BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dongwook Ghim (KIAS) DTSTART:20220214T010000Z DTEND:20220214T014000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/1 DESCRIPTION:Title: Toric Calabi-Yau 4-folds\, 2d (0\,2) gauge theories and Brane Brick Models\nby Dongwook Ghim (KIAS) as part of UNIST International Worksh op on Geometry and Mathematical Physics 2022\n\n\nAbstract\nA special clas s of 2d (0\,2) supersymmetric gauge theories\, named as Brane Brick Models (BBM)\, is obtained by the low-energy limit of world-volume theories of D 1 branes probing toric Calabi-Yau 4-fold along its transverse directions. This talk will pedagogically introduce the combinatorial concepts involved in BBMs and how these are connected to the physics of 2d (0\,2) gauge the ories. In particular\, I will focus on the recent developments\, called 3d printing and orbifold reduction\, respectively\, which systematically gen erate 2d (0\,2) gauge theories from the data of 4d N=1 gauge theories rela ted to dimer models and toric Calabi-Yau 3-folds. Time permitting\, I will also mention about an enumerative tool of 2d gauge theories\, elliptic ge nus\, which captures the infared behavior of BBMs.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Kazushi Ueda (Tokyo University) DTSTART:20220214T015000Z DTEND:20220214T023000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/2 DESCRIPTION:Title: Noncommutative local Calabi-Yau 3-folds\nby Kazushi Ueda (Tokyo University) as part of UNIST International Workshop on Geometry and Mathe matical Physics 2022\n\n\nAbstract\nBased on joint works with Tarig Abdelg adir\, Akira Ishii\, Álvaro Nolla de Celis\, and Shinnosuke Okawa\,\nI wi ll discuss generalization of the description of toric Calabi-Yau 3-folds b y quivers with potentials coming from dimer models to non-toric or noncomm utative cases.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/2/ END:VEVENT BEGIN:VEVENT SUMMARY:David Vegh (Queen Mary London) DTSTART:20220214T100000Z DTEND:20220214T104000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/3 DESCRIPTION:Title: The spectral curve of segmented strings\nby David Vegh (Queen M ary London) as part of UNIST International Workshop on Geometry and Mathem atical Physics 2022\n\n\nAbstract\nIn this talk\, I will discuss how to co mpute the spectral curve of ``segmented strings'' in 3d anti-de Sitter spa cetime. The motion of a string in this target space is integrable and the worldsheet theory can be discretized while preserving integrability. The c orresponding embeddings are segmented strings\, which generalize piecewise linear strings in flat space. I will present several examples. Next\, I w ill introduce ``brane tilings''\, which are doubly-periodic planar biparti te graphs. I will show that the motion of a closed segmented string can be embedded into the mutation dynamics of a certain brane tiling. This will enable us to compute the spectral curve by taking the determinant of the d ressed adjacency matrix of the tiling.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Wei Li (ITP CAS Beijing) DTSTART:20220214T105000Z DTEND:20220214T113000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/4 DESCRIPTION:Title: From BPS crystals to BPS algebras: constructions\, representations\ , and applications\nby Wei Li (ITP CAS Beijing) as part of UNIST Inter national Workshop on Geometry and Mathematical Physics 2022\n\n\nAbstract\ nThe BPS sectors of supersymmetric gauge theories have underlying algebrai c structures\, manifesting themselves in wall-crossing phenomena\, BPS/CF T correspondences\, Bethe/Gauge correspondences\, twisted holographies\, e tc. I will first explain how to construct BPS algebras for string theory o n general toric Calabi-Yau threefolds\, based on the crystal melting descr iption of the BPS sectors. The resulting quiver Yangians\, together with t heir trigonometric and elliptic versions\, unify various known results and generalize them to a much larger class. I will then explain how to descri be their representations using subcrystals and how they can be translated to the framings of the quivers. Time permitting\, I will also discuss some applications.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ralf Schiffler (University of Connecticut) DTSTART:20220215T010000Z DTEND:20220215T014000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/5 DESCRIPTION:Title: Knot Theory and Cluster Algebras\nby Ralf Schiffler (University of Connecticut) as part of UNIST International Workshop on Geometry and M athematical Physics 2022\n\n\nAbstract\nTo every diagram K of knot (or lin k) we associate a quiver with potential (Q\,W) cluster algebra and\, hence \, a cluster algebra A(Q\,W) as well as a Jacobian algebra B=Jac(Q\,W). Th e vertices of the quiver are in bijection with the segments of the knot di agram. \n\nFor every segment i of K\, we construct an indecomposable B-mod ule T(i) and let T be the direct sum of these indecomposables. Each module T(i) corresponds to an element F(i) in the cluster algebra A(Q\,W)\, the so-called F-polynomial of the module. F(i) is a polynomial in several vari ables y_1\,...\, y_n with positive integer coefficients. \n\nWe prove that \, for each segment i of K\, the Alexander polynomial of K is equal to a s pecific specialization of F(i). For an alternating knot\, this specializat ion is simply y_i= -t if i is even\; y_i=-t^{-1} if i is odd\, where we la bel the segments of the knot in order of appearance along the knot.