BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eric Sharpe (Virginia Tech) DTSTART:20220302T133000Z DTEND:20220302T143000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/1 DESCRIPTION:Title: An introduction to decomposition\nby Eric Sharpe (Virginia Tech) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nIn this talk I wi ll review work on `decomposition\,' a property of 2d theories with 1-form symmetries and\, more generally\, d-dim'l theories with (d-1)-form symmetr ies.  Decomposition is the observation that such quantum field theories a re equivalent to ('decompose into’) disjoint unions of other QFTs\, know n in this context as "universes.” Examples include two-dimensional gauge theories and orbifolds with matter invariant under a subgroup of the gaug e group. Decomposition explains and relates several physical properties of these theories -- for example\, restrictions on allowed instantons arise as a "multiverse interference effect" between contributions from constitue nt universes. First worked out in 2006 as part of efforts to understand st ring propagation on stacks\, decomposition has been the driver of a number of developments since. In the first half of this talk\, I will review dec omposition\; in the second half\, I will focus on the recent application t o anomaly resolution of Wang-Wen-Witten in two-dimensional orbifolds.\n\nT alk joint with the ICTS string seminar series (https://researchseminars.or g/seminar/ictsvirtual).\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Vargas (ENS) DTSTART:20220407T073000Z DTEND:20220407T083000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/3 DESCRIPTION:Title: (Postponed) Liouville conformal field theory: from probability theory to the conformal bootstrap\nby Vincent Vargas (ENS) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nLiouville conformal field theory ( LCFT) was introduced by\nPolyakov in 1981 as an essential ingredient in hi s path integral\nconstruction of string theory. Since then Liouville theor y has appeared in\na wide variety of contexts ranging from random conforma l geometry to 4d\nYang-Mills theory with supersymmetry. Recently\, a proba bilistic\nconstruction of LCFT on general Riemann surfaces was provided us ing the 2d\nGaussian Free Field. This construction can be seen as a rigoro us\nconstruction of the 2d path integral introduced in Polyakov's 1981 wor k.\nIn contrast to this construction\, modern conformal field theory is ba sed\non representation theory and the so-called bootstrap procedure (based on\nrecursive techniques) introduced in 1984 by\nBelavin-Polyakov-Zamolod chikov. In particular\, a bootstrap construction\nfor LCFT has been propos ed in the mid 90's by\nDorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ) on the sphere. The aim of\nthis talk is to review a recent series of work which shows the equivalence\nbetween the probabilistic construction and the boot strap construction of\nLCFT on general Riemann surfaces. In particular\, t he equivalence is based\non showing that LCFT satisfies a set of natural g eometric axioms known as\nSegal's axioms.\n\nBased on works with: G. Baver ez\, F. David\, C. Guillarmou\, A. Kupiainen\, R.\nRhodes\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Heller (Hannover) DTSTART:20220324T103000Z DTEND:20220324T113000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/4 DESCRIPTION:Title: Real holomorphic sections of Deligne-Hitchin moduli spaces and integrable PDEs\nby Sebastian Heller (Hannover) as part of ICTS Math- Phys Seminars\n\n\nAbstract\nThe Deligne-Hitchin moduli space of a Riemann surface is the complex analytic reincarnation of the twistor space of the hyper-kaehler moduli space of solutions of Hitchin’s selfduality equati ons.\nIt is constructed by gluing the moduli spaces of lambda-connections on the Riemann surface with that of the complex conjugate Riemann surface. The twistor lines correspond\nto solutions of the self-duality equations. In this talk I will show that the Deligne-Hitchin moduli space contains v arious other complex lines which (in the rank 2 case) give rise to equivar iant harmonic maps into the\n3-sphere\, anti-deSitter and deSitter 3-spac e. The talk is based on joint work with Lynn Heller\, and on joint work wi th Indranil Biswas and Markus Roeser.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Samuel (ICTS/RRI) DTSTART:20220317T103000Z DTEND:20220317T113000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/5 DESCRIPTION:Title: Why radioastronomers need to understand Holonomy/Wilson loops< /a>\nby Joseph Samuel (ICTS/RRI) as part of ICTS Math-Phys Seminars\n\n\nA bstract\nAstronomers use interferometry to observe and study objects\nin t he sky. The early evidence for compact objects like black holes\nand neutr on stars came from radioastronomy. More recently the Event Horizon\nTelesc ope has imaged a black hole in the centre of M87 using VLBI (very long\nba seline interferometry).These observations are important\nto fundamental ph ysics as they push the limits of our understanding. However\nthese interfe rometric observations are dogged by noise\, which can alter the amplitude \nand phase of the signal received at each telescope. This noise introduce s spurious\neffects which come in the way of getting an accurate image of the object in the sky. \nThere is a need for extracting information from t he measurements which is immune to such distortions.\nAstronomers call the se quantities closure phases and closure amplitudes. The current state\no f understanding of such quantities is incomplete\, especially in the case of polarised\nobservations\, which would be needed to understand the magne tic field structure\nof a source. This is where fundamental physics can he lp astronomers. \nI will describe recent progress in understanding closure invariants in terms of gauge\ntheory. The theory of Wilson loops (aka gau ge theory\, Geometric Phase\, anholonomy\,loop variables)\npermits us the identify a complete and independent set of closure quantities. Our treatme nt \ngives a unified view of closure phases and closure amplitudes and set s the theory on a firm mathematical\nbasis.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shu-Heng Shao (Stony Brook) DTSTART:20220401T133000Z DTEND:20220401T143000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/6 DESCRIPTION:Title: Non-invertible symmetries from higher gauging\nby Shu-Heng Shao (Stony Brook) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nWe d iscuss invertible and non-invertible topological defects arising from gaug ing a discrete higher-form symmetry on a higher codimensional manifold in spacetime\, which we define as higher gauging. A higher-form symmetry is c alled p-gaugeable if it can be gauged on a codimension-p manifold in space time. We focus on 1-gaugeable 1-form symmetries in general 2+1d QFT\, and gauge them on a surface in spacetime. The universal fusion rules of the re sulting invertible and non-invertible condensation surfaces are determined . In the special case of 2+1d TQFT\, every ordinary global symmetry is rea lized from higher gauging. We further determine the fusion rules be- tween the surfaces\, lines\, and lines that only live on the surfaces\, making the first step towards building a fusion 2-category. We emphasize that the fusion “coefficients” in these non-invertible fusion rules are genera lly not numbers\, but 1+1d TQFTs. Finally\, we discuss examples of non-inv ertible symmetries in non-topological QFT such as the free compact scalar theory and QED.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Costello (Perimeter) DTSTART:20220427T130000Z DTEND:20220427T140000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/7 DESCRIPTION:Title: On the associativity of one loop corrections to the celestial OPE\nby Kevin Costello (Perimeter) as part of ICTS Math-Phys Seminars\ n\n\nAbstract\nThe celestial holography program suggests that collinear si ngularities in gauge theory and gravity can form the OPE coefficients of a two-dimensional CFT. We investigate whether known one-loop corrections to QCD collinear singularities satisfy the associativity conditions of an OP E. We find they do not\, but that associativity can be restored for certa in gauge groups by a certain Green-Schwarz mechanism. This is joint work w ith Natalie Paquette.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcos Marino (Geneva) DTSTART:20220512T103000Z DTEND:20220512T113000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/8 DESCRIPTION:Title: Resurgence and quantum topology\nby Marcos Marino (Geneva) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nQuantum field theories and string theories often lead to perturbative series which encode geometr ic information. In this talk I will argue that\, in the case of complex Ch ern-Simons theory\, perturbative series secretly encode integer invariants \, related in some cases to BPS counting. The framework which makes this r elation possible is the theory of resurgence\, where perturbative series l ead to additional non-perturbative sectors\, and the integer invariants ar ise as Stokes constants. I will illustrate these claims with explicit exam ples related to quantum invariants of hyperbolic knots. If time permits\, I will mention similar results in topological string theory.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Arpan Saha (ICMAT) DTSTART:20220414T103000Z DTEND:20220414T113000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/9 DESCRIPTION:Title: The GW/DT correspondence\, resurgence\, and geometry\nby A rpan Saha (ICMAT) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nGromov –Witten and Donaldson–Thomas invariants are enumerative invariants tha t can be defined for a Calabi–Yau threefold X. Whereas the GW invariants count stable holomorphic maps from a complex curve into X\, the DT invari ants count coherent sheaves supported on a holomorphic curve in X subject to some stability condition. Although superficially different\, it has bee n conjectured by Maulik–Nekrasov–Okounkov–Pandharipande that the two sets of invariants contain the same information. In this talk\, we shall be exploring a realisation of this conjectural equivalence inspired by top ological string theory wherein the DT invariants appear as Stokes data ass ociated to Borel resummations of the generating function of the GW invaria nts\, at least in the case where X is the resolved conifold. In particular \, we will find in this case that all the Borel resummations are transform ations of the triple sine function studied in a recent work of Bridgeland. Finally\, we will be seeing how the ambiguity from Borel resummations has a natural geometric interpretation in context of the c-map construction i n supergravity. All of this is based on the arXiv preprints 2109.06878 wit h Murad Alim\, Jörg Teschner\, and Iván Tulli\; 2106.11976 with Murad Al im and Iván Tulli\; and 2103.05060 with Mauro Mantegazza (to appear in Ge ometriae Dedicata).\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Elliott (UMass) DTSTART:20220422T130000Z DTEND:20220422T140000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/10 DESCRIPTION:Title: Framing Anomalies in TQFT\nby Chris Elliott (UMass) as pa rt of ICTS Math-Phys Seminars\n\n\nAbstract\nI'll discuss an approach to t he general problem of taking a quantization of a topological field theory on R^n\, and extending it to a quantization defined on more general orient ed n-manifolds. In general there is an obstruction to performing this qua ntization\, and we can characterize this obstruction concretely for a broa d class of topological theories (those of "AKSZ type"). This is based on joint work with Owen Gwilliam and Brian Williams.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuji Tachikawa (IPMU) DTSTART:20220525T060000Z DTEND:20220525T070000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/11 DESCRIPTION:Title: Undecidable problems in quantum field theory\nby Yuji Tac hikawa (IPMU) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nWe point o ut that some questions in quantum field theory are undecidable in a precis e mathematical sense. More concretely\, it will be demonstrated that there is no algorithm answering whether a given 2d supersymmetric Lagrangian th eory breaks supersymmetry or not. It will also be shown that there is a sp ecific 2d supersymmetric Lagrangian theory which breaks supersymmetry if a nd only if the standard Zermelo-Fraenkel set theory with the axiom of choi ce is consistent\, which can never be proved or disproved as the consequen ce of Gödel's second incompleteness theorem. The article includes a brief and informal introduction to the phenomenon of undecidability and its pre vious appearances in theoretical physics. This talk is based on 2203.16689 .\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Vargas (ENS) DTSTART:20220519T073000Z DTEND:20220519T083000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/12 DESCRIPTION:Title: Liouville conformal field theory: from probability theory to the conformal bootstrap\nby Vincent Vargas (ENS) as part of ICTS Math- Phys Seminars\n\n\nAbstract\nLiouville conformal field theory (LCFT) was i ntroduced by\nPolyakov in 1981 as an essential ingredient in his path inte gral\nconstruction of string theory. Since then Liouville theory has appea red in\na wide variety of contexts ranging from random conformal geometry to 4d\nYang-Mills theory with supersymmetry. Recently\, a probabilistic\nc onstruction of LCFT on general Riemann surfaces was provided using the 2d\ nGaussian Free Field. This construction can be seen as a rigorous\nconstru ction of the 2d path integral introduced in Polyakov's 1981 work.\nIn cont rast to this construction\, modern conformal field theory is based\non rep resentation theory and the so-called bootstrap procedure (based on\nrecurs ive techniques) introduced in 1984 by\nBelavin-Polyakov-Zamolodchikov. In particular\, a bootstrap construction\nfor LCFT has been proposed in the m id 90's by\nDorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ) on the sphere. Th e aim of\nthis talk is to review a recent series of work which shows the e quivalence\nbetween the probabilistic construction and the bootstrap const ruction of\nLCFT on general Riemann surfaces. In particular\, the equivale nce is based\non showing that LCFT satisfies a set of natural geometric ax ioms known as\nSegal's axioms.\n\nBased on works with: G. Baverez\, F. Dav id\, C. Guillarmou\, A. Kupiainen\, R.\nRhodes\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Tanvi Jain (ISI) DTSTART:20220804T063000Z DTEND:20220804T073000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/13 DESCRIPTION:Title: Symplectic eigenvalues : An introduction and recent results\nby Tanvi Jain (ISI) as part of ICTS Math-Phys Seminars\n\n\nAbstract\n For every 2n×2n real positive definite matrix A there exists a symplectic matrix M such that A = M^T D M\, where D is an n × n positive diagonal m atrix. The diagonal entries of D are called the symplectic eigenvalues of A. We will talk about the relevance of symplectic eigenvalues in quantum i nformation theory and discuss some recent results on them.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Sage (LSU) DTSTART:20220616T150000Z DTEND:20220616T160000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/14 DESCRIPTION:Title: Meromorphic connections on the projective line with specified local behavior\nby Daniel Sage (LSU) as part of ICTS Math-Phys Semina rs\n\n\nAbstract\nA fundamental problem in the theory of meromorphic conne ctions on $P^1$ is to understand the space of such systems with given loca l behavior. Here\, the local behavior of a connection at a singular point means the "formal type" there--the isomorphism class of the induced forma l connection. Given a collection of singular points and corresponding for mal types\, there are several natural questions one might ask: \n\n1) Doe s there exist a connection with these formal types? \n\n2) If such a conn ection exists\, is it unique up to isomorphism?\n\n3) Can one construct an explicit moduli space of such connections?\n\nClassically\, these questio ns were studied under the assumption that all singularities are regular si ngular (i.e. simple poles). For example\, in 2003\, Crawley-Boevey solved the Deligne-Simpson problem for Fuchsian connections (a variant of questi on 1) by reinterpreting the problem in terms of quiver varieties. Later\, mathematicians including Boalch\, Hiroe\, and Yamakawa investigated thes e questions when "unramified" irregular singularities are allowed. (Unram ified means that the formal types can be expressed in upper triangular for m without introducing roots of the local parameter.) \n\nIn recent years\, there has been increasing interest in meromorphic connections (and $G$-co nnections where $G$ is a reductive group) with ramified singularities due to developments in the geometric Langlands program. In this talk\, I will give an overview of recent progress on the ramified version of these prob lems due to myself and various collaborators.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Mohan Swaminathan (Princeton) DTSTART:20220714T053000Z DTEND:20220714T063000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/15 DESCRIPTION:Title: Extending Taubes' Gromov invariant to Calabi-Yau 3-folds\ nby Mohan Swaminathan (Princeton) as part of ICTS Math-Phys Seminars\n\n\n Abstract\nI will describe the construction of an integer-valued symplectic invariant counting embedded pseudo-holomorphic curves in a Calabi-Yau 3-f old in certain cases. This may be seen as an analogue of the Gromov invari ant defined by Taubes for symplectic 4-manifolds. The construction depends on a detailed bifurcation analysis of the moduli space of embedded curves along generic paths of almost complex structures. This is based on joint work with Shaoyun Bai.\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/15/ END:VEVENT BEGIN:VEVENT SUMMARY:T. R. Ramadas (CMI) DTSTART:20220728T093000Z DTEND:20220728T103000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/16 DESCRIPTION:Title: Symplectic Geometry of $SU(2)$ character varieties and lattic e gauge theory\nby T. R. Ramadas (CMI) as part of ICTS Math-Phys Semin ars\n\n\nAbstract\nI present evidence that $SU(2)$ lattice theory integral s on a\nfinite lattice can be approximated (in the thermodynamic limit) by \nintegrals over the $SU(2)$ character variety of an associated surface.\n By results of Goldman and Jeffrey-Weitsman the formalism of\nDuistermaat-H eckman applies to the latter.\n(http://arxiv.org/abs/2206.07455)\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/16/ END:VEVENT BEGIN:VEVENT SUMMARY:David Sauzin (Institute of Celestial Mechanics and Computation of the Ephemerides\, Paris) DTSTART:20220805T053000Z DTEND:20220805T063000Z DTSTAMP:20260404T094559Z UID:ictsmathphys/17 DESCRIPTION:Title: Resurgence and Partial Theta Series\nby David Sauzin (Ins titute of Celestial Mechanics and Computation of the Ephemerides\, Paris) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nFollowing arXiv:2112.152 23 with L. Han\, Y. Li\, S. Sun\, I will show how partial theta series\, i .e. functions of the form Θ(𝜏):=∑𝑓(𝑛)𝑒^{𝑖𝜋𝜏𝑛^2/ 𝑀} with 𝑓:ℤ→ℂ an 𝑀-periodic function (or the product of a p ower of 𝑛 by such function)\, give rise to divergent asymptotic series at every rational point of the boundary of their domain of definition {ℑ 𝜏>0}. I will discuss the summability and resurgence properties of these series by means of explicit formulas for their formal Borel transforms\, and the consequences for the modularity properties of Θ\, or its ``quantu m modularity'' properties in the sense of Zagier's recent theory. Interest ing examples stem from the study of Gukov-Pei-Putrov-Vafa invariants and W itten-Reshetikhin-Turaev invariants for the Poincaré homology sphere (cf. [Gukov-Putrov-Marino\, arXiv:1605.07615]) or more generally Seifert homol ogy 3-spheres ([Andersen-Mistegaard\, J. Lond. Math. Soc. 2022])\n LOCATION:https://stable.researchseminars.org/talk/ictsmathphys/17/ END:VEVENT END:VCALENDAR