations. But contrary to the Twistor String formulas, they can be written in for any dimension and for a variety of massless theories. Behind the original CHY formula and the scattering equations lies a 2D CFT called the Ambitwistor String, much like the original Twistor String, this is a chiral CFT in which correlators of vertex operators reproduce the CHY formulas and give a geometric interpretation of the scattering equations. The Ambitwistor string possesses a few peculiar characteristics when viewed as a string theory, its low energy efective action is the same as Type II closed strings but the appearance of the scattering equations suggests a high-energy limit has been taken a la Gross and Mende. Besides, its genus one correlation functions are modular invariant but UV divergent since they correspond to 10D SUGRA amplitudes. In this talk I'll talk about a program started with P. Tourkine in which the Ambitwistor String (and other Twistor Strings) are treated as coming from the tensionless limit of classcial string theories. These are know as null strings and have a long history in the literature. I'll review the null string and its supersymmetric extensions and show how the Ambitwistor String can be obtained from a particular gauge fixing of the null string. In doing so, I'll address the issue of possible inequivalent quantizations of the null string and compare it to the case of the usual string and shed a light its relation to the Ambitwistor String.

We discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. These observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 Super Yang-Mills theory.