Professor Andreas BrandhuberHead of Centre for Theoretical Physics | Professor of Theoretical PhysicsEmail: a.brandhuber@qmul.ac.ukRoom Number: G. O. Jones Building, Room 603Website: http://www.strings.ph.qmul.ac.uk/~andreas/ProfileTeachingResearchPublicationsSupervisionDisseminationGrantsProfileI am a director of the Centre for Theoretical Physics (CTP). I have held postdoctoral fellowships at Tel Aviv University, CERN and Caltech, before joining QMUL in 2003. I received my PhD jointly from CERN and Technical University Vienna. My current research interests are centred around modern methods for the computation of scattering amplitudes with the twofold goal of exhibiting novel symmetries and mathematical structures, and exploiting these insights to develop vastly more efficient tools to compute amplitudes. The theories of concern include N=4 supersymmetric gauge theory, QCD and gravity. Very recently I have employed these techniques to extract results in general relativity relevant to the binary blackhole problem and gravitational radiation. Prizes and Awards: Feinberg Foundation Visiting Faculty Program Fellowship, Weizmann Institute, Israel (2011-2012) Nuclear Physics B Most Cited Article 2006-2010 Award, with Paul Heslop and Gabriele Travaglini, for the paper MHV Amplitudes in N=4 super Yang-Mills and Wilson Loops. The paper is also available through the arXiv. Ludwig Boltzmann Prize of the Austrian Physical Society (2005) TeachingIn the academic year 2022/2023 I teach Quantum Mechanics B (3rd year BSc, Semester A) and will supervise BSc/MSci and MSc projects (potential project titles).ResearchResearch Interests:I am a director of the Centre for Theoretical Physics (CTP). My main research interests are aimed at gaining a deeper understanding of gauge theories and theories of gravity and their interrelations, exploiting insights from string theory and dualities. In the past this has included: the study of the non-perturbative dynamics of supersymmetric gauge theories using exactly calculable anomalies, branes in string theory and dualities; M-theory compactifications on G_2 manifolds and their implications for model building; and the AdS/CFT correspondence. Since 2004 I have been working in the rapidly growing and fertile area of modern methods for scattering amplitudes. Due to the extensive work of me and my collaborators at the CRST we are now one of the leading groups in amplitudes research with currently seven group members working in this area. Topics that I am particularly interested in include: Discovery of novel on-shell methods for scattering amplitudes in gauge theories and gravity. This includes supersymmetric and non-supersymmetric theories such as pure Yang-Mills and QCD, and theories in various dimensions including ABJM-type Chern-Simons matter theories in d=3 and six-dimensional theories. The duality of Wilson loops and amplitudes, and its relation to hidden mathematical structures such as dual conformal symmetry and integrable structures The study of form factors and their relations to amplitudes in QCD. In particular the exploration of the unexpected similarity of form factors in N=4 supersymmetric Yang-Mills and Higgs plus parton amplitudes in QCD, and its relation to new mathematical structures such as transcendentality. Applications of modern amplitude methods to extract classical observables in General Relativity relevant for gravitational wave physis. Examples of research funding:Current Grants: STFC Consolidated Grant: "Amplitudes, Strings and Duality" ST/X00063X/1, A Brandhuber (PI), D Berman, M