string math 2021

Berkeley Informal String-Math Seminar. [Slides] [Video], Antoine Bourget (CEA Saclay) One can define correlation functions and derive conformal bootstrap equations constraining the spectrum. [Slides]. Title: A Yang-Mills matrix theory I will then outline work in progress with Gunningham and Safronov to prove the conjecture in a number of special cases. Of course, a few minutes earlier Witten had explained that no one knows what the theory actually is, which means there is no way to show that it is mathematically inconsistent. Strings 2021 will be held online during the two-week period June 21 July 2, 2021 from 9:30 15:00 in So Paulo (8:30 14:00 in NY, 14:30 20:00 in Paris). In my view, this anxiety to communicate to the public the latest developments is a sign of certain immaturity. In this talk, I will explain how to prove their conjecture for a big class of link complements by making use of the R-matrix for Verma modules. The choice of flat connection at infinity for E8 or Spin(32)/Z2 respectively captures the feature of the 6D conformal matter theory built on F-theory geometry. We are going to perform a construction of such quantum curves using the mathematical language of vertex operator algebras. Robert A. Wilson, Finally, I will mention how some of these features are likely to persist in a proposal for the worldsheet dual of free N=4 Super Yang-Mills theory. A Triangle of Influence: Bringing Together Physics, Pure Mathematics, and Computer Science. These higher-categories are constructed by equivariantizing higher-categories corresponding to invertible higher-form symmetries. Organizing Committee:Henrique Bursztyn (IMPA)Reimundo Heluani (IMPA)Marcos Jardim (IMECC-UNICAMP)Gonalo Oliveira (UFF) Scientific Committee:Anton Alexeev (Universit de Genve)David Ben-Zvi (University of Texas)Alexander Braverman (Brown University)Ron Donagi (University of Pennsylvania)Giovanni Felder (ETH Zrich)Dan Freed (University of Texas)Edward Frenkel (University of California)Marco Gualtieri (University of Toronto)Nigel Hitchin (University of Oxford)Sheldon Katz (University of Illinois)Maxim Kontsevich (IHS)David Morrison (University of California)Andrei Okounkov (Columbia University)Vasily Pestun (IHS)Boris Pioline (Sorbonne Universit \u0026 CNRS)Nicolai Reshetikhin (University of California)Pedro Vieira (Perimeter Institute for Theoretical Physics)Katrin Wendland (Albert-Ludwigs-Universitt Freiburg)Edward Witten (Institute for Advanced Study)Shing-Tung Yau (Harvard University \u0026 The Chinese University of Hong Kong)Maxim Zabzine (Uppsala University)Steering Committee: Ron Donagi (University of Pennsylvania)Dan Freed (University of Texas at Austin)Nigel Hitchin (University of Oxford)Sheldon Katz (University of Illinois)Maxim Kontsevich (IHS)David Morrison (University of California)Hiroshi Ooguri (Caltech \u0026 IPMU)Boris Pioline (Universit Pierre et Marie Curie)Joerg Teschner (DESY)Edward Witten (Institute for Advanced Study)Shing-Tung Yau (Harvard University)Redes Sociais do IMPA: https://linktr.ee/impabrIMPA - Instituto de Matemtica Pura e Aplicada https://impa.br | http://impa.br/videos#stringmath2021 Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemtica Pura e Aplicada, sendo vedada a utilizao total ou parcial do contedo sem autorizao prvia e por escrito do referido titular, salvo nas hipteses previstas na legislao vigente.The rights over all the material in this channel belong to the Instituto de Matemtica Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation. Participant responses to online questionnaire, Clickhereto use the Slack workspace of Strings 2021. This approach is based on 2105.06039 and is joint work with Aganagic and Rapcak. We propose that the matching of 5d coulomb branches plus the 2-group structure constants determined by the higher form symmetry of LSTs as criteria to predict heterotic T-dual candidates.The exploitation are generalized by picking non-trivial flat connections at the infinity to break E8 and Spin(32)/Z2 into their subgroups and confirm these T-dualities by the matching of criteria aforementioned. IMPA, Rio de Janeiro, June 14 18, 2021 Turned into an online eventSpeaker: Mina Aganagic (UC Berkeley)Lecture title: Knot homologies from mirror symmetryEvent page: http://bit.ly/stringmath2021Videos playlist: https://bit.ly/3v2lHlsThe series of String-Math conferences has developed into a central event on the interface between mathematics and physics related to string theory, quantum field theory and neighboring subjects. The latter approach allows