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:20260422T225820Z 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 will revi ew work on `decomposition\,' a property of 2d theories with 1-form symmetr ies and\, more generally\, d-dim'l theories with (d-1)-form symmetries.  Decomposition is the observation that such quantum field theories are equi valent to ('decompose into’) disjoint unions of other QFTs\, known in th is context as "universes.” Examples include two-dimensional gauge theori es and orbifolds with matter invariant under a subgroup of the gauge group . Decomposition explains and relates several physical properties of these theories -- for example\, restrictions on allowed instantons arise as a "m ultiverse interference effect" between contributions from constituent univ erses. First worked out in 2006 as part of efforts to understand string pr opagation on stacks\, decomposition has been the driver of a number of dev elopments since. In the first half of this talk\, I will review decomposit ion\; in the second half\, I will focus on the recent application to anoma ly resolution of Wang-Wen-Witten in two-dimensional orbifolds.\n\nTalk joi nt with the ICTS string seminar series (https://researchseminars.org/semin ar/ictsvirtual).\n LOCATION:https://researchseminars.org/talk/ictsmathphys/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Vargas (ENS) DTSTART:20220407T073000Z DTEND:20220407T083000Z DTSTAMP:20260422T225820Z 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 M ath-Phys Seminars\n\n\nAbstract\nLiouville conformal field theory (LCFT) w as introduced by\nPolyakov in 1981 as an essential ingredient in his path integral\nconstruction of string theory. Since then Liouville theory has a ppeared in\na wide variety of contexts ranging from random conformal geome try to 4d\nYang-Mills theory with supersymmetry. Recently\, a probabilisti c\nconstruction of LCFT on general Riemann surfaces was provided using the 2d\nGaussian Free Field. This construction can be seen as a rigorous\ncon struction of the 2d path integral introduced in Polyakov's 1981 work.\nIn contrast to this construction\, modern conformal field theory is based\non representation theory and the so-called bootstrap procedure (based on\nre cursive techniques) introduced in 1984 by\nBelavin-Polyakov-Zamolodchikov. In particular\, a bootstrap construction\nfor LCFT has been proposed in t he 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 t he equivalence\nbetween the probabilistic construction and the bootstrap c onstruction of\nLCFT on general Riemann surfaces. In particular\, the equi valence is based\non showing that LCFT satisfies a set of natural geometri c axioms known as\nSegal's axioms.\n\nBased on works with: G. Baverez\, F. David\, C. Guillarmou\, A. Kupiainen\, R.\nRhodes\n LOCATION:https://researchseminars.org/talk/ictsmathphys/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Heller (Hannover) DTSTART:20220324T103000Z DTEND:20220324T113000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/4 DESCRIPTION:Title: Real holomorphic sections of Deligne-Hitchin moduli spaces and integr able PDEs\nby Sebastian Heller (Hannover) as part of ICTS Math-Phys Se minars\n\n\nAbstract\nThe Deligne-Hitchin moduli space of a Riemann surfac e is the complex analytic reincarnation of the twistor space of the hyper- kaehler moduli space of solutions of Hitchin’s selfduality equations.\nI t is constructed by gluing the moduli spaces of lambda-connections on the Riemann surface with that of the complex conjugate Riemann surface. The tw istor lines correspond\nto solutions of the self-duality equations. In thi s talk I will show that the Deligne-Hitchin moduli space contains various other complex lines which (in the rank 2 case) give rise to equivariant h armonic maps into the\n3-sphere\, anti-deSitter and deSitter 3-space. The talk is based on joint work with Lynn Heller\, and on joint work with Indr anil Biswas and Markus Roeser.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Samuel (ICTS/RRI) DTSTART:20220317T103000Z DTEND:20220317T113000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/5 DESCRIPTION:Title: Why radioastronomers need to understand Holonomy/Wilson loops\nby Joseph Samuel (ICTS/RRI) as part of ICTS Math-Phys Seminars\n\n\nAbstract \nAstronomers use interferometry to observe and study objects\nin the sky. The early evidence for compact objects like black holes\nand neutron star s came from radioastronomy. More recently the Event Horizon\nTelescope has imaged a black hole in the centre of M87 using VLBI (very long\nbaseline interferometry).These observations are important\nto fundamental physics a s they push the limits of our understanding. However\nthese interferometri c observations are dogged by noise\, which can alter the amplitude \nand p hase of the signal received at each telescope. This noise introduces spuri ous\neffects which come in the way of getting an accurate image of the obj ect in the sky. \nThere is a need for extracting information from the meas urements which is immune to such distortions.\nAstronomers call these quan tities closure phases and closure amplitudes. The current state\nof under standing of such quantities is incomplete\, especially in the case of pola rised\nobservations\, which would be needed to understand the magnetic fie ld structure\nof a source. This is where fundamental physics can help astr onomers. \nI will describe recent progress in understanding closure invari ants in terms of gauge\ntheory. The theory of Wilson loops (aka gauge theo ry\, Geometric Phase\, anholonomy\,loop variables)\npermits us the identif y a complete and independent set of closure quantities. Our treatment \ngi ves a unified view of closure phases and closure amplitudes and sets the t heory on a firm mathematical\nbasis.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shu-Heng Shao (Stony Brook) DTSTART:20220401T133000Z DTEND:20220401T143000Z DTSTAMP:20260422T225820Z 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 discuss invertible and non-invertible topological defects arising from gauging a d iscrete higher-form symmetry on a higher codimensional manifold in spaceti me\, which we define as higher gauging. A higher-form symmetry is called p -gaugeable if it can be gauged on a codimension-p manifold in spacetime. W e focus on 1-gaugeable 1-form symmetries in general 2+1d QFT\, and gauge t hem on a surface in spacetime. The universal fusion rules of the resulting invertible and non-invertible condensation surfaces are determined. In th e special case of 2+1d TQFT\, every ordinary global symmetry is realized f rom higher gauging. We further determine the fusion rules be- tween the su rfaces\, lines\, and lines that only live on the surfaces\, making the fir st step towards building a fusion 2-category. We emphasize that the fusion “coefficients” in these non-invertible fusion rules are generally not numbers\, but 1+1d TQFTs. Finally\, we discuss examples of non-invertible symmetries in non-topological QFT such as the free compact scalar theory and QED.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Costello (Perimeter) DTSTART:20220427T130000Z DTEND:20220427T140000Z DTSTAMP:20260422T225820Z 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\nAb stract\nThe celestial holography program suggests that collinear singulari ties in gauge theory and gravity can form the OPE coefficients of a two-di mensional CFT. We investigate whether known one-loop corrections to QCD co llinear singularities satisfy the associativity conditions of an OPE. We find they do not\, but that associativity can be restored for certain gaug e groups by a certain Green-Schwarz mechanism. This is joint work with Nat alie Paquette.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcos Marino (Geneva) DTSTART:20220512T103000Z DTEND:20220512T113000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/8 DESCRIPTION:Title: Resurgence and quantum topology\nby Marcos Marino (Geneva) as par t of ICTS Math-Phys Seminars\n\n\nAbstract\nQuantum field theories and str ing theories often lead to perturbative series which encode geometric info rmation. In this talk I will argue that\, in the case of complex Chern-Sim ons theory\, perturbative series secretly encode integer invariants\, rela ted in some cases to BPS counting. The framework which makes this relation possible is the theory of resurgence\, where perturbative series lead to additional non-perturbative sectors\, and the integer invariants arise as Stokes constants. I will illustrate these claims with explicit examples re lated to quantum invariants of hyperbolic knots. If time permits\, I will mention similar results in topological string theory.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Arpan Saha (ICMAT) DTSTART:20220414T103000Z DTEND:20220414T113000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/9 DESCRIPTION:Title: The GW/DT correspondence\, resurgence\, and geometry\nby Arpan Sa ha (ICMAT) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nGromov–Witt en and Donaldson–Thomas invariants are enumerative invariants that can b e defined for a Calabi–Yau threefold X. Whereas the GW invariants count stable holomorphic maps from a complex curve into X\, the DT invariants co unt coherent sheaves supported on a holomorphic curve in X subject to some stability condition. Although superficially different\, it has been conje ctured by Maulik–Nekrasov–Okounkov–Pandharipande that the two sets o f invariants contain the same