Buican, R Monteiro, C Papageorgakis, M Perry, S Ramgoolam, R Russo, B Spence, G Travaglini, D Vegh, C Wen, C White, £1,477,965 (2023-2026). Marie Sklodowska Curie Individual Fellowship (H2020): "Bootstrap and Uniqueness for Form Factors and the S-matrix" (EC grant agreement number 101025095), A Brandhuber (PI), L Rodina (PDRA), €224,934 (2022-2024). STFC Consolidated Grant: "Amplitudes, Strings and Duality" ST/T000686/1, A Brandhuber (PI), DS Berman, M Buican, MB Green, RJF Monteiro, C Papageorgakis, MG Perry, S Ramgoolam, R Russo, G Travaglini, C White, £890,210 (2020-2023). European Training Network "SAGEX", Scattering Amplitudes: from Geometry to Experiment, PI G Travaglini, 8 academic partner universities, ca. €4,000,000 (2018-2022). Previous Grants: STFC Consolidated Grant: "String Theory, Gauge Theory and Duality" ST/P000754/1, A Brandhuber (PI), DS Berman, S Ramgoolam, R Russo, M Shigemori, WJ Spence, S Thomas, G Travaglini, C Papageorgakis, C White, £710,337 (2017-2021). STFC Consolidated Grant, String Theory, Gauge Theory and Duality, A Brandhuber (PI), DS Berman, S Ramgoolam, R Russo, WJ Spence, S Thomas, G Travaglini, and B Wecht, £726,605 (2014-2017). STFC Consolidated Grant, String Theory, Gauge Theory and Duality, A Brandhuber (PI), DS Berman, S Ramgoolam, R Russo, WJ Spence, S Thomas, G Travaglini, and B Wecht, £632,431 (2011-2014). Engineering and Physical Sciences Research Council (EPSRC): A. Brandhuber, WJ Spence and G. Travaglini: Grant for the International Workshop: "Amplitudes 2010", £6,363 (May 2010). STFC Rolling Grant, String Theory, Gauge Theory and Duality, A Brandhuber (PI), DS Berman, S Ramgoolam, R Russo, WJ Spence, S Thomas, G Travaglini, £1,405,736 (2008-2013); superceded in 2011 by STFC Consolidated Grant. INFN (Italy): Brandhuber, Spence, Travaglini, V. Del Duca (INFN, Torino), N. Glover (IPPP, Durham), D. Kosower (CEA, Saclay), E. Laenen (Nikhef, Amsterdam), G. Passarino (University of Torino), D. Zeppenfeld (University of Karlsruhe). Two month workshop "Advancing Collider Physics: from Twistors to Monte Carlos" at the Galileo Galilei Institute for Theoretical Physics, Arcetri, Florence, Italy, August 27-October 26 2007, (€125,000). PPARC Rolling Grant "String theory, gauge theory and gravity", Berman, Brandhuber, Ramgoolam, Spence, Thomas, £249,800 (2006-2008). Engineering and Physical Sciences Research Council (EPSRC): A. Brandhuber and B. Spence: Grant for the International Workshop: "From Twistors to Amplitudes", £4,700 (November 2005). Particle Physics and Astronomy Research Council (PPARC) Special Project Grant: A. Brandhuber and B. Spence, "Gauge theory, string theory and twistor space techniques", £134,010, (2005-2007). European Union, Framework 6, Marie Curie Training and Mobility of Researchers Grant, "Superstrings", €259,980, (2004-2008). PublicationsMy list of publications: Complete list of publications on inspirehep.net Brandhuber A, Brown GR, Pichini P et al. (2024). Spinning binary dynamics in cubic effective field theories of gravity. nameOfConference DOI: 10.1007/JHEP08(2024)188 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/99164 Brandhuber A, Brown GR, Chen G et al. (2024). Resummed spinning waveforms from five-point amplitudes. nameOfConference DOI: 10.1007/jhep02(2024)026 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/94544 Brandhuber A, Brown GR, Chen G et al. (2023). One-loop gravitational bremsstrahlung and waveforms from a heavy-mass effective field theory. nameOfConference DOI: 10.1007/jhep06(2023)048 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/89128 