
This is my webpage. I'm a mathematical physicist, meaning that I study the mathematical structures that underlie my favourite physical theories. These include vertex operator algebras / conformal field theories and their relation with string theory, integrable models, and anything else that I can think of. At the moment, this means logarithmic conformal field theory, string theory on Lie supergroups, Temperley–Lieb representations (and its generalisations), and the integrability of nonlinear sigma models. I'm especially interested in the appearance of indecomposable (but reducible) representations in physics, but pretty much anything that involves cool math is fine with me. Currently, I'm studying examples of conformal field theories in which the correlation functions exhibit logarithmic singularities. In representationtheoretic terms, these logarithmic theories are built from representations which are indecomposable but not irreducible. Such theories arise naturally when considering socalled nonlocal observables (crossing probabilities, fractal dimensions) in the conformal limit of many exactly solvable lattice models (percolation, Ising). They are also relevant to stringtheoretic considerations, especially when the target space admits fermionic directions, AdS/CFT, and perhaps even to black hole holography. In mathematics, there is a tantalising suggestion that logarithmic conformal field theory and Schramm–Loewner Evolution may be equivalent in some sense. My current research aims to further our knowledge of the algebraic structures underpinning logarithmic conformal field theories. Expected outcomes include an improved understanding of the applications to statistical physics and string theory, as well as developing beautiful connections with pure mathematics. 





A Gainutdinov, D Ridout and I Runkel (Eds). Logarithmic conformal field theory, a special issue of the Journal of Physics A46:490301, 2013. Preface (5 pages).
Z Fehily, K Kawasetsu and D Ridout. Classifying relaxed highestweight modules for admissiblelevel Bershadsky–Polyakov algebras. 2020, arXiv:2007.03917 [math.RT] (35 pages).
D Adamović, K Kawasetsu and D Ridout. A realisation of the Bershadsky–Polyakov algebras and their relaxed modules. 2020, arXiv:2007.00396 [math.QA] (23 pages).
T Creutzig, C Jiang, F Orosz Hunziker, D Ridout and J Yang. Tensor categories arising from the Virasoro algebra. 2020, arXiv:2002.03180 [math.RT] (30 pages).
K Kawasetsu and D Ridout. Relaxed highestweight modules II: classifications for affine vertex algebras. 2019, arXiv:1906.02935 [math.RT] (29 pages).
T Creutzig, T Liu, D Ridout and S Wood. Unitary and nonunitary N=2 minimal models. Journal of High Energy Physics 1906:024, 2019, arXiv:1902.08370 [mathph] (32 pages).
S Kanade and D Ridout. NGK and HLZ: fusion for physicists and mathematicians. in Affine, Vertex and Walgebras, Springer INdAM Series 37:135–181, 2019, arXiv:1812.10713 [mathph].
T Creutzig, S Kanade, T Liu and D Ridout. Cosets, characters and fusion for admissiblelevel osp(12) minimal models. Nuclear Physics B938:22–55, 2018, arXiv:1806.09146 [hepth].
K Kawasetsu and D Ridout. Relaxed highestweight modules I: rank 1 cases. Communications in Mathematical Physics 368:627–663, 2019, arXiv:1803.01989 [math.RT].
D Ridout, S Siu and S Wood. Singular vectors for the W_N algebras. Journal of Mathematical Physics 59:031701, 2018, arXiv:1711.10804 [mathph] (18 pages).
D Ridout, J Snadden and S Wood. An admissible level osp(12)model: modular transformations and the Verlinde formula. Letters in Mathematical Physics 108:2363–2423, 2018, arXiv:1705.04006 [hepth].
J Auger, T Creutzig and D Ridout. Modularity of logarithmic parafermion vertex algebras. Letters in Mathematical Physics 108:2543–2587, 2018, arXiv:1704.05168 [math.QA].
T Creutzig, S Kanade, A Linshaw and D Ridout. Schur–Weyl duality for Heisenberg cosets. Transformation Groups 24:301–354, 2019, arXiv:1611.00305 [math.QA].