to realize holomorphically and topologically twisted field theories directly as worldvolume theories in deformed supergravity backgrounds, and we make extensive use of this. String theory calculations that can be done in unphysical situations (wrong dimension, lots of SUSY, extremal black holes) claim to reproduce the semiclassical limit. What I wanted with my post was to point out that (in my view, again), you were selecting particular phrases that sounded negative, in what other wise were quite interesting exchanges among physicists. [Slides] [Video], Vincent Vargas (University of Geneva) Abstract: The heterotic G2 system is the 7-dimensional analogue of the Hull-Strominger system. Moving away from such orbifold points requires generalizing the flow tree formula from the Abelian category of quiver representations to the derived category of the same. Theres a long list of things they are talking about under the name string theory, with the generic problem that the ones that are reasonably well-defined have nothing to do with the real world (e.g., wrong dimension). The general picture is nicely illustrated by the Borel Asking for help, clarification, or responding to other answers. Abstract: Three-dimensional N =4 supersymmetric field theories admit a natural class of chiral half-BPS boundary conditions that preserve N = (0, 4) supersymmetry. [Slides], Sam Gunningham (Montana State University) From a mathematical perspective, these solutions involve interesting constructions in geometry such as integrable G2-structures and G2-instantons. Title: Approximations for Calabi-Yau and other special holonomy/structure metrics By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. [Slides], Thorsten Schimannek (LPTHE Paris) [Slides] [Video], Mayuko Yamashita (Kyoto University) Odbya stae podoktorskie na uniwersytecie Humboldta w Berlinie oraz uniwersytecie w Princeton w USA, a nastpnie zostaa profesorem w cole Polytechnique Fdrale de Lausanne (EPFL) w Szwajcarii, gdzie od 2018 roku kieruje Katedr Teorii Liczb. June 14-18: Pre-Strings 2021 school (IIP, Natal), [D] Nima Arkani-Hamed (Institute for Advanced Study), [T] Horacio Casini (Centro Atmico Bariloche), [T] Lorenz Eberhardt (Institute for Advanced Study), [T] Clifford Johnson (U of Southern California), [D] Vladimir Kazakov (Ecole Normale Superieure), [T] Zohar Komargodski (Simons Center for Geom. A limit involving the quotient of two sums. Caltech's Feynman Centennial Symposium on 12 May 2018. Experimentalist: I have to compute QCD, Wikipedia says I need to add unphysical ghosts on a local section and their fiberwise duals and project out the quotient Fock space isomorphic to the supergraded BRST cohomology pullback of the field configuration along a vertical diffeomorphism of the principal BatalinVilkovisky anafestic G-bundle, as if it were antani. Do roots of these polynomials approach the negative of the Euler-Mascheroni constant? Title: Families of Modular Flux Vacua on Symmetric CY Threefolds Thank you. Unfortunately, finding explicit solutions to the system is a challenging problem due to the existence of an anomaly cancellation condition for the gauge fields. problemu upakowania sfer w wymiarze 8, a take we wsppracy z innymi matematykami rozwizanie tego problemu w wymiarze 24. Lakshya Bhardwaj (University of Oxford) [Slides] [Video], Wei Li (Chinese Academy of Sciences) Abstract: Quantum curves can be associated with the singular vectors in the Verma modules over the Virasoro algebra. In response to the obvious question about relation to experiment and testability, people have clearly completely given up on this, with nothing to say (other than a bogus claim that string theory makes some prediction about B-mode polarization), going on about how it took thousands of years for the atomic hypothesis to be vindicated. Finally, I will discuss some applications. Penroses talk is interesting (https://www.youtube.com/watch?v=hk_6EtWUatM), as is the discussion between him and string folks afterwards. Based on 2103.10271, 2111.07663 and upcoming work. How would you please implement. Title: Topological Langlands duality and 1-form symmetries Abstract: In this talk I will introduce a refined notion of Gopakumar-Vafa invariants on singular Calabi-Yau threefolds that generate a discrete gauge symmetry in M-theory. In particular, i can not find a derivation of any black hole entropy from first principles in quantum gravity outside of string theory. Piotr Kucharski (University of Amsterdam) Abstract: The theory of Categorical Enumerative Invariants (CEIs) is a non-commutative generalization of the theory of Gromov-Witten invariants. Just viewed the last question and answer session. At the time I drop those lines, more than 50 years from dual resonance models?, I havent found any convincingly argument. Piotr Sukowski (chair) you see Ed Witten, and then Shiraz Minwalla, basically agreeing with you. Abstract: Gross and Siebert developed a program for understanding mirror symmetry algebro-geometrically. Greg Moore Abstract: Knizhnik-Zamolodchikov equation, originally found in the context of a two dimensional conformal field theory, has recently been found in the context of instanton counting, albeit with a significantly extended domain of allowed parameters (level, spins etc). From this description, we propose a symmetry for the space of instantons on C^2 by an exceptional super Lie algebra called E(3|6). This provides an enumerative interpretation of the A-model topological string partition function on non-commutative resolutions of the singular Calabi-Yaus. How to store objects in HTML5 localStorage/sessionStorage. Divergence of perturbation theory in quantum electrodynamics. Determinant operators in the chiral algebra insert Giant Graviton branes in the dual geometry. On the other hand, differential cohomology theories, whose relationships with physics are classical, are most modernly understood in terms of sheaves on manifolds with values in (\infty, 1)-categories. Depending on the coupling constant and dimension, they exhibit several distinct scaling behaviors (or if you prefer the high energy jargon, various renormalization group flows). . In this talk, I will present a match between the large-N saddles of the correlation functions of determinants with semiclassical D-brane configurations in the dual theory, using a spectral curve construction. Title: Emergence of Time from Unitary Equivalence Matilde Marcolli Sat 3 Apr 2021 12.00 EDT Last modified on Tue 6 Apr 2021 09.54 EDT. In this talk, I will review the probabilistic construction and its equivalence with the bootstrap construction used in the physics literature. I wonder how to find the number of ternary strings that have at least one 0, one 1 and one 2. We hereby certify that, Alex Buchel, THE UNIVERSITY OF WESTERN ONTARIO, AP Computer Science A 2021-22. This is a joint work with Kwokwai Chan and Ziming Ma. He never actually gets anywhere near discussing the topic of the title for the talks, but does give a very nice leisurely introduction to computing amplitudes for zero-mass particles. Ta strona wykorzystuje ciasteczka (cookies) w celu zapewnienia maksymalnej wygody w korzystaniu z naszego serwisu. Title: Perturbative calculations in twisted 4d gauge theories [online talk] Fall 2021. - rgbk21. This is joint work with Mark Gross. Miosz Panfil 3 years ago, F_K invariants of knot complements in 3-sphere have been proposed. Title: On topology change in Poisson-Lie T-duality Dr. Kessner. Abstract: I will review the Cohomological Hall algebra associated to a quiver and an oriented cohomology theory. Blasting is well underway in South Dakota for the $2 billion + LBNF/DUNE facility. We provide new the structure that allows this, whose quantisation turns out to be lead to a multimatrix ensemble. Abstract: We discuss the partition functions of topologically twisted 5d SU(2) supersymmetric Yang-Mills theory on X x S1, where X is a smooth closed four-manifold. In other physical contexts you have different symmetries than Poincare, often approximate symmetries. These boring predictions, if confirmed by DUNE, will show that also in experimental physics no real stuff is happening. But I went through the hard road, being told just to accept all fundamental questions I raised above as unanswered and move on to the cutting-edge problems whatever and whonever decides what these are. In this case, because the string is assumed to be safe and trusted, we would expect use of either eval() or the Function constructor to be reasonable. Abstract: The interpretation of semiclassical gravity as an average of CFTs has provided much progress in understanding the factorization problem and the information paradox. The linking numbers of plumbing graphs are interpreted as the effective mixed Chern-Simons levels of 3d N=2 theories with chiral multiplets. This is a joint work with K. Ohmori (U. Tokyo). Equivalent plumbing graphs suggest dual theories. Suomynona, 2013 Jul. People are attempting to understand things, with the tools at hand. IMPA, Rio de Janeiro, June 14 18, 2021 Turned into an online eventSpeaker: Si Li (Tsinghua University)Lecture title: Elliptic chiral homology and quantum master equationEvent page: http://bit.ly/stringmath2021Videos playlist: https://bit.ly/3v2lHlsThe series of String-Math conferences has developed into a central event on the interface between mathematics and physics related to string theory, quantum field theory and neighboring subjects. General string perturbation theory using 2d conformal field theory. The following articles by Carlip provide a nice overall perspective, drawing attention to the universality of BH entropy derived in different approaches to QG what he refers to as an embarrassment of riches. Thanks for contributing an answer to Stack Overflow! A hyperbolic d-manifold gives rise to a Hilbert space which is a unitary representation of the conformal group in d-1 dimensions. StringStringfinal . How to format a number with commas as thousands separators? What is a word for the arcane equivalent of a monastery? Well, that would be the case if people follow the hype for last 20-30 years or more. Title: Magnetic quivers for Superconformal Field Theories David Ben-Zwi Symmetries, Horizons, and Black Hole Entropy [https://arxiv.org/abs/0705.3024] Hawking tells you what the semiclassical limit is. I suppose I shouldnt have even let that get started. You will have to use the Number.isNaN() method to do it. All major operations, constants, and methods are supported. To address this issue, we use the fusion-matrix bootstrap, which is recently developed in the context of the light-cone bootstrap. The derivations listed in 0705.3024 seem to fall into three classes: String Theory (D-brane/String state counting, AdS/CFT, Fuzzballs) A better version was given September 22, 2021 at Yan Soibelman's M-seminar. Mina Aganagic What is the point of Thrower's Bandolier? There is also an open source implementation on GitHub, evaluator.js, and an NPM package. Rio de Janeiro, June 18th, 2021. Check this JSBenchmark. [Slides] [Video], Jan Dereziski (University of Warsaw) Besides reviews of major developments in the field and specialized talks on specific topics, an important novelty will be several informal discussions involving two researchers and the conference participants. For different choices of superpotential, the LG theory categorifies the quantum knot invariants associated with any simply-laced Lie algebra. CEIs should be thought of as a precise realization of the general idea, due to Kontsevich, that the category of open strings (plus data of the splitting) determine closed string invariants. Title: The character of M-theory Ive personally never understood why showing that (unphysical limits of) your quantum theory gives the expected semi-classical result is anything other than a rather weak consistency check on your theory. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. Yes, I was ignoring some other things they had to say, for example, Arkani-Hameds An exchange that was otherwise quite lively and interesting, you paint in the worst possible way. Physical Review, 85(4), p.631. Title: Quantum curves and vertex algebras Abstract: It has been found, originally in the context of black hole thermodynamics, that the concept of entropy is better-defined in the presence of gravity than in ordinary quantum field theory without gravity. Here is an implementation of the Shunting-yard algorithm with additional support for unary prefix (e.g. [Slides] [Video], Fabian Ruehle (Northeastern University) Title: Path integral derivations of K-theoretic Donaldson invariants Estrada Dona Castorina 110, Jardim Botnico I watched the entire video on the Poincare group and, although the path was the same as Weinberg, there was a lot of new information I thought it was excellent. This construction has several advantages and opens perspectives towards generalization to the case of the $cW$-algebras +1 upvote from me, and I've already used it in a project. Title: Calculating Quantum Knot Homology from Homological Mirror Symmetry APCS. The proof in these cases uses the notion of 1-form symmetries (= co-dimension 2 topological defects) to express PGL(N)-skein modules as certain twisted SL(N)-skein-modules, and then to further relate these to well-known formulas for the cohomology of twisted character varietiesof surfaces. I will discussa phenomenon similar to Frobenius of modular representation theory. In our examples we find agreement with the flux modularity conjecture of Kachru, Nally, and Yang. Abstract: Liouville field theory was introduced by Polyakov in the eighties in the context of