Brandhuber A, Brown GR, Chen G et al. (2022). Amplitudes, Hopf algebras and the colour-kinematics duality. nameOfConference DOI: 10.1007/jhep12(2022)101 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/83931 Travaglini G, Brandhuber A, Dorey P et al. (2022). The SAGEX review on scattering amplitudes. nameOfConference DOI: 10.1088/1751-8121/ac8380 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/83486 Brandhuber A, Plefka J, Travaglini G (2022). The SAGEX review on scattering amplitudes Chapter 1: Modern fundamentals of amplitudes. nameOfConference DOI: 10.1088/1751-8121/ac8254 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/83930 Brandhuber A, Chen G, Johansson H et al. (2022). Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory. nameOfConference DOI: 10.1103/physrevlett.128.121601 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/78378 Brandhuber A, Chen G, Travaglini G et al. (2021). Classical gravitational scattering from a gauge-invariant double copy. nameOfConference DOI: 10.1007/JHEP10(2021)118 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/75160 Brandhuber A, Brown GR, Gowdy J et al. (2021). Celestial superamplitudes. nameOfConference DOI: 10.1103/PhysRevD.104.045016 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/74210 Brandhuber A, Chen G, Travaglini G et al. (2021). A new gauge-invariant double copy for heavy-mass effective theory. nameOfConference DOI: 10.1007/jhep07(2021)047 QMRO: https://qmro.qmul.ac.uk/xmlui/handle/123456789/73369 Accettulli Huber M, Brandhuber A, De Angelis S et al. (2021). From amplitudes to gravitational radiation with cubic interactions and tidal effects. nameOfConference DOI: 10.1103/physrevd.103.045015 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/71037 Accettulli Huber M, Brandhuber A, De Angelis S et al. (2020). Eikonal phase matrix, deflection angle, and time delay in effective field theories of gravity. nameOfConference DOI: 10.1103/physrevd.102.046014 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/66963 Accettulli Huber M, Brandhuber A, De Angelis S et al. (2020). Note on the absence of R2 corrections to Newton’s potential. nameOfConference DOI: 10.1103/physrevd.101.046011 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/62842 Accettulli Huber M, Brandhuber A, De Angelis S et al. (2020). Complete form factors in Yang-Mills from unitarity and spinor helicity in six dimensions. nameOfConference DOI: 10.1103/physrevd.101.026004 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/62372 Brandhuber A, Travaglini G (2020). On higher-derivative effects on the gravitational potential and particle bending. nameOfConference DOI: 10.1007/jhep01(2020)010 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/62397 Bianchi L, Brandhuber A, Panerai R et al. (2019). Form factor recursion relations at loop level. nameOfConference DOI: 10.1007/JHEP02(2019)182 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/56375 Bianchi L, Brandhuber A, Panerai R et al. (2019). Dual conformal invariance for form factors. nameOfConference DOI: 10.1007/JHEP02(2019)134 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/56377 Brandhuber A, Kostacińska M, Penante B et al. (2018). Tr(F^3) supersymmetric form factors and maximal transcendentality. Part I. N = 4 super Yang-Mills. nameOfConference DOI: 10.1007/JHEP12(2018)076 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/54183 Brandhuber A, Kostacińska M, Penante B et al. (2018). Tr(F^3) supersymmetric form factors and maximal transcendentality. Part II. 0 < N < 4 super Yang-Mills. nameOfConference