O Blondeau–Fournier, P Mathieu, D Ridout and S Wood. Superconformal minimal models and admissible Jack polynomials. Advances in Mathematics 314:71–123, 2017, arXiv:1606.04187 [hepth].
O Blondeau–Fournier, P Mathieu, D Ridout and S Wood. The superVirasoro singular vectors and Jack superpolynomials relationship revisited. Nuclear Physics B913:34–63, 2016, arXiv:1605.08621 [mathph].
J Belletête, D Ridout and Y Saint–Aubin. Restriction and induction of indecomposable modules over the Temperley–Lieb algebras. Journal of Physics A51:045201, 2018, arXiv:1605.05159 [mathph] (55 pages).
M Canagasabey and D Ridout. Fusion rules for the logarithmic N=1 superconformal minimal models II: including the Ramond sector. Nuclear Physics B905:132–187, 2016, arXiv:1512.05837 [hepth].
M Canagasabey, J Rasmussen and D Ridout. Fusion rules for the logarithmic N=1 superconformal minimal models I: the Neveu–Schwarz sector. Journal of Physics A48:415402, 2015, arXiv:1504.03155 [hepth] (49 pages).
A Morin–Duchesne, J Rasmussen and D Ridout. Boundary algebras and Kac modules for logarithmic minimal models. Nuclear Physics B899:677–769, 2015, arXiv:1503.07584 [hepth].
D Ridout and S Wood. Relaxed singular vectors, Jack symmetric functions and fractional level sl(2) models. Nuclear Physics B894:621–664, 2015, arXiv:1501.07318 [hepth].
D Ridout and S Wood. From Jack polynomials to minimal model spectra. Journal of Physics A48:045201, 2015, arXiv:1409.4847 [hepth] (17 pages).
D Ridout and S Wood. The Verlinde formula in logarithmic CFT. Journal of Physics: Conference Series 597:012065, 2015, arXiv:1409.0670 [hepth] (11 pages).
D Ridout and S Wood. Bosonic ghosts at c=2 as a logarithmic CFT. Letters in Mathematical Physics 105:279–307, 2015, arXiv:1408.4185 [hepth].
D Ridout and S Wood. Modular transformations and Verlinde formulae for logarithmic (p_+,p_)models. Nuclear Physics B880:175–202, 2014, arXiv:1310.6479 [hepth].
T Creutzig and D Ridout. Modular data and Verlinde formulae for fractional level WZW models II. Nuclear Physics B875:423–458, 2013, arXiv:1306.4388 [hepth].
T Creutzig, D Ridout and S Wood. Coset constructions of logarithmic (1,p)models. Letters in Mathematical Physics 104:553–583, 2014, arXiv:1305.2665 [math.QA].
T Creutzig and D Ridout. Logarithmic conformal field theory: beyond an introduction. Journal of Physics A46:494006, 2013, arXiv:1303.0847 [hepth] (72 pages).
A Babichenko and D Ridout. Takiff superalgebras and conformal field theory. Journal of Physics A46:125204, 2013, arXiv:1210.7094 [mathph] (26 pages).
T Creutzig and D Ridout. Modular data and Verlinde formulae for fractional level WZW models I. Nuclear Physics B865:83–114, 2012, arXiv:1205.6513 [hepth].
D Ridout and Y Saint–Aubin. Standard modules, induction and the Temperley–Lieb algebra. Advances in Theoretical and Mathematical Physics 18:957–1041, 2014, arXiv:1204.4505 [mathph].
D Ridout. Nonchiral logarithmic couplings for the Virasoro algebra. Journal of Physics A45:255203, 2012, arXiv:1203.3247 [hepth] (12 pages).
T Creutzig and D Ridout. Walgebras extending gl(11). Springer Proceedings in Mathematics and Statistics 36:349–368, 2013, arXiv:1111.5049 [hepth].
T Creutzig and D Ridout. Relating the archetypes of logarithmic conformal field theory. Nuclear Physics B872:348–391, 2013, arXiv:1107.2135 [hepth].