string theory. This finding suggests that the dual domain wall systems are integrable to all loop orders and for any value of the bond dimension. Title: Automorphic Spectra and the Conformal Bootstrap [Slides], Meng-Chwan Tan (National University of Singapore) Abstract: We revisit Vafa-Witten theory in the more general setting whereby the underlying moduli space is not that of instantons, but of the full Vafa-Witten equations. In other words, a ternary string is a n-permutation with a repetion of the set {0,1,2}. Strings 2021 started today, program is available here. Nevertheless, from a theory claiming to be the only mathematically self-consistent unification program, something regarded as just a mere technicality now requires an answer. Marlborough School. Mathematically, they can be identified with the K-theoretic versions of the Donaldson invariants on X. Abstract: We implement the unitary equivalence of modular Hamiltonian $hat{H}_{mathrm{mod}}$ and Hamiltonian $hat{H}$,$hat{H}simhat{U}^{dagger}hat{H}_{mathrm{mod}}hat{U}$, to realize the emergence of time from an unitary operator $hat{U}$. The two domain wall systems are thought to be integrable; the evidence comes mainly from the study of correlation functions at weak coupling. I will present a general overview of the theory of CEIs, and discuss how it provides a conjectural approach to understanding enumerative mirror symmetry for the quintic threefold, in arbitrary genus. Reimundo Heluani Organizing Committee. This is damaging. I am not a fan of string theory. [Slides] [Video], Mirjam Cvetic (University of Pennsylvania) for Fundamental Research), [D] Juan Maldacena (Institute for Advanced Study), [T] Shiraz Minwalla (Tata Inst. He notes that to get at non-perturbative string theory we seem to need some more general understanding of quantum theories, going beyond the usual quantization starting with an action, and ends by saying maybe quantum information theory can help. Jednym z najwaniejszych osigni Maryny Viazovskiej jest rozwizanie tzw. Title: Langlands duality for 3-manifolds Its explicit description as a QFT has remained elusive. I will then summarise recent work (with Matthias Gaberdiel and others) on the AdS_3/CFT_2 correspondence, in the tensionless limit, which gives a proof of concept of the above ideas. W 2018 zostaa zaproszona jako wykadowczyni podczas Midzynarodowego Kongresu Matematycznego jest to jedno z najwaniejszych wyrnie dla matematykw. Abstract: Gauge-String duality(or the AdS/CFT correspondence, as a special case) has wide ranging ramifications in physics as well as mathematics. Share. Does a barbarian benefit from the fast movement ability while wearing medium armor? Title: The higher dimensional tropical vertex In other words, the string boundary conditions on the probe branes preserve the integrability of the corresponding Green-Schwarz sigma models. Title: Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification [online talk] Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Elliott Gesteau (California Institute of Technology) If one knows how to read between the lines, then at this lecture you finally can hear what, in different words, could well be re-phrased as: the search for M-theory using dualities failed. Here's a quick basic example I came up with (updated (2011-06-26): cleaner w/ input boxes). But this procedure you adopted in this post, is not the best way of understanding science, or communicating it. Java basics Unit 2 - Functions and Testing Unit 3 - String & Math Unit 4 - Loops & Algorithms Unit 5 - Classes and objects Unit 6 - Processing libraries Unit 7 - Arrays Unit 8 . rev2023.3.3.43278. While Ooguri has his own interpretation about this observation (incoming flux of young people in the field is as healthy as ever), I wonder what others think about it. String-Math 2015, Hainan Island, China (December 31, 2015 - January 4, 2016; How to Quantize Gravity. The String Math series of conferences have become an important event for anyone working at the interface between mathematics and theoretical physics (string theory, quantum field theory and adjacent topics), bringing together an interdisciplinary cohort of pure mathematicians and theoretical physicists. 2. Zygmunt Lalak Francis (Skip) Fennell | Nov 3, 2021 . But this is just an opinion. [Slides], Muyang Liu (Uppsala University) In particular, we provide two different path integral derivations of their wall-crossing formula for b_2^+(X)=1. Non-QG QFT derivations that are not attempting to identify the microstates. The string community has been dishonest for at least 20 years, and has absolutely no right to give any lessons about ethics in science. One can add superpotentials, which lead to Seiberg-like dualities between plumbing graphs with triangles. I will also discuss a second application, a new definition of FJRW invariants in the presence of an arbitrary symmetry group. [Video], Hulya Arguz (IST Austria) Pyry Kuusela (University of Oxford) Abstract: The D3-D5 and D2-D4 probe-brane systems with nonzero worldvolume flux are holographically dual to N=4 super Yang-Mills and ABJM theory in the presence of half-BPS domain walls. 10. The LQG derivation, involving an ad-hoc choice for the Immirzi parameter Explicit $q$-series form for $\hat Z$ is known for $SU(2)$ group, supergroup $SU(2|1)$ and ortho-symplectic supergroup $OSP(2|2)$. We will explain how ideas from oriented matroids, tropical geometry, and cluster algebras shed light on the structure of the positive Grassmannian and the amplituhedron. Title: The Penrose Inequality as Swampland Condition? [Slides] [Video], Brian Williams (University of Edinburgh) I will illustrate this construction on examples of low rank 4d N=2 SCFTs. that perturbation series following from superstring S-matrix, already known to diverge as one sums over all moduli parameters (which isnt really the issue, since this happens even in QED, see Dyson, F.J., 1952. Much as I love this general topic, its getting far from the topic of the posting, so Ill just advise: read my book. The unitary equivalence relation implies a duality between the modular flow and time evolution. (Anyway, String Theory is mainly about Quantum Gravity). Abstract: I will be discussing my recent work [2110.08179] with Chris Blair and Dan Thompson on topology change in Poisson-Lie T-duality with spectators (i.e. Likely Witten was thinking of things like the 6d (2,0) superconformal theory which has not classical limit and its construction is somewhat mysterious. Brittany Goerig | Oct 14, 2020 | 00:56:54. But keep in mind that using the Function constructor in this way is similar to eval() in that the risks may be comparable. (i) No one convincingly proved the mathematical equivalence between the RNS superstrings and GS formalism. In this talk, I will give a slightly abstract explanation of this phenomenon, at least for the case of a black hole. This is exactly the place where you should be using eval(), or you will have to loop through the string and generate the numbers. To learn more, see our tips on writing great answers. Math 435 (Differential Geometry) Fall 2020. [Slides], Peter Spacek (TU Chemnitz) The point though is that there are plenty of much simpler examples, which often can be understood purely in terms of representation theory. Title: From BPS crystals to BPS algebras The String Math series of conferences have become an important eventfor anyone working at the interface between mathematics and theoretical physics (string theory, quantum field theory and adjacent topics), bringing together an interdisciplinary cohort of pure mathematicians and theoretical physicists. Anyway, truly bold attempt! for Fundamental Research), [T] Sebastian Mizera (Institute for Advanced Study), [T] Sameer Murthy (Kings College London), [S] Hirosi Ooguri (Caltech and Kavli IPMU), [D] Joo Penedones (cole Polytech. In this talk I will present how these two threads of research can be combined and what comes as a reward. Jerome Gauntlett, Rajesh Gopakumar, Mariana Grana, Michael Green, David Gross, Daniel Grumiller, Jeff Harvey, Marc Henneaux, Veronika Hubeny, Marina Huerta, Janet Hung, Antal Jevicki, Clifford Johnson, Shamit Kachru, Zohar Komargodski, Finn Larsen, Yolanda Lozano, Kimyeong Lee, Dieter Luest, Juan Maldacena, Shiraz Minwalla, Jeff Murugan, Rob Myers, Hirosi Ooguri, Leo Pando-Zayas, Silvia Penati, Fernando Quevedo, Eliezer Rabinovici, John Schwarz, Nathan Seiberg, Ashoke Sen, Steve Shenker, Eva Silverstein, Wei Song, Andy Strominger, Tadashi Takayanagi, Sandeep Trivedi, Cumrun Vafa, Pedro Vieira, Anastasia Volovich, Spenta Wadia, Edward Witten, Konstantin Zarembo. (iii) Most superstring calculations are performed under euclidean worldsheet for many practical reasons, as we all know and love from Wicks rotation in standard q.f.t.s. If you're looking for a syntactical equivalent to eval, you could use new Function. [Slides] [Video], Netta Engelhardt (MIT) Za te oraz inne osignicia otrzymaa wiele prestiowych nagrd i wyrnie, m.in. He goes on to explain the landscape philosophy, which he sees string theorists (and himself) as now adopting.