DOI: 10.1007/JHEP12(2018)077 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/54184 BRANDHUBER A, Jones M, Penante B et al. (2017). Higgs amplitudes from N=4 super Yang-Mills theory. nameOfConference DOI: 10.1103/PhysRevLett.119.161601 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/28533 Brandhuber A, Hughes E, Panerai R et al. (2016). The connected prescription for form factors in twistor space. nameOfConference DOI: 10.1007/JHEP11(2016)143 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/18787 BRANDHUBER A, Kostacinska M, Penante B et al. (2016). The SU(2|3) dynamic two-loop form factors. nameOfConference DOI: 10.1007/JHEP08(2016)134 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/15899 Brandhuber A, Hughes E, Spence B et al. (2016). One-loop soft theorems via dual superconformal symmetry. nameOfConference DOI: 10.1007/JHEP03(2016)084 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/11916 Brandhuber A, Heslop P, Travaglini G et al. (2015). Yangian Symmetry of Scattering Amplitudes and the Dilatation Operator in N = 4 Supersymmetric Yang-Mills Theory. nameOfConference DOI: 10.1103/PhysRevLett.115.141602 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/9186 Brandhuber A, Penante B, Travaglini G et al. (2015). Integrability and unitarity. nameOfConference DOI: 10.1007/JHEP05(2015)005 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/7645 Brandhuber A, Penante B, Travaglini G et al. (2015). Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory. nameOfConference DOI: 10.1103/PhysRevLett.114.071602 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/7655 Brandhuber A, Penante B, Travaglini G et al. (2014). The last of the simple remainders. nameOfConference DOI: 10.1007/JHEP08(2014)100 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/7646 Bianchi M, Brandhuber A, Travaglini G et al. (2014). Simplifying instanton corrections to N=4 SYM correlators. nameOfConference DOI: 10.1007/JHEP04(2014)101 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/7648 Brandhuber A, Guerdogan O, Korres D et al. (2013). Two-loop Sudakov form factor in ABJM. nameOfConference DOI: 10.1007/JHEP11(2013)022 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/7647 Brandhuber A, Travaglini G, Wen C (2012). All one-loop amplitudes in N=6 superconformal Chern-Simons theory. nameOfConference DOI: 10.1007/JHEP10(2012)145 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/4120 Brandhuber A, Travaglini G, Wen C (2012). A note on amplitudes in N=6 superconformal Chern-Simons theory. nameOfConference DOI: 10.1007/JHEP07(2012)160 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/3764 Brandhuber A, Travaglini G, Yang G (2012). Analytic two-loop form factors in N=4 SYM. nameOfConference DOI: 10.1007/JHEP05(2012)082 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/3760 BRANDHUBER A, TRAVAGLINI G (2007). QUANTUM MHV DIAGRAMS. Continuous Advances in QCD 2006 DOI: 10.1142/9789812708267_0054 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/11239 Brandhuber A, Guerdogan O, Mooney R et al. (2011). Harmony of super form factors. nameOfConference DOI: 10.1007/JHEP10(2011)046 QMRO: qmroHref Brandhuber A, Korres D, Koschade D et al. (2011). One-loop amplitudes in six-dimensional (1,1) theories from generalised unitarity. nameOfConference DOI: 10.1007/JHEP02(2011)077 QMRO: qmroHref Brandhuber A, Spence B, Travaglini G et al. (2011). Form factors in N=4 super Yang-Mills and periodic Wilson loops. nameOfConference DOI: 10.1007/JHEP01(2011)134 QMRO: qmroHref Brandhuber A, Spence B, Travaglini G (2011). Tree-level formalism. nameOfConference DOI: 10.1088/1751-8113/44/45/454002 QMRO: qmroHref Brandhuber A, Spence B, Travaglini G et al. (2010). A note on dual MHV diagrams in N=4 SYM. nameOfConference DOI: 10.1007/JHEP12(2010)087 QMRO: qmroHref Brandhuber A, Heslop P, Katsaroumpas P et al. (2010). A Surprise in the Amplitude/Wilson Loop Duality. nameOfConference DOI: 10.1007/JHEP07(2010)080 QMRO: https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/3083 Brandhuber A, Heslop P, Khoze VV et al. (2010). Simplicity of polygon Wilson loops in N=4 SYM. nameOfConference DOI: 10.1007/JHEP01(2010)050 QMRO: qmroHref Brandhuber A, Heslop P, Travaglini G (2009). Proof of the dual conformal anomaly of one-loop amplitudes in N=4 SYM. nameOfConference DOI: 10.1088/1126-6708/2009/10/063 QMRO: qmroHref Brandhuber A, Heslop P, Travaglini G (2009). One-loop amplitudes in N=4 super Yang-Mills and anomalous dual conformal symmetry. nameOfConference DOI: 10.1088/1126-6708/2009/08/095 QMRO: qmroHref Anastasiou C, Brandhuber A, Heslop P et al. (2009). Two-loop polygon Wilson loops in N=4 SYM. nameOfConference DOI: 10.1088/1126-6708/2009/05/115 QMRO: qmroHref Brandhuber A, Heslop P, Nasti A et al. (2009). Four-point amplitudes in N=8 supergravity and Wilson loops. nameOfConference DOI: 10.1016/j.nuclphysb.2008.09.010 QMRO: qmroHref Brandhuber A, Heslop P, Travaglini G (2008). Note on dual superconformal symmetry of the N=4 super Yang-Mills S matrix. nameOfConference DOI: 10.1103/PhysRevD.78.125005 QMRO: qmroHref Brandhuber A, Vincon M (2008). MHV one-loop amplitudes in Yang-Mills from generalised unitarity. nameOfConference DOI: 10.1088/1126-6708/2008/11/078 QMRO: qmroHref Brandhuber A, Heslop P, Travaglini G (2008). MHV amplitudes in N=4 super-Yang-Mills and Wilson Loops. nameOfConference DOI: 10.1016/j.nuclphysb.2007.11.002 QMRO: qmroHref Brandhuber A, Spence B, Travaglini G et al. (2007). One-loop MHV rules and pure yang-mills. nameOfConference DOI: 10.1088/1126-6708/2007/07/002 QMRO: qmroHref Brandhuber A, Spence B, Travaglini G (2007). Twistor inspired methods in gauge theory and gravity. nameOfConference DOI: 10.1080/00107510701546947 QMRO: qmroHref Brandhuber A, McNamara S, Spence B et al. (2007). Recursion relations for one-loop gravity amplitudes. nameOfConference DOI: 10.1088/1126-6708/2007/03/029 QMRO: qmroHref Brandhuber A, Spence B, Travaglini G (2007). Amplitudes in pure Yang-Mills and MHV diagrams. nameOfConference DOI: 10.1088/1126-6708/2007/02/088 QMRO: qmroHref Brandhuber A (2006). Twistor approach to one-loop amplitudes. nameOfConference DOI: 10.1016/j.nima.2005.11.173 QMRO: qmroHref Brandhuber A, Spence B, Travaglini G (2006). From trees to loops and back. nameOfConference DOI: 10.1088/1126-6708/2006/01/142 QMRO: qmroHref Brandhuber A, McNamara S, Spence B et al. (2005). Loop amplitudes in pure Yang-Mills from generalised unitarity. nameOfConference DOI: 10.1088/1126-6708/2005/10/011 QMRO: qmroHref Bedford J, Brandhuber A, Spence B et al. (2005). A recursion relation for gravity amplitudes. nameOfConference DOI: 10.1016/j.nuclphysb.2005.05.016 QMRO: qmroHref Bedford J, Brandhuber A, Spence B et al. (2005). Non-supersymmetric loop amplitudes and MHV vertices. nameOfConference DOI: 10.1016/j.nuclphysb.2005.01.032 QMRO: qmroHref Bedford J, Brandhuber A, Spence B et al. (2005). A twistor approach to one-loop amplitudes in N=1 supersymmetric Yang-Mills theory. nameOfConference DOI: 10.1016/j.nuclphys.2004.11.031 QMRO: qmroHref Brandhuber A, Spence B, Travaglini G (2005). One-loop gauge theory amplitudes in N=4 super Yang-Mills from MHV vertices. nameOfConference DOI: 10.1016/j.nuclphysb.2004.11.023 QMRO: qmroHref Spence WJ, BRANDHUBER A, Travaglini G et al. (2005). A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory. nameOfConference DOI: 10.1016/j.nuclphysb.2004.11.031 QMRO: qmroHref Spence WJ, TRAVAGLINI G, Brandhuber A et al. (2005). A recursion relation for gravity amplitudes. nameOfConference DOI: 10.1088/1126-6708/2007/03/029 QMRO: qmroHref Spence WJ, TRAVAGLINI G, Brandhuber A et al. (2005). Non-supersymmetric loop amplitudes and MHV vertices. nameOfConference DOI: doi QMRO: qmroHref Spence WJ, TRAVAGLINI G, Brandhuber A (2005). One-loop gauge theory amplitudes in N=4 super Yang-Mills from MHV vertices. nameOfConference DOI: 10.1016/j.nuclphysb.2004.11.023 QMRO: qmroHref BRANDHUBER A, Ita H, Romelsberger C et al. (2003). Chiral Rings, Superpotentials and the Vacuum Structure of N=1 Supersymmetric Gauge Theories. nameOfConference DOI: 10.4310/atmp.2003.v7.n2.a3 QMRO: qmroHref Brandhuber A, Sfetsos K (2002). PP-waves from rotating and continuously distributed D3-branes. nameOfConference DOI: 10.1088/1126-6708/2002/12/050 QMRO: qmroHref Berglund P, Brandhuber A (2002). Matter from G(2) manifolds. nameOfConference DOI: 10.1016/S0550-3213(02)00612-0 QMRO: qmroHref Brandhuber A (2002). G(2) holonomy spaces from invariant three-forms. nameOfConference DOI: 10.1016/S0550-3213(02)00146-3 QMRO: qmroHref Brandhuber A, Gomis J, Gubser SS et al. (2001). Gauge theory at large N and new G(2) holonomy metrics. nameOfConference DOI: 10.1016/S0550-3213(01)00340-6 QMRO: qmroHref Brandhuber A, Sfetsos K (2000). Current correlators in the Coulomb branch of N=4 SYM. nameOfConference DOI: doi QMRO: qmroHref SupervisionScattering Amplitudes describes broadly the research direction I am planning to work on with PhD students. I am more than happy to discuss details of my current research focus with potential applicants. Project Title Classical general relativity and gravitational waves from scattering amplitudes DisseminationConference Talks: 8/2022 "Stringfest@Swansea", fpuk 2022 , Swansea 6/2022 SAGEX Closing Meeting, QMUL 9/2018 SAGEX Kickoff Meeting, QMUL 7/2017 Amplitudes 2017, Edinburgh 4/2017 KITP Conference: "Scattering Amplitudes: from Gauge Theory to Gravity", Santa Barbara 4/2013 Amplitudes 2013, Ringberg Castle Conferences Organised: 6/2022 SAGEX Closing Meeting, QMUL 11/2019 Breakthroughs in Quantum Field Theory and Gravity: an Afternoon with Bern, Dixon and Kosower, QMUL 9/2018 SAGEX Kickoff Meeting, QMUL 4/2012 Recent Advances in Scattering Amplitudes, Cambridge 5/2010 Amplitudes 2010, QMUL 11/2005 From Twistors to Amplitudes, QMUL General Public: Article on scattering amplitudes: Picture perfectGrantsCurrent Grants: STFC Consolidated Grant: "Amplitudes, Strings and Duality" ST/X00063X/1, A Brandhuber (PI), D Berman, M Buican, R Monteiro, C Papageorgakis, M Perry, S Ramgoolam, R Russo, B Spence, G Travaglini, D Vegh, C Wen, C White, £1,477,965 (2023-2026). Marie Sklodowska Curie Individual Fellowship (H2020): "Bootstrap and Uniqueness for Form Factors and the S-matrix" (EC grant agreement number 101025095), A Brandhuber (PI), L Rodina (PDRA), €224,934 (2022-2024). STFC Consolidated Grant: "Amplitudes, Strings and Duality" ST/T000686/1, A Brandhuber (PI), DS Berman, M Buican, MB Green, RJF Monteiro, C Papageorgakis, MG Perry, S Ramgoolam, R Russo, G Travaglini, C White, £890,210 (2020-2023). European Training Network "SAGEX", Scattering Amplitudes: from Geometry to Experiment, PI G Travaglini, 8 academic partner universities, ca. €4,000,000 (2018-2022).