Mathematically, they can be identified with the K-theoretic versions of the Donaldson invariants on X. Math 435 (Differential Geometry) Fall 2020. Reimundo Heluani Organizing Committee. We will focus on understanding 3d mirror symmetry viachiralalgebras. This topic has been recently explored,from several differentperspectives,by Kontsevich-Soibelman and Doan-Rezchikov. Rio de Janeiro, RJ, CEP 22460-320, Brasil Davide Gaiotto Abstract: Quantum curves can be associated with the singular vectors in the Verma modules over the Virasoro algebra. LQG calculations claim to reproduce the semi-classical limit. Title: Holomorphic Floer theory and Donaldson-Thomas invariants In the case of rank one instantons this factors through a `Heisenberg type super Lie algebra and the story is analogous to Nakajimas action on the Hilbert scheme. Title: Liouville conformal field theory: from the probabilistic construction to the bootstrap construction The general picture is nicely illustrated by the Borel Abstract: I will explain some recent and ongoing work on the state spaces associated to 3-manifolds in the Kapustin-Witten twists of 4d N=4 SYM. These symmetries vastly generalize the standard notion of global symmetries, and can be used in a similar way to obtain insights into strongly-coupled physical phenomena. In 2019, S. Gukov and C. Manolescu initiated a program to mathematically construct via Dehn surgery, and as part of that they conjectured that the Melvin-Morton-Rozansky expansion of the colored Jones polynomials can be re-summed into a two-variable series for knot complements. Abstract: I will present some conjectures for higher-rank K-theoretic Donaldson-Thomas theory on toric three-folds, and some lessons that we learned from working equivariantly on non-compact spaces. IMPA, Rio de Janeiro, June 14 18, 2021 Turned into an online event. Note also that I was making no comment about the work people were presenting at the conference, was sticking to discussing particular important points about the current state of the subject being made by the two most talented and hard-w0rking leaders of the field. Chen-Te Ma (Asia Pacific Center for Theoretical Physics) 1 Let n be a natural number, n3. Postal Address:Instituto de Matemtica Pura e Aplicada https://arxiv.org/pdf/0809.0305.pdf, Already at p.1 one reads, The Problem: According to textbooks, the passage from classical mechanics to quantum mechanics is made by replacing Poisson brackets with commutators. There are many equivalent graphs that are related by Kirby moves which are interpreted as integrating out gauge nodes from the perspectives of 3d theories. Probably the best answer. 2013 Nov. Osaka City University, Japan. 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. Another series of talks that I took a look at and that I can recommend is Nima Arkani-Hameds lectures on Physics at Future Colliders at the ICTP summer school on particle physics. 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. Chrome's Content Security Policy will still throw EvalError, Creating constructor doesn't make sense here and it takes unnecessary resources. Title: Path integral derivations of K-theoretic Donaldson invariants Of course, I do not justify equally wrong comments from certain string theorists We construct a trace map on the elliptic chiral homology of the free beta gamma-bc system using the BV quantization framework. Im no whit wiser than when I began. String Math 2021 IMPA, Rio de Janeiro, June 14 - 18, 2021- Turned into an online event The 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. Abstract: Trace map on deformation quantized algebra leads to the algebraic index theorem. commutative) spacetime case is well-known to yield the Yang-Mills(-Higgs) theory, namely almost-commutative manifolds, has to be replaced by its fuzzy counterpart already the classical level. Is there a way to calculate a formula stored in a string in JavaScript without using eval()? We provide significant evidence that averaging plays an important role in reproducing. with the exact opposite agenda.. Abstract: One aspect of the relation between physics and arithmetic geometry is the conjectured correspondence between supersymmetric flux vacua and weight-2 modular CY threefolds. Everything is in the description. Theres no reason to get into the technical argument over whether the perturbative expansion of various versions of the superstring in 10d is mathematically well-defined. Hiraku Nakajima Abstract: We will discuss how dualities of quantum field theories can be understood as analogous to Morita equivalences for algebras of various types. Juan Maldacena Is it possible to create a concave light? Recently, a rigorous probabilistic construction of the path integral