D Ridout and J Teschner. Integrability of a family of quantum field theories related to sigma models. Nuclear Physics B853:327–378, 2011, arXiv:1102.5716 [hepth].
D Ridout. Fusion in fractional level sl(2)theories with k=1/2. Nuclear Physics B848:216–250, 2011, arXiv:1012.2905 [hepth].
D Ridout. sl(2)_{1/2} and the triplet model. Nuclear Physics B835:314–342, 2010, arXiv:1001.3960 [hepth].
K Kytölä and D Ridout. On staggered indecomposable Virasoro modules. Journal of Mathematical Physics 50:123503, 2009, arXiv:0905.0108 [mathph] (51 pages).
D Ridout. sl(2)_{1/2}: A case study. Nuclear Physics B814:485–521, 2009, arXiv:0810.3532 [hepth].
D Ridout. On the percolation BCFT and the crossing probability of Watts. Nuclear Physics B810:503–526, 2009, arXiv:0808.3530 [hepth].
P Mathieu and D Ridout. Logarithmic M(2,p) minimal models, their logarithmic couplings, and duality. Nuclear Physics B801:268–295, 2008, arXiv:0711.3541 [hepth].
P Mathieu and D Ridout. From percolation to logarithmic conformal field theory. Physics Letters B657:120–129, 2007, arXiv:0708.0802 [hepth].
P Mathieu and D Ridout. The extended algebra of the minimal models. Nuclear Physics B776:365–404, 2007, arXiv:hepth/0701250 .
P Mathieu and D Ridout. The extended algebra of the SU(2) Wess–Zumino–Witten models. Nuclear Physics B765:201–239, 2007, arXiv:hepth/0609226 .
P Bouwknegt and D Ridout. Presentations of Wess‐Zumino–Witten fusion rings. Reviews in Mathematical Physics 18:201–232, 2006, arXiv:hepth/0602057 .
P Bouwknegt and D Ridout. A note on the equality of algebraic and geometric Dbrane charges in WZW models. Journal of High Energy Physics 05 (2004) 029, 2004, arXiv:hepth/0312259 (13 pages).
P Bouwknegt, P Dawson, and D Ridout. Dbranes on group manifolds and fusion rings. Journal of High Energy Physics 12 (2002) 065, 2002, arXiv:hepth/0210302 (22 pages).
D Ridout and K Judd. Convergence properties of gradient descent noise reduction. Physica D165:26–47, 2002.
P Bouwknegt, L Chim, and D Ridout. Exclusion statistics in conformal field theory and the UCPF for WZW models. Nuclear Physics B572:547–573, 2000, arXiv:hepth/9903176.
A new approach to Walgebras, Geometry, Algebra, Mathematical Physics and Topology Seminar, Cardiff University (virtual seminar), 25/6/2020.
Bosonic ghosts: modularity for a nonrational CFT, University of Tokyo (virtual seminar), 18/5/2020.
Fractionallevel WZW models, ANZAMP Congress, Tweed Heads, 5/2/2020.
Representations of affine vertex algebras: beyond category O, AustMS Meeting, Monash University, 4/12/2019.
Representations of affine vertex algebras, Workshop on Vertex Operator Algebras and Related Topics, Tianyuan Mathematical Center, Chengdu, 19/8/2019.
Representations of affine vertex algebras, The Mathematical Foundation of Conformal Field Theory and Related Topics, Chern Institute of Mathematics, Tianjin, 14/6/2019.
A higherrank fractionallevel WessZuminoWitten model, ANZAMP Congress, Merimbula, 6/2/2019.
Modularity beyond rationality, Subfactors in Sydney, UNSW, 4/2/2019.
An introduction to logarithmic conformal field theory, International Congress on Mathematical Physics, Montreal, 24/7/2018.
sl_{3} weight modules and higherrank logarithmic CFT, ANZAMP Congress, Auckland, 31/1/2018.
The standard module formalism: modularity and logarithmic CFT, Integrability in LowDimensional Systems, MATRIX Creswick, 29/6/2017.
A (gentle) introduction to logarithmic conformal field theory, Integrability in LowDimensional Systems, MATRIX Creswick, 27/6/2017.
Boundary algebras and scaling limits for logarithmic minimal models, School of Mathematics and Statistics, University of Melbourne, 24/10/2016.
Nonrational CFTs and the Verlinde formula, AustMS Meeting, Flinders University, 30/9/2015.
NonC_{2}cofinite VOAs and the Verlinde formula, Lie Algebras, Vertex Operator Algebras and Related Topics, University of Notre Dame, 16/8/2015.
Classifying Representations for Conformal Field Theory, School of Mathematics and Statistics, University of Melbourne, 6/8/2015.
Beyond Rational Conformal Field Theory, School of Mathematics and Statistics, University of Melbourne, 18/6/2015.
Modular Transformations, Representation Theory and Physics, Department of Mathematics Colloquium, University of New South Wales, 19/5/2015.
TwoDimensional Superconformal Algebras, Institute for Geometry and its Applications, University of Adelaide, 17/4/2015.
Symmetric Jack Polynomials and Fractional Level WZW Models, ANZMP8 Meeting, Melbourne, 10/12/2014.
Parabolic Verma Modules, Bosonic Ghost Systems and Logarithmic CFT, 30th International Colloquium on Group Theoretical Methods in Physics, Ghent, 15/7/2014.
Module Categories for Affine VOAs at Admissible Level, Erwin Schrödinger Institute, Vienna, 17/3/2014.
Modular Properties of NonRational Conformal Field Theory, ANZAMP Congress, Mooloolaba, 27/11/2013.
NonNegative Integer Verlinde Coefficients for Fractional Level WZW Models, AustMS Meeting, University of Sydney, 3/10/2013.
The WessZuminoWitten Model on SL(2;R), Pacific Rim Mathematical Association Congress, Shanghai, 25/6/2013.
Fractional Level WessZuminoWitten Models, Modular Transformations and Verlinde Formulae, Hausdorff Institute for Mathematics, Bonn, 10/12/2012.
Modular Properties of Fractional Level WZW Models, ANZAMP Congress, Lorne, 4/12/2012.
WessZuminoWitten Models on Lie Supergroups, Institute for Geometry and its Applications, University of Adelaide, 17/10/2012.
Conformal Field Theory and the Modular Group, Department of Mathematics Colloquium, University of Queensland, 17/9/2012.
What's New in Critical Lattice Phenomena?, Research School of Physics and Engineering, Australian National University, 1/12/2011.
Lattice Discretisations of Integrable Sigma Models, Mathematical Sciences Institute, Australian National University, 9/11/2011.
Affine sl(2) at k=1/2, beta gamma Ghosts and Logarithmic CFT, Institut Henri Poincaré, Paris, 3/10/2011.
Lattice Discretisations of Integrable Sigma Models, Istituto Nazionale di Fisica Nucleare, Bologna, 15/9/2011.
Indecomposable Modules for the Virasoro Algebra, University of Melbourne, 2/5/2011.
A (Gentle) Introduction to Lie Superalgebras, La Trobe University, 29/4/2011.
DBrane Charges in WessZuminoWitten Models, University of Adelaide, 18/10/2010.
Anything You Can Do..., Founder's Day Talk, Australian National University, 15/10/2010.
Indecomposable Representations in Physics, AustMS Meeting, University of Queensland, Brisbane, 29/9/2010.
Whither Indecomposability?, Lethbridge University, Alberta, 25/8/2010.
Fractional Level WZW Models as Logarithmic CFTs, University of North Carolina at Chapel Hill, 25/2/2010.
Indecomposable Modules for the Virasoro Algebra, Centre de Recherche Mathématiques, Montréal, 15/9/2009.
Quantum Symmetries and Integrable Sigma Models, Albert Einstein Institute, Potsdam, 1/7/2009.
Quantum Symmetries and Lattice Regularisations, DESY, Hamburg, 3/6/2009.
D Ridout. DBrane Charge Groups and Fusion Rings in WessZuminoWitten Models. Doctoral Thesis, University of Adelaide, 2005. [Adelaide Library link]
D Ridout. Convergence Properties of Noise Reduction by Gradient Descent. Masters Thesis, University of Western Australia, 2001.