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Kenyon (Yale University) DTSTART:20220215T015000Z DTEND:20220215T023000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/6 DESCRIPTION:Title: Dimers and SL_n\nby Richard Kenyon (Yale University) as part of UNIST International Workshop on Geometry and Mathematical Physics 2022\n\ n\nAbstract\nWe consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”). This is joint work with Dan Douglas and Haolin Shi.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Cyril Closset (University of Birmingham) DTSTART:20220215T100000Z DTEND:20220215T104000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/7 DESCRIPTION:Title: Comments on BPS quivers: the view from the U-plane\nby Cyril Cl osset (University of Birmingham) as part of UNIST International Workshop o n Geometry and Mathematical Physics 2022\n\n\nAbstract\nI will discuss 5d BPS quivers\, which are quivers associated to Calabi-Yau threefold singula rities that admit a crepant resolution\, reinterpreted as the quantum mech anics of BPS particles of a 5d SCFT compactified on a circle. Using local mirror symmetry\, we will discuss how to derive some BPS quivers from the Seiberg-Witten geometry of these theories. Some open questions will be lef t open.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Pressland (University of Glasgow) DTSTART:20220215T105000Z DTEND:20220215T113000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/8 DESCRIPTION:Title: Grassmannian twists categorified\nby Matthew Pressland (Univers ity of Glasgow) as part of UNIST International Workshop on Geometry and Ma thematical Physics 2022\n\n\nAbstract\nThe Grassmannian of k-dimensional s ubspaces of an n-dimensional space carries a birational automorphism calle d the twist (or sometimes the Donaldson–Thomas transformation)\, defined by Berenstein–Fomin–Zelevinsky and Marsh–Scott. This automorphism r espects the cluster algebra structure on the coordinate ring\, being a qua si-cluster automorphism in the sense of Fraser. By work of Muller–Speyer \, similar results hold for positroid strata in the Grassmannian. The clus ter algebras in this picture have been categorified\, by Jensen–King–S u in the case of the full Grassmannian\, and by myself for more general (c onnected) positroid varieties. In this talk I will report on joint work wi th İlke Çanakçı and Alastair King\, in which we describe the twist in terms of these categorifications. The key ingredient is provided by perfec t matching modules\, certain combinatorially defined representations for a quiver 'with faces'\, and I will also explain this construction.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Xin Wang (KIAS) DTSTART:20220216T010000Z DTEND:20220216T014000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/9 DESCRIPTION:Title: Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometri es\nby Xin Wang (KIAS) as part of UNIST International Workshop on Geom etry and Mathematical Physics 2022\n\n\nAbstract\nFor a given toric Calabi -Yau threefold\, the quantum mirror curve from B-model describes the quant um Seiberg-Witten curve of the correspondence 5d N=1 supersymmetric gauge theory. On the other hand\, this quantum curve is also the spectral curve of the integrable system that arises from the Dimer model\, where the dim er model can be written down from the study of 4d N=1 quiver gauge theorie s. The eigenvalues of the Hamiltonians are supposed to be the quantized co mplex structure parameters of the quantum mirror curve. In this talk\, I w ill review the story\, and test the correspondence for genus two mirror cu rves.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergei Gukov (Caltech) DTSTART:20220216T015000Z DTEND:20220216T023000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/10 DESCRIPTION:Title: Quivers\, 3-manifolds\, and Fermionic Characters\nby Sergei Gu kov (Caltech) as part of UNIST International Workshop on Geometry and Math ematical Physics 2022\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Shlomo Razamat (Technion) DTSTART:20220216T100000Z DTEND:20220216T104000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/11 DESCRIPTION:Title: Comments on Quivers and Fractons\nby Shlomo Razamat (Technion) as part of UNIST International Workshop on Geometry and Mathematical Phys ics 2022\n\n\nAbstract\nWe will discuss certain structural analogies betwe en supersymmetric quiver gauge theories and lattice models leading to frac ton phases of matter. In particular\, classes of quiver models can be view ed as lattice models having subsystem symmetries\, dimensions of moduli sp aces growing linearly with the size of the lattice\, and having excitation s with limited mobility (with “excitations” and “mobility” properl y defined). The talk will be based on 2107.06465.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Sulkowski (University of Warsaw) DTSTART:20220216T105000Z DTEND:20220216T113000Z DTSTAMP:20260419T090000Z UID:UNIST_GMT_2022/12 DESCRIPTION:Title: Knots\, quivers\, and BPS states\nby Piotr Sulkowski (Universi ty of Warsaw) as part of UNIST International Workshop on Geometry and Math ematical Physics 2022\n\n\nAbstract\nI will review a recently discovered r elation between quivers and knots\, as well as – more generally – tori c Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence\, and it states that various invari ants of a given knot are captured by characteristics of a certain quiver\, which can be associated to this knot. Among others\, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver quiver \, it provides a new insight on knot categorification\, etc. This correspo ndence arises from string theory interpretation and engineering of knots i n brane systems in the conifold geometry\; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such mani folds and quivers.\n LOCATION:https://researchseminars.org/talk/UNIST_GMT_2022/12/ END:VEVENT END:VCALENDAR