was provided using the Gaussian Free Field. [Slides], Nicolo Piazzalunga (Uppsala University) Rio de Janeiro, June 18th, 2021. Title: Finite symmetry in field theory [Slides] [Video], Boris Pioline (Sorbonne Universit and CNRS) 4. Hawking tells you what the semiclassical limit is. Of course even his brightest former student couldnt accept that: The experimental community pretty much politely ignores the string theory community, and has, well, since 1974 or so when the analytic S-matrix failed to predict the charmed quark. Zhengping Gui (International Centre for Theoretical Physics) I just work on Theoretical Physics topics. (ii) Every-time I receive a grant report asking for resources, penned by a senior string theorist, Im already able to guess the 1st lines: ST is the only mathematically consistent candidate for understanding quantum gravity while providing a framework potentially unifying all know fundamental interactions. Breaking news: on July 5, 2022, Maryna Viazovska was awarded with the Fields medal, the highest recognition in mathematics! crickets]. Adrian, 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. [Slides] [Video], Yaping Yang (University of Melbourne) This is based on arXiv:2202.01788, with Matilde Marcolli and Sarthak Parikh. Katrin Wendland, Ron Donagi (University of Pennsylvania) [Slides], Peter Spacek (TU Chemnitz) [Slides], Meng-Chwan Tan (National University of Singapore) We investigate a two-dimensional chiral analogue of the algebraic index theorem via the theory of chiral algebras developed by Beilinson and Drinfeld. In this tutorial, we'll discuss various approaches to evaluate a math expression using Java. Pawe Caputa Elliott Gesteau (California Institute of Technology) 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. 2. He mentions that one basic problem with this is that there is no understanding of what happens in time-dependent backgrounds, so, in particular, this is useless for addressing the big bang, which is the one place people now point to as a possible connection to real world data. Paul-Konstantin Oehlmann (Uppsala University) Off topic, but the European congress of Mathematics has finished up. Of course, I do not justify equally wrong comments from certain string theorists Title: Perturbative calculations in twisted 4d gauge theories [online talk] I will also explain how the Hecke operators from geometric and analytic Langlands correspondence are realized in the four dimensional super-Yang-Mills theory. Maryna Viazovska was awarded with the Fields medal, https://www.fuw.edu.pl/faculty-of-physics-home.html, Hera guesthouse of the University of Warsaw (budget option), https://warsawgenomics.pl/en/sars-cov-2/koronawirus-rtpcr. The two-step procedure involves first finding points on the Calabi-Yau manifold and then approximating the Ricci-flat metric by approximating solutions to the underlying Monge-Ampere equation. [Slides]. In particular, i can not find a derivation of any black hole entropy from first principles in quantum gravity outside of string theory. Knots and Natural Language. The resulting quivers highlight fractionalization of those branes, that we determine for single and multiple brane stacks. These boring predictions, if confirmed by DUNE, will show that also in experimental physics no real stuff is happening. When the quiver comes from a smooth local toric Calabi-Yau 3-fold, we obtain a generalization of shifted Yangian, which acts on the cohomology of the moduli space of certain sheaves of the 3-fold. Abstract: I will review the Cohomological Hall algebra associated to a quiver and an oriented cohomology theory. Can they make mistakes? We provide new the structure that allows this, whose quantisation turns out to be lead to a multimatrix ensemble. As an example, we compute the trace evaluated on the unit constant chiral chain and obtain the formal Witten genus in the Lie algebra cohomology. At the time I drop those lines, more than 50 years from dual resonance models?, I havent found any convincingly argument. Abstract: By studying M-theory on singular non-compact special holonomy spaces X we demonstrate, via a process of cutting and gluing of singularities that extend to the boundary of X, the appearance of 0-form, 1-form and 2-group symmetries in the resulting supersymmetric quantum field theory. In this talk, I explain an ongoing work to combine them, and to give a higher relations between QFTs and differential cohomology. Extending this story, I will talk about other physical realizations of analytically continued systems, such as Regge poles, replicas, or dimensional regularization. In this talk I will introduce the heterotic G2 system and show how to construct families of solutions using homogeneous 3-Sasakian