D Ridout. Applications of Functional Analysis in Quantum Scattering Theory. Honours Thesis, Murdoch University, 1998.
Kazuya Kawasetsu (ARC Research Associate). UMelb, 201719. Now tenured at Kumamoto University.
Shashank Kanade (Endeavour Fellowship). UMelb, 2017. Now tenuretrack at Denver University.
Simon Wood (ARC DECRA Fellowship). ANU, 201416. Now tenured at Cardiff University.
Zachary Fehily. , UMelb, 2018 .
Christopher Raymond. Algebraic aspects of conformal field theory, UQ, 201619. Now postdoc at the ANU.
Tianshu Liu. Coset construction for the N=2 and osp(12) minimal models, UMelb, 201519. Now postdoc at the Yukawa Institute for Theoretical Physics, Kyoto University.
Steve Siu. Singular vectors for the W_{N} algebras and the BRST cohomology for relaxed highestweight L_{k}(sl(2)) modules, UMelb, 201419.
Michael Cromer. Free field realisations in logarithmic conformal field theory, ANU, 2013  2019.
Michael Canagasabey. Fusion rules in logarithmic superconformal minimal models, ANU, 2012  2016.
Will Stewart. On the NappiWitten model H_{4}, UMelb, 201819. Now PhD at University of Texas at Austin.
John Snadden. An admissible level osp(12)model, ANU, 201416. Now PhD at Northwestern University.
Benjamin Gerraty. , UMelb, 202021.
Daniel Tan. , UMelb, 201920.
Tyson Field. WessZuminoWitten Models and the KnizhnikZamolodchikov Equations, UMelb, 201718. Now working for Accenture.
William Stewart. On the twisted sector of WessZuminoWitten models, UMelb, 2016  2017.
Matthew Geleta (Physics). The Coulomb Gas, ANU, 2015. Now PhD at Cambridge.
Tianshu Liu (Physics). The BosonFermion Correspondence, ANU, 2014.
Hiroyuki Nagamine (Physics). An Introduction to String Theory, ANU, 201213. Now working for the Japanese Patent Office.
Bridget Gatt (Applied Mathematics). UMelb, Jan. 2020  Feb. 2020.
Eric Ma (Mathematical Physics). UMelb, Jan. 2020  Feb. 2020.
Steven Xu (Pure Mathematics). UMelb, Jan. 2020  Feb. 2020.
Steven Xu (Pure Mathematics). UMelb, Jan. 2019  Feb. 2019.
Lukas Anagnostou (Mathematical Physics). UMelb, Jan. 2018  Feb. 2018.
Daniel Tan (Pure Mathematics). UMelb, Jan. 2018  Feb. 2018.
Madeleine Johnson (Pure Mathematics). UMelb, Jan. 2017  Feb. 2017.
Lawrence Dam (Physics). ANU, Dec. 2014  Jan. 2015.
Scott Melville (Physics). ANU, Dec. 2014  Jan. 2015. Now PhD at Imperial College.
Thao Le (Mathematics). ANU, Dec. 2014  Jan. 2015.
Hadleigh Frost (Physics). ANU, Dec. 2013  Jan. 2014. Now PhD (Rhodes Scholar) at Oxford.
James Bonifacio (Mathematics). ANU, Dec. 2011  Jan. 2012. Now PhD (Rhodes Scholar) at Oxford.
James Fletcher (Mathematics). ANU, Dec. 2011  Jan. 2012.
Elisabeth Kava (Mathematics). ANU, Dec. 2011  Jan. 2012. Now with the NSW Department of Family and Community Services.
Steven Sammut (Physics). ANU, Dec. 2010  Jan. 2011.
Yu Zheng (Mathematics). Introduction to String Theory, ANU, Autumn Term, 2015.
Maxim Jeffs (Mathematics). Lie Algebras and their Representation Theory, ANU, Semester 1, 2015.
Tianshu Liu (Physics). Introduction to String Theory, ANU, Semester 2, 2013.
Clement Schlegel (Mathematics). An Introduction to Lie Theory, ANU, Semester 2, 2013.
Saptarshi Das (Mathematics). Lie Algebras and Applications in Physics, ANU, Semester 2, 2012.
Hao He (Physics). Introduction to String Theory, ANU, Semester 2, 2012.
Sebastian Mueller (Mathematics). Introduction to Lie Algebras, ANU, Semester 1, 2012.
Alan Yin (Mathematics). Introduction to Lie Algebras, ANU, Semester 1, 2012.
Sarama Tonetto (Physics). Introduction to String Theory, ANU, Semester 2, 2011.
Yu Zheng (Mathematics). ANU, 2014  .
Hannah Smith (Physics). ANU, 2011  2013. Now Phd at Oxford.
Daniel ComberTodd (Physics). ANU, 2011  2014.
I'm an Australian, a sandgroper from Perth. You can tell this by my impeccable spelling. I graduated from Rossmoyne Senior High School before starting a BSc at Murdoch University. A few years later, I found myself burdened with a double degree in mathematics and physics (and 3/4 of a degree in chemistry). Embracing the financial poverty that was now my destiny, I completed an honours degree in operator theory and threebody quantum scattering. I then moved on to the University of Western Australia (who will no doubt complain that I haven't capitalised the "T" in "the") where I occupied myself with a masters degree in the theory of topological chaotic dynamics and its application to noise reduction algorithms.
I then moved to Adelaide to start a PhD at the University of Adelaide. There, I was introduced to the wonderful world of conformal field theory and tried in vain to pick up the rudiments of string theory. With a little Lie theory, algebraic topology, differential geometry, and commutative algebra, I wrote a thesis on Dbrane charges and fusion rings in WessZuminoWitten models. The last two years of my doctoral studies were completed as a guest of the maths department at La Trobe University in Melbourne; without their generosity, things would have been rather difficult.
I then moved to Québec as a postdoc with Pierre Mathieu. There, I worked on extending the chiral algebras of various conformal field theories and made some forays into the world of logarithmic conformal field theory. I also managed to find time to try a bit of skiing and skating, though the intricate art of curling remained elusive. As did a solid grasp of the french language, or at least the local dialect.
Then, I moved to the DESY Theory Group in Hamburg with Jörg Teschner. There, I continued my romping in logarithmic conformal fields and also branched out into the wider world of deformed conformal field theories, integrable models and quantum groups. I tried once again to learn some basic string theory, but it seems that my brain is set on rejecting all such knowledge transplants. Luckily, I had ample opportunity to sample the joys of living in continental Europe, with its myriad of confusing cultures and its myriad of confusing languages. I will miss the cheese most of all...
Well, I ended up back in Canada, this time in Montréal, with Yvan SaintAubin, doing mathematics once again. I also had the luck to get some lecturing in the McGill University maths department while I worked on my French. It certainly wasn't hard to recreate the joy of living in that beautiful country, while simultaneously working very hard on new and interesting problems. And getting fat on the ubiquitous (and cheap!) french patisseries! Plus, Montréal has lots of cheese, lovely lovely cheese (and I don't count that horrible poutine cheese either!).
As luck would have it, my time in Montréal was cut short by a nottoberefused grant application unexpectedly getting funded. I returned to Australia as an Australian Research Fellow at the Australian National University in Canberra. There, I got to wallow in the muddy waters of logarithmic conformal field theories and teach myself some vertex algebra theory for five whole years. Happy times, though I was horrified at how expensive Australia had become. Even the local cheeses exceeded expectations hugely (mmm, Small Cow Farm's Redella).
This saga has a happy ending. The clever sods in the School of Mathematics and Statistics at the University of Melbourne decided to take pity on me and give me a continuing position. This was a dangerous gambit given the University's close proximity to the cheesemongers of the Queen Vic Markets, but so far everyone seems to be happy. Especially me. All I need to do now is a bit of work (and not to think about property prices). Wish me luck! I promise to return the favour someday...