Poisson-Lie T-duality was originally introduced to identify the dynamics of closed strings probing different target spaces. But nowadays it also has become a crucial ingredient in the construction of integrable, two-dimensional $\sigma$-models. After reviewing this intriguing connection from a worldsheet perspective, I will switch to the target space. There we are going to see that Poisson-Lie T-duality naturally appears in the context of gauged SUGRAs and consistent truncations which help to construct new AdS vacua.

Integrability, duality and beyond , 3rd - 5th June 2019, Facultade de Física, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

Both constituents of my title are well established areas of research with a wide range of applications. Unfortunately, in the current standard formulation of DFT only the tiny subset of PL symmetry which gives rise to abelian T-duality is manifest. In my talk, I present an altered DFT version, DFT on group manifolds, which make the full PL symmetry manifest. We discuss both the NS/NS and R/R sector of the theory. Later allows us to derive the transformation rules for R/R field strengths under full PL T-duality for the first time. If time permits, I will also comment on applications in integral deformations and the extension of the framework to also capture dressing cosets.

"String: T-duality, Integrability and Geometry", 4th - 8th March 2019, Tohoku University, Sendai, Japan

A formulation of Double Field Theory is presented which makes Poisson-Lie T-duality manifest. It allows to identify the doubled space with a Drinfeld double and provides a powerful tool to extract the transformation of the metric, B-field, dilaton and R/R potentials under Poisson-Lie T-duality.

Fundamental Interactions, Geometry and Topology., 25th October 2018, University of Naples Federico II, Department of Physics "Ettore Pancini", Italy

Dualities and Generalized Geometries, 10th - 15th September 2018, Corfu, Greece

I review how integrability allows us to explore the planar limit of the AdS/CFT correspondence for arbitrary values of the t'Hooft coupling. In string theory integrability of the 2D $\sigma$-model is closely related to Poisson-Lie Symmetry. Double Field Theory can be used to make this symmetry manifest and therewith provides a new tool to study the implications for the gravity side of the correspondence.

• USU Strings and Black Holes Workshop, 30th April - 2nd May 2018, Department of Physics, Utah State University, Logan, USA
• Exceptional Field Theories, Strings and Holography, 23rd - 25th April 2018, Mitchell Institute, Texas A&M, College Station, USA

A formulation of Double Field Theory is presented which makes Poisson-Lie T-duality manifest. It allows to identify the doubled space with a Drinfeld double and provides a powerful tool to extract the transformation of the metric, $B$-field, dilaton and R/R potentials under Poisson-Lie T-duality.

String Dualities and Geometry, 15th - 19th January 2018, Centro Atomico Bariloche, San Carlos de Bariloche, Argentina

Theories of class S are 4D N=2 SCFTs which result from the compactification of 6D N=(2,0) SCFTs on punctured Riemann surfaces. They provide a geometric perspective on S-duality and are essential in the AGT correspondence. I will present the first step in extending this construction to N=1. To this end, we discuss the punctures relevant in the compactification of the world-volume theory of M5-branes probing an ADE-singularity. They are closely related to the time evolution of a dynamical system and exhibit a surprisingly rice and complex structure compared to N=2.

String Pheno 2017, 3rd - 7th July 2017, Virgina Tech, Blacksburg, USA

Recent Advances in T/U-dualities and Generalized Geometries, 6th - 9th June 2017, Rudjer Bošković Institute, Zagreb, Croatia

Theories of class S are 4D N=2 SCFTs which result from the compactification of 6D N=(2,0) SCFTs on punctured Riemann surfaces. They provide a geometric perspective on S-duality and are essential in the AGT correspondence. I will present the first step in extending this construction to N=1. To this end, we discuss the punctures relevant in the compactification of the world-volume theory of M5-branes probing an ADE-singularity. They are closely related to the time evolution of a dynamical system and exhibit a surprisingly rich and complex structure compared to N=2.

17th southeastern regional mathematical string theory meeting, 8th April 2017, UNC Chapel Hill, Chapel Hill, USA

Generalized Geometry & T-dualities, 9th - 13th May 2016, Simons Center for Geometry and Physics, Stony Brook, USA

CERN-CKC TH Institute on Duality Symmetries in String and M-Theories, 3rd - 14th August 2015, CERN, Switzerland

Besides propagating in target space like a point particle, a closed string is also able to wind around non-contractible circles. A direct consequence thereof is T-duality. In the textbook example, it identifies the closed string dynamics on a large and a small circle by interchanging its winding and momentum modes. Patching a background by such dualities clearly goes beyond the notion of conventional geometry. However, there are extensive efforts to embed them into a framework called string geometry. It provides access to a vast number of new backgrounds with intriguing phenomenology, like e.g. the possibility to obtain de Sitter vacua. Double Field Theory (DFT) is the most promising approach to describe these backgrounds and their properties. But still, it is closely related to the torus. I will present a theory based on Closed String Field theory starting from a Wess-Zumino-Witten model which goes beyond the torus. It plays an important role in clarifying the recent confusion about different constraints in DFT. Furthermore it allows to uplift a large class of new backgrounds to string theory. These backgrounds are not T-dual to any geometric ones.

12th southeastern regional mathematical string theory meeting, 25th October 2014, Duke University, Durham, USA

Workshop "Frontiers in String Phenomenology'', 28th July - 1st August 2014, Ringberg Castle, Tegernsee, Germany

Bayrischzell Workshop 2014 on quantized geometry and physics, 23rd - 26th May 2014, Bayrischzell, Germany

Science Week 2013, 2nd - 5th December 2013, Max-Planck Institut for Extraterrestrial Physics, Garching, Germany

International Research Program "The Particle Physics and Cosmology of Supersymmetry and String Theory", Spring 2013 Meeting, 21st - 23rd March 2013, Ludwig-Maximilians-University Munich, Munich, Germany

Generalised Scherk-Schwarz reductions are a powerful tool to construct consistent truncations in Double and Exceptional Field Theories. Recently, it turned out that they are also closely related to Poisson-Lie T-duality. However, the most general form of Poisson-Lie T-duality, the dressing coset construction, can not be implemented in terms of a generalised Scherk-Schwarz ansatz. I will show that implementing it in generalised geometry leads to a natural extension of the generalised Scherk-Schwarz ansatz which comes with many new features: 1) Partial or full breaking of SUSY which allows to find many new examples of generalised Kähler or Calabi-Yau Manifolds. 2) Singular backgrounds with localised sources. 3) Localised vector multiplets while still resulting in consistent truncations.

• Group Seminar, 19th December 2019, Arnold Sommerfeld Center for Theoretical Physics, Munich, Germany
• CRST Seminar, 11th December 2019, Centre for Research in String Theory (CRST), Queen Mary University of London, London, UK

A formulation of Double Field Theory is presented which makes Poisson-Lie T-duality manifest. It allows to identify the doubled space with a Drinfeld double and provides a powerful tool to extract the transformation of the metric, B-field, dilaton and R/R potentials under Poisson-Lie T-duality.

• Quantum Field and String Theory Group Seminar, 20th March 2019, Humboldt-University Berlin, Berlin, Germany
• Swansea Theory Seminar, 13th March 2019, Swansea University, Swansea, UK
• "Strings, CFT & Integrability", 20th November 2018, ETH Zurich, Zurich, Switzerland

I review how integrability allows us to explore the planar limit of the AdS/CFT correspondence for arbitrary values of the t'Hooft coupling. In string theory integrability of the 2D $\sigma$-model is closely related to Poisson-Lie Symmetry. Double Field Theory can be used to make this symmetry manifest and therewith provides a new tool to study the implications for the gravity side of the correspondence.

• String Theory Seminar, 15th March 2019, Imperial College London, London, UK
• Fields and Strings, 20th December 2018, Ludwig Maximilian University of Munich, Munich, Germany
• AdS(Algeometry, duality and Strings) seminar, 8th November 2018, Yau Mathematical Sciences Center, Tsinghua University, Beijing, China

String theory's secret in approaching an UV complete theory of gravity is the transition from point particles to extended objects. A direct consequence is the emergence of dualities, like T-, S- and U-duality. They have numerous applications and are essential for studying string theory, but for me the most intriguing question is: "Can they teach us more about (quantum) gravity?". My talk gives a short introduction to double / exceptional field theory, a framework which is exactly motivated by this question. Instead of presenting all the formal details, I will try to focus on the underlying ideas and important applications, like the construction of new flux vacua or consistent truncations of supergravity. Finally, I explain some open questions which are currently under active research and motivate why their answers could also be beneficial for other research areas, like the gauge gravity correspondence.

OIST Seminar, 9th January 2018, Okinawa Institute of Science and Technology Graduate University, Japan

Poisson-Lie T-duality is a generalization of traditional non-abelian T-duality and enjoys, at least at the classical level, all features of abelian T-duality. Recently, it got a lot of attention in the context of integrable $\eta$- and $\lambda$-deformations. I review this intriguing framework, outline its applications and show that it naturally admits a double field theory description. Latter has many applications in the realm of abelian T-duality but did not really touch Poisson-Lie T-duality until now. I present an extension of the current double field theory formulation which makes Poisson-Lie T-duality manifest. It gives rise to various new applications and also introduces powerful new mathematical structures, like Drinfeld doubles and quantum groups, in the theory.

YITP Seminar, 9th November 2017, C.N. Yang Institute for Theoretical Physics, Stony Brook, USA

While only three spheres, $S^1$, $S^3$ and $S^7$, are parallelizable, it was recently shown that all spheres are generalized parallelizable. In addition to its beautiful mathematical structure, this extended notion of parallelizability allows to identify certain maximal gauged supergravities as consistent truncations of 10/11D supergravity. In this talk, I present the first systematic construction of generalized parallelize spaces and demonstrate how this string theory inspired concept captures T-duality in a natural way.

• High-Energy Theory Seminars, 23rd October 2017, Mitchell Institute, Texas A&M, College Station, USA
• String Theory Seminar, 27th September 2017, Virgina Tech, Blacksburg, USA
• HEP Theory Seminar, 18th September 2017, University of Pennsylvania, Philadelphia, USA

Dualities are at the heart of string theory. They identify closed string theories in different target spaces (T-duality) and at inverse values of the string coupling (S-duality). To exploit their full potential, it would be great to make them manifest already at the level of the low energy effective action. Double Field Theory (DFT) exactly follows this idea for T-duality on a torus. Incorporating also S-duality in this framework, Exceptional Field Theory (EFT) is born. I review these two approaches and show how they are expect to give new insights in subject like flux compactifications, moduli stabilization and cosmology. I emphasize their weak spots and present my humble contribution to deal with some of these problems.

ISCAP Seminar, 3rd March 2016, Columbia University, New York, USA

Only a fraction of the vast landscape of vacua in string theory is accessible from supergravity. Stringy geometries, whose properties are governed by the extended nature of the string, are beyond its scope. Double Field Theory (DFT), which makes T-duality on tori manifest at the level of an effective field theory, provides a convenient tool to explore vacua beyond the supergravity regime. Despite the substantial progresses made in this direction, there are still open questions and technical ambiguities. Some of them can be solved by extending the derivation of DFT from a torus to more general non-abelian group manifolds. After a short review of the existing formalism, I derive such a theory, called DFT$_{\mathrm{WZW}}$, using Closed String Field Theory applied to Wess-Zumino-Witten models. Further, I discuss its connection to half maximal gauged supergravities in lower dimensions. Even for those of them who can not be generated by a supergravity compactification, DFT$_{\mathrm{WZW}}$ provides a higher dimensional origin.

High-Energy Theory Seminar, 19th October 2015, Mitchell Institute, Texas A&M, College Station, USA

Besides propagating in target space like a point particle, a closed string is also able to wind around non-contractible circles. A direct consequence thereof is T-duality. In the textbook example, it identifies the closed string dynamics on a large and a small circle by interchanging its winding and momentum modes. Patching a background by such dualities clearly goes beyond the notion of conventional geometry. However, there are extensive efforts to embed them into a framework called string geometry. It provides access to a vast number of new backgrounds with intriguing phenomenology, like e.g. the possibility to obtain de Sitter vacua. Double Field Theory (DFT) is the most promising approach to describe these backgrounds and their properties. But still, it is closely related to the torus. I will present a theory based on Closed String Field theory starting from a Wess-Zumino-Witten model which goes beyond the torus. It plays an important role in clarifying the recent confusion about different constraints in DFT. Furthermore it allows to uplift a large class of new backgrounds to string theory. These backgrounds are not T-dual to any geometric ones.

• Matrices, Strings & Random Geometries Seminar, 5th December 2014, IPhT CEA-Saclay, Saclay, Franace
• High Energy Theory Informal Meeting, 19th November 2014, Caltech, Pasadena, USA
• Theoretical Elementary Particle Physics Seminar, 13th November 2014, UCLA, Los Angeles, USA
• Theoretical High Energy Physics Seminar, 12th November 2014, University of Southern California, Los Angeles, USA
• String Theory Group Meeting, 4th November 2014, Berkeley Center for Theoretical Physics, Berkeley, USA
• Theory Seminar, 29th October 2014, University of Chicago, Chicago, USA
• String Club, 20th October 2014, MIT, Cambridge, USA
• YITP Seminar, 15th October 2014, C.N. Yang Institute for Theoretical Physics, Stony Brook, USA