manifolds with squashed metrics. How to transform string into integers and operators in Javascript? [Slides] [Video], Jan Dereziski (University of Warsaw) Leonardo Rastelli Abstract: The spectrum of BPS states in D=4 supersymmetric field theories and string vacua famously jumps across codimension-one walls in vector multiplet moduli space. This lecture is aimed for the general public and does not request much prerequisites in mathematics. We determine the T-dual theories and match those global symmetries across the dualities. Greg Moore For different choices of superpotential, the LG theory categorifies the quantum knot invariants associated with any simply-laced Lie algebra. Particularly, the change of variable relating $SU(2)$ link invariants to the $SO(3)$ \& $OSP(1|2)$ link invariants plays a crucial role in explicitly writing the $q$-series. This is joint work with Mark Gross. The simplest example is the qubit. We highlight prototype examples of elliptically fibered non-compact Calabi-Yau fewfolds and comment on the fate of these symmetries when these spaces become compact. Abstract: Three-manifold invariants $\hat Z$ (Z-hat), also known as homological blocks, are $q$-series with integer coefficients. The match can be extended to saddles which appear in non-trivial Coulomb branch vacua. Math 250 (Vector Analysis) . Evaluator.js is a small, zero-dependency module for evaluating mathematical expressions. We provide significant evidence that averaging plays an important role in reproducingsemiclassical gravity in AdS/BCFT. There are slight differences regarding scoping, but they mostly behave the same, including exposure to much of the same security risks: You can't, at most you could do something retort like parsing the numbers and then separating the operations with a switch, and making them. The powerpoint is here in powerpoint and here in pdf . How to properly convert string into int to calculate in JS? Calculate string value in javascript, not using eval, How Intuit democratizes AI development across teams through reusability. LHC will discover SUSY To each 3-manifold equipped with a spin^c structure, is supposed to assign a q-series with integer coefficients that is categorifiable and provides an analytic continuation of the Witten-Reshetikhin-Turaev invariants. [Slides], Sachin Chauhan (Indian Institute of Technology, Bombay) Title: From BPS crystals to BPS algebras F-theory vacua with exactly one Higgs field and no vector-like exotics. What am I doing wrong here in the PlotLegends specification? Requiring the unitary equivalence also implies Modular Chaos Bound = Chaos Bound''. The LQG derivation, involving an ad-hoc choice for the Immirzi parameter [Slides] [Video], Brian Williams (University of Edinburgh) I will then explain how to describe their representations using subcrystals and how they can be translated into the framings of the quivers. Ironically, the very fact that he had to refer to it at all should alarm them. The linking numbers of plumbing graphs are interpreted as the effective mixed Chern-Simons levels of 3d N=2 theories with chiral multiplets. Are there any actual attempts in the literature to build such an intrinsically quantum theory, or is this just pie in the sky? [Slides] [Video], Mirjam Cvetic (University of Pennsylvania) Title: Families of Modular Flux Vacua on Symmetric CY Threefolds 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. We can exhibit for instance a duality between a trivial bundle with abelian isometries and a non-trivial *bibundle* with a nonabelian Poisson-Lie group action. In our examples we find agreement with the flux modularity conjecture of Kachru, Nally, and Yang. I suppose I shouldnt have even let that get started. Correlation functions in the worldsheet theory on AdS_3 are shown to agree with those of the dual CFT_2, with both being given in terms of branched covers. [Slides] [Video], Netta Engelhardt (MIT) But in my view a real mistake in the long run. Quantum physics studies the smallest objects in the universelike atoms and subatomic particleswhile general relativity typically focuses on larger-scale objects in the universe. Abstract: We explore little string theories in six dimensions, constructed via F-theory that are dual to heterotic stringswith NS5 branes probing ADE type singularities. [Slides], Aranya Bhattacharya (IISc, Bangalore) Abstract: I will review the holomorphic twist of four-dimensional N=1 gauge theories and present the Feynman diagrams which control the perturbative corrections to the twistingsupercharge and to the higher operations available in the twisted theories. 