information. In this talk\, we shall be expl oring a realisation of this conjectural equivalence inspired by topologica l string theory wherein the DT invariants appear as Stokes data associated to Borel resummations of the generating function of the GW invariants\, a t least in the case where X is the resolved conifold. In particular\, we w ill find in this case that all the Borel resummations are transformations of the triple sine function studied in a recent work of Bridgeland. Finall y\, we will be seeing how the ambiguity from Borel resummations has a natu ral geometric interpretation in context of the c-map construction in super gravity. All of this is based on the arXiv preprints 2109.06878 with Murad Alim\, Jörg Teschner\, and Iván Tulli\; 2106.11976 with Murad Alim and Iván Tulli\; and 2103.05060 with Mauro Mantegazza (to appear in Geometria e Dedicata).\n LOCATION:https://researchseminars.org/talk/ictsmathphys/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Elliott (UMass) DTSTART:20220422T130000Z DTEND:20220422T140000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/10 DESCRIPTION:Title: Framing Anomalies in TQFT\nby Chris Elliott (UMass) as part of I CTS Math-Phys Seminars\n\n\nAbstract\nI'll discuss an approach to the gene ral problem of taking a quantization of a topological field theory on R^n\ , and extending it to a quantization defined on more general oriented n-ma nifolds. In general there is an obstruction to performing this quantizati on\, and we can characterize this obstruction concretely for a broad class of topological theories (those of "AKSZ type"). This is based on joint w ork with Owen Gwilliam and Brian Williams.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuji Tachikawa (IPMU) DTSTART:20220525T060000Z DTEND:20220525T070000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/11 DESCRIPTION:Title: Undecidable problems in quantum field theory\nby Yuji Tachikawa (IPMU) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nWe point out that some questions in quantum field theory are undecidable in a precise mathe matical sense. More concretely\, it will be demonstrated that there is no algorithm answering whether a given 2d supersymmetric Lagrangian theory br eaks supersymmetry or not. It will also be shown that there is a specific 2d supersymmetric Lagrangian theory which breaks supersymmetry if and only if the standard Zermelo-Fraenkel set theory with the axiom of choice is c onsistent\, which can never be proved or disproved as the consequence of G ödel's second incompleteness theorem. The article includes a brief and in formal introduction to the phenomenon of undecidability and its previous a ppearances in theoretical physics. This talk is based on 2203.16689 .\n LOCATION:https://researchseminars.org/talk/ictsmathphys/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Vargas (ENS) DTSTART:20220519T073000Z DTEND:20220519T083000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/12 DESCRIPTION:Title: Liouville conformal field theory: from probability theory to the con formal bootstrap\nby Vincent Vargas (ENS) as part of ICTS Math-Phys Se minars\n\n\nAbstract\nLiouville conformal field theory (LCFT) was introduc ed by\nPolyakov in 1981 as an essential ingredient in his path integral\nc onstruction of string theory. Since then Liouville theory has appeared in\ na wide variety of contexts ranging from random conformal geometry to 4d\n Yang-Mills theory with supersymmetry. Recently\, a probabilistic\nconstruc tion of LCFT on general Riemann surfaces was provided using the 2d\nGaussi an Free Field. This construction can be seen as a rigorous\nconstruction o f the 2d path integral introduced in Polyakov's 1981 work.\nIn contrast to this construction\, modern conformal field theory is based\non representa tion theory and the so-called bootstrap procedure (based on\nrecursive tec hniques) introduced in 1984 by\nBelavin-Polyakov-Zamolodchikov. In particu lar\, a bootstrap construction\nfor LCFT has been proposed in the mid 90's by\nDorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ) on the sphere. The aim o f\nthis talk is to review a recent series of work which shows the equivale nce\nbetween the probabilistic construction and the bootstrap construction of\nLCFT on general Riemann surfaces. In particular\, the equivalence is based\non showing that LCFT satisfies a set of natural geometric axioms kn own as\nSegal's axioms.\n\nBased on works with: G. Baverez\, F. David\, C. Guillarmou\, A. Kupiainen\, R.\nRhodes\n LOCATION:https://researchseminars.org/talk/ictsmathphys/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Tanvi Jain (ISI) DTSTART:20220804T063000Z DTEND:20220804T073000Z DTSTAMP:20260422T225820Z 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\nFor eve ry 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 matrix. The diagonal entries of D are called the symplectic eigenvalues of A. We w ill talk about the relevance of symplectic eigenvalues in quantum informat ion theory and discuss some recent results on them.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Sage (LSU) DTSTART:20220616T150000Z DTEND:20220616T160000Z DTSTAMP:20260422T225820Z 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 Seminars\n\n\ nAbstract\nA fundamental problem in the theory of meromorphic connections on $P^1$ is to understand the space of such systems with given local behav ior. Here\, the local behavior of a connection at a singular point means the "formal type" there--the isomorphism class of the induced formal conne ction. Given a collection of singular points and corresponding formal typ es\, there are several natural questions one might ask: \n\n1) Does there exist a connection with these formal types? \n\n2) If such a connection exists\, is it unique up to isomorphism?\n\n3) Can one construct an explic it moduli space of such connections?\n\nClassically\, these questions were studied under the assumption that all singularities are regular singular (i.e. simple poles). For example\, in 2003\, Crawley-Boevey solved the De ligne-Simpson problem for Fuchsian connections (a variant of question 1) b y reinterpreting the problem in terms of quiver varieties. Later\, mathem aticians including Boalch\, Hiroe\, and Yamakawa investigated these quest ions when "unramified" irregular singularities are allowed. (Unramified m eans that the formal types can be expressed in upper triangular form witho ut introducing roots of the local parameter.) \n\nIn recent years\, there has been increasing interest in meromorphic connections (and $G$-connectio ns where $G$ is a reductive group) with ramified singularities due to deve lopments in the geometric Langlands program. In this talk\, I will give a n overview of recent progress on the ramified version of these problems du e to myself and various collaborators.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Mohan Swaminathan (Princeton) DTSTART:20220714T053000Z DTEND:20220714T063000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/15 DESCRIPTION:Title: Extending Taubes' Gromov invariant to Calabi-Yau 3-folds\nby Moh an Swaminathan (Princeton) as part of ICTS Math-Phys Seminars\n\n\nAbstrac t\nI will describe the construction of an integer-valued symplectic invari ant counting embedded pseudo-holomorphic curves in a Calabi-Yau 3-fold in certain cases. This may be seen as an analogue of the Gromov invariant def ined by Taubes for symplectic 4-manifolds. The construction depends on a d etailed bifurcation analysis of the moduli space of embedded curves along generic paths of almost complex structures. This is based on joint work wi th Shaoyun Bai.\n LOCATION:https://researchseminars.org/talk/ictsmathphys/15/ END:VEVENT BEGIN:VEVENT SUMMARY:T. R. Ramadas (CMI) DTSTART:20220728T093000Z DTEND:20220728T103000Z DTSTAMP:20260422T225820Z UID:ictsmathphys/16 DESCRIPTION:Title: Symplectic Geometry of $SU(2)$ character varieties and lattice gauge theory\nby T. R. Ramadas (CMI) as part of ICTS Math-Phys Seminars\n\n \nAbstract\nI present evidence that $SU(2)$ lattice theory integrals on a\ nfinite lattice can be approximated (in the thermodynamic limit) by\ninteg rals over the $SU(2)$ character variety of an associated surface.\nBy resu lts of Goldman and Jeffrey-Weitsman the formalism of\nDuistermaat-Heckman applies to the latter.\n(http://arxiv.org/abs/2206.07455)\n LOCATION:https://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:20260422T225820Z UID:ictsmathphys/17 DESCRIPTION:Title: Resurgence and Partial Theta Series\nby David Sauzin (Institute of Celestial Mechanics and Computation of the Ephemerides\, Paris) as part of ICTS Math-Phys Seminars\n\n\nAbstract\nFollowing arXiv:2112.15223 with L. Han\, Y. Li\, S. Sun\, I will show how partial theta series\, i.e. fun ctions of the form Θ(𝜏):=∑𝑓(𝑛)𝑒^{𝑖𝜋𝜏𝑛^2/𝑀} w ith 𝑓:ℤ→ℂ an 𝑀-periodic function (or the product of a power of 𝑛 by such function)\, give rise to divergent asymptotic series at ever y rational point of the boundary of their domain of definition {ℑ𝜏>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 ``quantum modul arity'' properties in the sense of Zagier's recent theory. Interesting exa mples stem from the study of Gukov-Pei-Putrov-Vafa invariants and Witten-R eshetikhin-Turaev invariants for the Poincaré homology sphere (cf. [Gukov -Putrov-Marino\, arXiv:1605.07615]) or more generally Seifert homology 3-s pheres ([Andersen-Mistegaard\, J. Lond. Math. Soc. 2022])\n LOCATION:https://researchseminars.org/talk/ictsmathphys/17/ END:VEVENT END:VCALENDAR