BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dylan Allegretti (Yau Mathematical Sciences Center at Tsinghua Uni versity) DTSTART:20221017T050000Z DTEND:20221017T063000Z DTSTAMP:20260422T225840Z UID:gapkias/1 DESCRIPTION:Title: Teichmüller spaces\, quadratic differentials\, and cluster coordinates\nby Dylan Allegretti (Yau Mathematical Sciences Center at Tsinghua Unive rsity) as part of Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\nIn the late 1980s\, Nigel Hitchin and Michael Wolf independently discovered a parametrization of the Teichmüller space of a compact surface by holomo rphic quadratic differentials. In this talk\, I will describe a generaliza tion of their result. I will explain how\, by replacing holomorphic differ entials by meromorphic differentials\, one is naturally led to consider an object called the enhanced Teichmüller space. The latter is an extension of the classical Teichmüller space which is important in mathematical ph ysics and the theory of cluster algebras.\n LOCATION:https://researchseminars.org/talk/gapkias/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Douglas (Yale University) DTSTART:20221024T010000Z DTEND:20221024T023000Z DTSTAMP:20260422T225840Z UID:gapkias/2 DESCRIPTION:Title: Dimers\, webs\, and local systems\nby Daniel Douglas (Yale University) as part of Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\nFor a pl anar bipartite graph G equipped with a SLn-local system\, we show that the determinant of the associated Kasteleyn matrix counts “n-multiwebs” ( generalizations of n-webs) in G\, weighted by their web-traces. We use thi s fact to study random n-multiwebs in graphs on some simple surfaces. Time permitting\, we will discuss some relations to Fock-Goncharov theory. Thi s is joint work with Rick Kenyon and Haolin Shi.\n LOCATION:https://researchseminars.org/talk/gapkias/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Hironori Oya (Tokyo Institute of Technology) DTSTART:20221222T010000Z DTEND:20221222T023000Z DTSTAMP:20260422T225840Z UID:gapkias/3 DESCRIPTION:Title: Wilson lines on the moduli space of $G$-local systems on a marked surface< /a>\nby Hironori Oya (Tokyo Institute of Technology) as part of Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\nFor a marked surface $\\Sigma$ \, there are two kinds of extensions of moduli spaces of local systems on $\\Sigma$\, written as $\\mathcal{A}_{\\widetilde{G}\, \\Sigma}$ and $\\ma thcal{P}_{G\, \\Sigma}$\, where $\\widetilde{G}$ is a connected simply-con nected complex simple algebraic group and $G=\\widetilde{G}/Z(\\widetilde{ G})$ its adjoint group. These are introduced by Fock--Goncharov and Goncha rov--Shen respectively\, and it is known that the pair $(\\mathcal{A}_{\\w idetilde{G}\, \\Sigma}\, \\mathcal{P}_{G\, \\Sigma})$ forms a cluster ense mble.\n In this talk\, we formulate a class of $\\widetilde{G}$ or $G$-va lued morphisms defined on these moduli spaces\, which we call Wilson lines . I explain their basic properties and application. In particular\, we giv e an affirmative answer to the $\\mathrm{A}=\\mathrm{U}$ problem for the c luster algebras arising from the cluster $K_2$-structures on $\\mathcal{A} _{\\widetilde{G}\, \\Sigma}$ under some assumptions on $G$ and $\\Sigma$.\ n This talk is based on a joint work with Tsukasa Ishibashi and Linhui Sh en.\n LOCATION:https://researchseminars.org/talk/gapkias/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Shunsuke Kano (Research Alliance Center for Mathematical Sciences\ , Tohoku University) DTSTART:20230112T050000Z DTEND:20230112T063000Z DTSTAMP:20260422T225840Z UID:gapkias/4 DESCRIPTION:Title: Unbounded sl(3)-laminations and their shear coordinates\nby Shunsuke K ano (Research Alliance Center for Mathematical Sciences\, Tohoku Universit y) as part of Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\nFock-- Goncharov pointed out the space of unbounded laminations on a marked surfa ce gives the set of tropical valued points of the moduli space of the fram ed PGL_2 local systems on the surface. The key point of this identificatio n is that the shear coordinate of the space of unbounded laminations gives the tropicalized cluster structure of the moduli space.\nIn this talk\, w e introduce the space of unbounded sl(3) laminations (with pinnings) and d efine the "shear coordinate" on it as a generalization of the sl(2) case.\ nIf time permits\, we discuss the graphical basis of the Ishibashi--Yuasa sl(3) skein algebra.\nThis talk is based on a joint work with Tsukasa Ishi bashi.\n LOCATION:https://researchseminars.org/talk/gapkias/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Tsukasa Ishibashi (Mathematical Institute\, Tohoku University) DTSTART:20230511T013000Z DTEND:20230511T030000Z DTSTAMP:20260422T225840Z UID:gapkias/5 DESCRIPTION:Title: Moduli space of decorated G-local systems and skein algebras\nby Tsuka sa Ishibashi (Mathematical Institute\, Tohoku University) as part of Geome try\, Algebra and Physics at KIAS\n\n\nAbstract\nThe moduli space of decor ated (twisted) G-local systems on a marked surface\, originally introduced by Fock–Goncharov\, is known to have a natural cluster K_2 structure. I n particular\, it admits a quantization via the framework of quantum clust er algebras\, due to Berenstein—Zelevinsky and Goncharov—Shen.\nIn thi s talk\, I will explain its (in general conjectural) relation to the skein algebras. This talk is based on joint works with Hironori Oya\, Linhui Sh en and Wataru Yuasa.\n LOCATION:https://researchseminars.org/talk/gapkias/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Wataru Yuasa (Graduate School of Science\, Division of Mathematics and Mathematical Sciences\, Kyoto University) DTSTART:20230629T013000Z DTEND:20230629T030000Z DTSTAMP:20260422T225840Z UID:gapkias/6 DESCRIPTION:Title: State-clasp correspondence for skein algebras\nby Wataru Yuasa (Gradua te School of Science\, Division of Mathematics and Mathematical Sciences\, Kyoto University) as part of Geometry\, Algebra and Physics at KIAS\n\n\n Abstract\nWe introduce the stated and the clasped sp_4-skein algebras for an oriented surface with marked points on the boundary. Moreover\, we show that the reduced version of the stated g-skein algebra is isomorphic to t he boundary-localization of the clasped g-skein algebra for g=sl_2\, sl_3\ , or sp_4. This isomorphism is a quantum counterpart of the two descriptio ns of the cluster algebra of the surface associated with g in terms of the matrix coefficients of Wilson lines and cluster variables\, respectively. This talk is based on a joint work with Tsukasa Ishibashi (Tohoku Univ.). \n LOCATION:https://researchseminars.org/talk/gapkias/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Sin-Myung Lee (Korea Institute for Advanced Study) DTSTART:20231023T020000Z DTEND:20231023T033000Z DTSTAMP:20260422T225840Z UID:gapkias/7 DESCRIPTION:Title: Representations of quantum affine (super)algebras from the R-matrix's poin t of view\nby Sin-Myung Lee (Korea Institute for Advanced Study) as pa rt of Geometry\, Algebra and Physics at KIAS\n\nLecture held in Room 1424\ , Korea Institute for Advanced Study.\n\nAbstract\nOne of the major proble ms in representation theory of quantum affine algebras is to understand th e tensor product structure\, for which it has been recognized that (normal ized) R-matrices and their poles play a crucial role. In this talk\, we fi rst give a brief survey on representations of quantum affine (super)algebr as from this perspective. Then we will explain a new approach motivated fr om the super duality for Lie superalgebras\, which is an ongoing project w ith Jae-Hoon Kwon and Masato Okado.\n LOCATION:https://researchseminars.org/talk/gapkias/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Davison (The University of Edinburgh) DTSTART:20231205T050000Z DTEND:20231205T063000Z DTSTAMP:20260422T225840Z UID:gapkias/8 DESCRIPTION:Title: Strong positivity for quantum cluster algebras\nby Ben Davison (The Un iversity of Edinburgh) as part of Geometry\, Algebra and Physics at KIAS\n \nLecture held in Room 1424\, Korea Institute for Advanced Study.\n\nAbstr act\nQuantum cluster algebras are quantizations of cluster algebras\, whic h are a class of algebras interpolating between integrable systems and com binatorics. These algebras were originally introduced to study positivity phenomena arising in the study of quantum groups\, and so one of the key q uestions regarding them (and their quantum analogues) is whether they admi t a basis for which the structure constants are positive. The classical ve rsion of this question was settled in the affirmative by Gross\, Hacking\, Keel and Kontsevich. I will present a proof of the quantum version of thi s positivity for skew-symmetric quantum cluster algebras\, due to joint wo rk with Travis Mandel\, based on results in categorified Donaldson-Thomas theory and scattering diagrams.\n LOCATION:https://researchseminars.org/talk/gapkias/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Buciumas (Pohang University of Science and Technology (PO STECH)) DTSTART:20240425T013000Z DTEND:20240425T030000Z DTSTAMP:20260422T225840Z UID:gapkias/9 DESCRIPTION:Title: Hecke algebras\, Whittaker functions and quantum groups\nby Valentin B uciumas (Pohang University of Science and Technology (POSTECH)) as part of Geometry\, Algebra and Physics at KIAS\n\nLecture held in KIAS 1424.\n\nA bstract\nI will give a brief overview of the Satake isomorphism and the Ca sselman-Shalika formula\, which are basic tools in the representation theo ry of p-adic groups. These two results essentially state that the spherica l Hecke algebra and the spherical Whittaker functions on a p-adic group ca n be understood in terms of the representation theory of the dual group.\n When passing from p-adic groups to their metaplectic covers\, it was conje ctured by Gaitsgory and Lurie (recently proved in different settings by Ca mpbell-Dhillon-Raskin and Buciumas-Patnaik) that the dual group gets repla ced by a certain quantum group at a root of unity. I will try to explain t he conjecture of Gaitsgory-Lurie and if time permits some of the ideas of the proof in the algebraic setting\, as well as some interactions to combi natorics and number theory.\n LOCATION:https://researchseminars.org/talk/gapkias/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Sunghyuk Park (Harvard University) DTSTART:20240430T010000Z DTEND:20240430T023000Z DTSTAMP:20260422T225840Z UID:gapkias/10 DESCRIPTION:Title: 3d quantum trace map\nby Sunghyuk Park (Harvard University) as part o f Geometry\, Algebra and Physics at KIAS\n\n\nAbstract\nI will speak about my recent joint work with Sam Panitch constructing the 3d quantum trace m ap\, a homomorphism from the Kauffman bracket skein module of an ideally t riangulated 3-manifold to its (square root) quantum gluing module\, thereb y giving a precise relationship between the two quantizations of the chara cter variety of ideally triangulated 3-manifolds. Our construction is base d on the study of stated skein modules and their behavior under splitting\ , especially into face suspensions.\n LOCATION:https://researchseminars.org/talk/gapkias/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitriy Voloshyn (IBS Center for Geometry and Physics) DTSTART:20240503T013000Z DTEND:20240503T030000Z DTSTAMP:20260422T225840Z UID:gapkias/11 DESCRIPTION:Title: Cluster algebras and Poisson geometry\nby Dmitriy Voloshyn (IBS Cente r for Geometry and Physics) as part of Geometry\, Algebra and Physics at K IAS\n\nLecture held in Room 1423\, Korea Institute for Advanced Study.\n\n Abstract\nCluster algebras are commutative rings with distinguished sets o f generators characterized by a remarkable combinatorial structure. Discov ered by S. Fomin and A. Zelevinsky in the early 2000s\, these algebraic st ructures have found applications across diverse mathematical fields\, incl uding integrable systems\, total positivity\, Teichmüller theory\, Poisso n geometry\, knot theory and mathematical physics.\n Fomin and Zelevinsky conjectured that numerous varieties in Lie theory are equipped with a clu ster structure. Early examples include double Bruhat cells\, Grassmannians and simple complex algebraic groups. M. Gekhtman\, M. Shapiro and A. Vain shtein observed that cluster algebras in these examples are compatible wit h certain Poisson brackets. Specifically\, for any given cluster $𝑥_1\, 𝑥_2\,...\,𝑥_n$\, there exist constants 𝟂ij such that $\\{𝑥_i\, 𝑥_j\\} = \\omega_{ij} 𝑥_i 𝑥_j$. This observation led to a program aiming to construct cluster algebras by addressing the inverse problem: g iven a Poisson bracket in the coordinate ring of an algebraic variety and a collection of regular functions $(𝑥_1\,𝑥_2\,...\,𝑥_n)$ satisfyi ng $\\{𝑥_i\,𝑥_j\\} = \\omega_{ij} 𝑥_i 𝑥_j$\, does there exist a compatible cluster algebra? The research initiative led to the formulati on of the GSV conjecture: for a given simple complex algebraic group and a Poisson bracket from the Belavin-Drinfeld class\, there exists a compatib le cluster structure.\n The plan for the talk is as follows. First\, we w ill discuss an example of a cluster structure on ${\\rm GL}_3(\\mathbb{C}) $. Then we will explore the connection between cluster algebras and Poisso n geometry\, as well as discuss how to construct a cluster structure compa tible with a Poisson bracket. After that\, we will discuss the recent resu lts on the three main families of objects: simple connected simple complex algebraic groups\, their Drinfeld doubles and their Poisson duals.\n LOCATION:https://researchseminars.org/talk/gapkias/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Volker Genz (IBS Center for Geometry and Physics) DTSTART:20240627T013000Z DTEND:20240627T030000Z DTSTAMP:20260422T225840Z UID:gapkias/12 DESCRIPTION:Title: Crystals and Cluster Algebras\nby Volker Genz (IBS Center for Geometr y and Physics) as part of Geometry\, Algebra and Physics at KIAS\n\nLectur e held in Room 1423\, Korea Institute for Advanced Study.\n\nAbstract\nCry stal operators on canonical bases as introduced by Kashiwara/Lusztig provi de in particular a toolbox to compute within the category of finite dimens ional representations of finite dimensional simple Lie algebras. Motivated by this we introduce certain operators on the lattice of tropical points of mirror dual A- and X-cluster spaces. In particular\, this yields a crys tal-like structure on the canonical basis due to Gross-Hacking-Keel-Kontse vich.\n LOCATION:https://researchseminars.org/talk/gapkias/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhihao Wang (Korea Institute for Advanced Study) DTSTART:20250919T013000Z DTEND:20250919T030000Z DTSTAMP:20260422T225840Z UID:gapkias/13 DESCRIPTION:Title: Centers and Representations of the SL(n) quantum Teichmüller Space\n by Zhihao Wang (Korea Institute for Advanced Study) as part of Geometry\, Algebra and Physics at KIAS\n\nLecture held in Room 8101\, KIAS.\n\nAbstra ct\nThe SL(n)-skein algebra of a surface can be thought of as a quantizati on of the surface’s character variety. When n=2\, it agrees with the fam iliar Kauffman bracket skein algebra\, so the \\mathrm{SL}(n) SL(n)-skein theory can be viewed as a natural generalization. Thanks to the work of L ê and Yu\, we know that the SL(n)-skein algebra is closely related to the SL(n) quantum Teichmüller space through the quantum trace map. In this t alk\, we will look at the centers and representations of both balanced Foc k–Goncharov algebras and SL(n)-skein algebras.\n LOCATION:https://researchseminars.org/talk/gapkias/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Davison (The Univ. of Edinburgh) DTSTART:20251205T020000Z DTEND:20251205T033000Z DTSTAMP:20260422T225840Z UID:gapkias/14 DESCRIPTION:Title: Tutte polynomials of graphs and symplectic duality\nby Ben Davison (T he Univ. of Edinburgh) as part of Geometry\, Algebra and Physics at KIAS\n \nLecture held in Room 8101\, KIAS.\n\nAbstract\nThe Tutte polynomial of a graph is a two-variable polynomial\, which is the universal polynomial sa tisfying the deletion contraction recursion. In this talk I will explain h ow this polynomial arises as a special case of a bicharacteristic polynomi al defined for pairs of symplectic dual conical resolutions of singulariti es. More precisely\, the Tutte polynomial records the dimensions of the gr aded pieces of the cohomology of hypertoric varieties (which I’ll introd uce) along with the two filtrations by cohomological degree\, coming from symplectic duality and Maulik-Okounkov stable envelopes (which I will also introduce). As well as recovering Tutte polynomials\, there are other bic haracteristic polynomials of symplectic resolutions to explore\, which I w ill describe if there is time. These results produce new inequalities of c oefficients of Tutte polynomials of matroids. This talk is based on joint work with Michael McBreen.\n LOCATION:https://researchseminars.org/talk/gapkias/14/ END:VEVENT END:VCALENDAR