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. [Slides] [Video], Maxim Kontsevich (IHS) My talk will be based on recent joint work with Baej Ruba. It seems that no one in the string theory community dares to publicly breathe a word of skepticism. A better version was given September 22, 2021 at Yan Soibelman's M-seminar. Title: Cohomological-type Hall algebras and their representation theory I could go on the whole night, but I believe, as most other string theorists do, there are more urgent or at least doable problems to solve now. The real stuff happens in physics without a press release, book, or blog. 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. Connect and share knowledge within a single location that is structured and easy to search. Please, watch the discussions (there were many) and appreciate that these were honest discussion. In this talk, we will discuss recent progress in constructing explicit examples of higher-categories describing non-invertible symmetries in quantum field theories of various spacetime dimensions ranging from d=3 to d=6. Title: The higher dimensional tropical vertex of Science), [T] Ying Zhao (Institute for Advanced Study), Luis Alday, Luis Alvarez-Gaume, Kostas Bachas, Micha Berkooz, Nathan Berkovits, Ruth Britto, Horacio Casini, Alejandra Castro, Mirjam Cvetic, Atish Dabholkar, Jan de Boer, Robbert Dijkgraaf, Johana Erdmenger, Mboyo Esole, Jim Gates, 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, Igor Klebanov, 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, A convenient link with all talks at previous Strings meetings is hosted by Yuji Tachikawa at, https://member.ipmu.jp/yuji.tachikawa/stringsmirrors/, All sessions were recorded and are available at the Youtube daily links below or by clicking on the lecture in the, Strings 2021 will be held online during the two-week period. Their definition involves subtle boundary conditions. Since it's online only, talks are much more accessible than usual (and since it's free, over 2000 people have registered to in principle participate via Zoom). https://8ecm.si/prizes, Ashoke Sen has computed the logarithmic corrections to the Bekenstein-Hawking entropy of various standard black hole solutions in this paper. Can I tell police to wait and call a lawyer when served with a search warrant? Little string theories also possess T-duality as well as higher form- and group symmetries. 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. I will present a rigorous version of this formula in the context of quivers with potential, which governs the BPS spectrum in type IIA string theory compactified on certain conical Calabi-Yau threefolds, in the vicinity of orbifold-type points in Kahler moduli space. CEIs are associated to an arbitrary Calabi-Yau category, together with a splitting of the Hodge filtration. 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. Following Nimas final recommendation, an experimentalist and a string theorist hang out together. All major operations, constants, and methods are supported. The program is based on two main ingredients: The complex geometry of the underlying moduli spaces on the one hand, and cluster algebra structures defined by BPS- or DT-invariants on the other hand. Our conjecture, which we have developed with Ben-Zvi, Gunningham and Safronov, asserts an equality of dimensions between the G- and G^L-skein modules of a 3-manifold at generic quantization parameter. Its explicit description as a QFT has remained elusive. Everything is in the description. Adrian Langer +1 upvote from me, and I've already used it in a project. This is a joint work with Kwokwai Chan and Ziming Ma. String Theory remains the most magical structure we have encountered in theoretical physics and the magic seems directly connected to the particle physics of the real world Ill explain this phenomenon, and propose a new effective algorithm for the calculation of the spectrum which is not based on quantum algebra at all (joint work in progress with A. Soibelman). Is there some function to create a simple calculator without eval. Institutode Matemtica Pura e Aplicada (IMPA), Organizers: Henrique Bursztyn (IMPA), Reimundo Heluani (IMPA), Marcos Jardim (IMECC-UNICAMP), Gonalo Oliveira (UFF). 2021-22. We are going to perform a construction of such quantum curves using the mathematical language of vertex operator algebras. Number Strings & Math Talk Routines for Grades 3-5. Mhh, you could use the Function() constructor: There's nothing wrong with eval, especially for cases like this. In other words, a ternary string is a n-permutation with a repetion of the set {0,1,2}. This includes joint work with David Ben-Zvi, David Jordan, Pavel Safronov, Monica Vazirani, and Haiping Yang. This construction has several advantages and opens perspectives towards generalization to the case of the $cW$-algebras 11. Based on joint work with Petr Kravchuk and Sridip Pal. They have obvious applications to atomic physics. 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. [Slides] [Video], Conan Leung (Chinese University of Hong Kong) In particular, we provide two different path integral derivations of their wall-crossing formula for b_2^+(X)=1. Abstract: Currently, there is a strong interest in the study of non-invertible symmetries of quantum field theories. It's december of 2021, and the java world has been rattled by a log4j vulnerability. Rafa R. Suszek, Louis Alvarez-Gaume In the presence of chiral multiplets that are added to plumbing graphs, we show that ST-transformations lead to many equivalent plumbing theories, and hence generalize the scope of Kirby moves. Dear Peter, Quantum gravity: String theory is a theory of quantum gravity because it attempts to merge quantum physics with the theory of general relativity. We present a novel construction of such flux vacua in permutation-symmetric multiparameter compactifications, and develop methods for efficiently computing the zeta functions of the corresponding geometries. In the discussion section, Vafa challenges him on this, saying he sees no indication that quantum information theory gives any insight into dualities he sees as the central aspect of the non-perturbative theory. What does "use strict" do in JavaScript, and what is the reasoning behind it? http://jsfiddle.net/vol7ron/6cdfA/. with the exact opposite agenda. Even without LQG, there are many ideas on/in QG which are physically well founded. Staging Ground Beta 1 Recap, and Reviewers needed for Beta 2, Evaluate an Equation in Javascript, without eval(), Stand-in mathematical replacement for eval. How to store objects in HTML5 localStorage/sessionStorage. What sort of strategies would a medieval military use against a fantasy giant? People are attempting to understand things, with the tools at hand. How can I guarantee that my enums definition doesn't change in JavaScript? The 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. Title: Magnetic quivers for Superconformal Field Theories 3. What is a word for the arcane equivalent of a monastery? We physically derive (i) a novel Vafa-Witten four-manifold invariant associated with this moduli space, (ii) their relation to Gromov-Witten invariants, (iii) a novel Vafa-Witten Floer homology assigned to three-manifold boundaries, (iv) a novel Vafa-Witten Atiyah-Floer correspondence, (v) a proof and generalization of a conjecture by Abouzaid-Manolescu about the hypercohomology of a perverse sheaf of vanishing cycles, (vi) a Langlands duality of these invariants, Floer homologies and hypercohomology, and (vii) a quantum geometric Langlands correspondence with purely imaginary parameter that specializes to the classical correspondence in the zero-coupling limit, where Higgs bundles feature in (ii), (iv), (vi) and (vii). Title: Langlands duality for 3-manifolds But this procedure you adopted in this post, is not the best way of understanding science, or communicating it. Based on numerous works with G. Baverez, F. David, C. Guillarmou, A. Kupiainen, R. Rhodes. Clay Mathematics Institute, ContactEnhancement and Partnership ProgramMillennium Prize ProblemsPublicationsHome. 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. Any other way wouldn't be as efficient. Thank you. The knot homology is calculated from homs between particular branes, and we are able to construct projective resolutions of these branes in terms of thimbles, making the computation entirely algebraic. Thats about the general problem of quantizing a symplectic manifold, but my impression was that Witten was thinking of the even more general problem of a quantum theory with no known symplectic manifold of which it is the quantization. String Math Summer School. This talk is based on joint work with Xenia de la Ossa, arXiv:2111.13221. I will present recent progress in this direction in the simplest case of local $P^2$, and argue that its global BPS spectrum and flow tree structure can be deduced from a scattering diagram with simple initial data. Whats remarkable is how powerful Poincare space-time symmetry is as a determinant of how elementary particles behave. Summary Talk. The Ryu-Takayanagi formula then encodes the fractal dimension of the boundary, while the extremal surfaces encode an important part of the geometry of the buildings, showing a new interplay between ideas from holography and geometric group theory. Title: Holographic tensor networks from hyperbolic buildings Certificates YouTube live YouTube playlist of the lectures Yuya Kusuki (California Institute of Technology) Hello, Robert A. Wilson The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup.