BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Fan Gao (Zhejiang University) DTSTART:20210127T010000Z DTEND:20210127T020000Z DTSTAMP:20260422T212709Z UID:GNTRT/1 DESCRIPTION:Title: So me results and problems on the genericity of genuine representations\n by Fan Gao (Zhejiang University) as part of Geometry\, Number Theory and R epresentation Theory Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GNTRT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Maarten Solleveld (Radboud Universiteit) DTSTART:20210202T160000Z DTEND:20210202T170000Z DTSTAMP:20260422T212709Z UID:GNTRT/2 DESCRIPTION:Title: Be rnstein Components and Hecke Algebras for $p$-adic Groups\nby Maarten Solleveld (Radboud Universiteit) as part of Geometry\, Number Theory and R epresentation Theory Seminar\n\n\nAbstract\nSuppose that one has a supercu spidal representation of a Levi subgroup of some reductive \n$p$-adic grou p $G$. Bernstein associated to this a block $\\mathrm{Rep}(G)^s$ in the ca tegory of smooth $G$-representations. We address the question: what does $ \\mathrm{Rep}(G)^s$ look like? Usually this is investigated with Bushnell- -Kutzko types\, but these are not always available. Instead\, we approach it via a progenerator of $\\mathrm{Rep}(G)^s.$ We will discuss the structu re of the $G$\n-endomorphism algebra of such a progenerator in detail. We will show that $\\mathrm{Rep}(G)^s$\nis "almost" equivalent with the modul e category of an affine Hecke algebra -- a statement that will be made pre cise in several ways. In the end\, this leads to a classification of the i rreducible representations in $\\mathrm{Rep}(G)^s$ in terms of the complex torus and the finite group that are canonically associated to this Bernst ein component.\n LOCATION:https://researchseminars.org/talk/GNTRT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Kei Yuen Chan (Shanghai Center for Mathematical Sciences) DTSTART:20210210T010000Z DTEND:20210210T020000Z DTSTAMP:20260422T212709Z UID:GNTRT/3 DESCRIPTION:Title: Be rnstein components for Whittaker models and branching laws\nby Kei Yue n Chan (Shanghai Center for Mathematical Sciences) as part of Geometry\, N umber Theory and Representation Theory Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GNTRT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Siarhei Finski (Université Grenoble Alpes) DTSTART:20210223T170000Z DTEND:20210223T180000Z DTSTAMP:20260422T212709Z UID:GNTRT/4 DESCRIPTION:Title: On Riemann-Roch-Grothendieck theorem for punctured curves with hyperbolic si ngularities\nby Siarhei Finski (Université Grenoble Alpes) as part of Geometry\, Number Theory and Representation Theory Seminar\n\n\nAbstract\ nWe will present a refinement of Riemann-Roch-Grothendieck theorem on the level of differential forms for families of curves with hyperbolic cusps. The study of spectral properties of the Kodaira Laplacian on those surface s\, and more precisely of its determinant\, lies in the heart of our appro ach.\n\nWhen our result is applied directly to the moduli space of punctur ed stable curves\, it expresses the extension of the Weil-Petersson form ( as a current) to the boundary of the moduli space in terms of the first Ch ern form of a Hermitian line bundle. This provides a generalisation of a r esult of Takhtajan-Zograf.\n\nWe will also explain how our results imply s ome bounds on the growth of Weil-Petersson form near the compactifying div isor of the moduli space of punctured stable curves. This would permit us to give a new approach to some well-known results of Wolpert on the Weil-P etersson geometry.\n LOCATION:https://researchseminars.org/talk/GNTRT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis Eriksson (Chalmers University Technology) DTSTART:20210302T170000Z DTEND:20210302T180000Z DTSTAMP:20260422T212709Z UID:GNTRT/5 DESCRIPTION:Title: Ge nus one mirror symmetry\nby Dennis Eriksson (Chalmers University Techn ology) as part of Geometry\, Number Theory and Representation Theory Semin ar\n\n\nAbstract\nMirror symmetry\, in a crude formulation\, is usually pr esented as a correspondence between curve counting on a Calabi-Yau variety X\, and some invariants extracted from a mirror family of Calabi-Yau vari eties. After the physicists Bershadsky-Cecotti-Ooguri-Vafa\, this is organ ised according to the genus of the curves in X we wish to enumerate\, and gives rise to an infinite recurrence of differential equations. In this ta lk\, I will give a general introduction to these problems based on joint w ork with Gerard Freixas and Christophe Mourougane. I will explain the main ideas of the proof of the conjecture for Calabi-Yau hypersurfaces in proj ective space\, relying on the Riemann-Roch theorem in Arakelov geometry. O ur results generalise from dimension 3 to arbitrary dimensions previous wo rk of Fang-Lu-Yoshikawa\n LOCATION:https://researchseminars.org/talk/GNTRT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Changjian Su (University of Toronto) DTSTART:20210309T170000Z DTEND:20210309T180000Z DTSTAMP:20260422T212709Z UID:GNTRT/6 DESCRIPTION:Title: Mo tivic Chern classes of Schubert cells and applications\nby Changjian S u (University of Toronto) as part of Geometry\, Number Theory and Represen tation Theory Seminar\n\n\nAbstract\nThe motivic Chern classes are K-theor etic generalization of the MacPherson classes in homology. The motivic Che rn classes of Schubert cells have a Langlands dual description in the Iwah ori invariants of principal series representation of the p-adic Langlands dual group. In joint works with Aluffi\, Mihalcea\, and Schurmann\, we use this relation to solve conjectures of Bump\, Nakasuji and Naruse about Ca sselman's basis\, and also relate the Euler characteristics of the motivic Chern classes to the Iwahori Whittaker functions.\n LOCATION:https://researchseminars.org/talk/GNTRT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Ip (Hong Kong University of Science and Technology) DTSTART:20210316T150000Z DTEND:20210316T160000Z DTSTAMP:20260422T212709Z UID:GNTRT/7 DESCRIPTION:Title: Pa rabolic Positive Representations of $\\mathcal{U}_q(\\mathfrak{g}_\\mathbb {R})$\nby Ivan Ip (Hong Kong University of Science and Technology) as part of Geometry\, Number Theory and Representation Theory Seminar\n\n\nAb stract\nWe construct a new family of irreducible representations of $\\mat hcal{U}_q(\\mathfrak{g}_\\mathbb{R})$ and its modular double by quantizing the classical parabolic induction corresponding to arbitrary parabolic su bgroups\, such that the generators of $\\mathcal{U}_q(\\mathfrak{g}_\\math bb{R})$ act by positive self-adjoint operators on a Hilbert space. This ge neralizes the well-established positive representations introduced by [Fre nkel-Ip] which correspond to induction by the minimal parabolic (i.e. Bore l) subgroup. We also study in detail the special case of type $A_n$ acting on $L^2(\\mathbb{R}^n)$ with minimal functional dimension\, and establish the properties of its central characters and universal $\\mathcal{R}$ ope rator. We construct a positive version of the evaluation module of the aff ine quantum group\n LOCATION:https://researchseminars.org/talk/GNTRT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Auguste Hébert (Institut de Mathématiques Elie Cartan Nancy) DTSTART:20210323T160000Z DTEND:20210323T170000Z DTSTAMP:20260422T212709Z UID:GNTRT/8 DESCRIPTION:Title: Pr incipal series representations of Iwahori-Hecke algebras for Kac-Moody gro ups over local fields\nby Auguste Hébert (Institut de Mathématiques Elie Cartan Nancy) as part of Geometry\, Number Theory and Representation Theory Seminar\n\n\nAbstract\nLet G be a split reductive group over a non- Archimedean local field and H be its Iwahori-Hecke algebra. Principal seri es representations of H\, introduced by Matsumoto at the end of 1970's\, a re important in the representation theory of H. Every irreducible represen tation of H is the quotient of and can be embedded in some principal serie s representation of H and thus studying these representations enables to g et information on the irreducible representations of H. S.Kato provided an irreducibility criterion for these representations in the beginning of th e 1980's.\n\nKac-Moody groups are interesting infinite dimensional general izations of reductive groups. Their study over non-Archimedean local field began in 1995 with the works of Garland. Let G be a split Kac-Moody group (à la Tits) over a non-Archimedean local field. Braverman\, Kazhdan and Patnaik and Bardy-Panse\, Gaussent and Rousseau associated an Iwahori-Heck e algebra to G in 2014. I recently defined principal series representation s of these algebras. In this talk\, I will talk of these representations\, of a generalization of Kato's irreducibility criterion for these represen tations and of how they decompose when they are reducible.\n LOCATION:https://researchseminars.org/talk/GNTRT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Punya Satpathy (U. Michigan) DTSTART:20210330T150000Z DTEND:20210330T160000Z DTSTAMP:20260422T212709Z UID:GNTRT/9 DESCRIPTION:Title: Sc attering theory on Locally Symmetric Spaces\nby Punya Satpathy (U. Mic higan) as part of Geometry\, Number Theory and Representation Theory Semin ar\n\n\nAbstract\nIn 1976\, Victor Guillemin published a paper discussing geometric scattering theory\, in which he related the Lax-Phillips Scatter ing matrices (associated to a noncompact hyperbolic surface with cusps) an d the sojourn times associated to a set of geodesics which run to infinity in either direction.\nLater\, the work of Guillemin was generalized to lo cally symmetric spaces by Lizhen Ji and Maciej Zworski. In the case of a $ \\Q$-rank one locally symmetric space $\\Gamma \\backslash X$\, they const ructed a class of scattering geodesics which move to infinity in both dire ctions and are distance minimizing near both infinities. An associated soj ourn time was defined for such a scattering geodesic\, which is the time it spends in a fixed compact region. One of their main results was that th e frequencies of oscillation coming from the singularities of the Fourier transforms of scattering matrices on $\\Gamma \\backslash X$ occur at sojo urn times of scattering geodesics on the locally symmetric space. \n\nIn t his talk I will review the work of Guillemin\, Ji and Zworski as well as d iscuss the work from my doctoral dissertation on analogous results for hig her rank locally symmetric spaces. In particular\, I will describe higher dimensional analogues of scattering geodesics called $\\textbf{Scattering Flat}$ and study these flats in the case of the locally symmetric space gi ven by the quotient\n$SL(3\,\\mathbb{Z}) \\backslash SL(3\,\\mathbb{R}) / SO(3)$. A parametrization space is discussed for such scattering flats as well as an associated vector valued parameter (bearing similarities to soj ourn times) called $\\textbf{sojourn vector}$ and these are related to the frequency of oscillations of the associated scattering matrices coming fr om the minimal parabolic subgroups of $\\text{SL}(3\,\\mathbb{R})$. The ke y technique is the factorization of higher rank scattering matrices.\n LOCATION:https://researchseminars.org/talk/GNTRT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuanqing Cai (Kanazawa University) DTSTART:20210407T000000Z DTEND:20210407T010000Z DTSTAMP:20260422T212709Z UID:GNTRT/10 DESCRIPTION:Title: D oubling integrals for Brylinski-Deligne extensions of classical groups \nby Yuanqing Cai (Kanazawa University) as part of Geometry\, Number Theor y and Representation Theory Seminar\n\n\nAbstract\nIn the 1980s\, Piatetsk i-Shapiro and Rallis discovered a family of\nRankin-Selberg integrals for the classical groups that did not rely on\nWhittaker models. This is the s o-called doubling method. It grew out of\nRallis' work on the inner produc ts of theta lifts -- the Rallis inner\nproduct formula.\n\nRecently\, a fa mily of global integrals that represent the tensor product\nL-functions fo r classical groups (joint with Friedberg\, Ginzburg\, and\nKaplan) and the tensor product L-functions for covers of symplectic\ngroups (Kaplan) was discovered. These can be viewed as generalizations\nof the doubling method . In this talk\, we explain how to develop the\ndoubling integrals for Bry linski-Deligne extensions of connected\nclassical groups. This gives a fam ily of Eulerian global integrals for\nthis class of non-linear extensions. \n LOCATION:https://researchseminars.org/talk/GNTRT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Siddharth Sankaran (U. Manitoba) DTSTART:20210413T160000Z DTEND:20210413T170000Z DTSTAMP:20260422T212709Z UID:GNTRT/11 DESCRIPTION:Title: G reen forms\, special cycles and modular forms.\nby Siddharth Sankaran (U. Manitoba) as part of Geometry\, Number Theory and Representation Theor y Seminar\n\n\nAbstract\nShimura varieties attached to orthogonal groups ( of which modular curves are examples) are interesting objects of study for many reasons\, not least of which is the fact that they possess an abunda nce of “special” cycles. These cycles are at the centre of a conjectur al program proposed by Kudla\; roughly speaking\, Kudla’s conjectures su ggest that upon passing to an (arithmetic) Chow group\, the special cycles behave like the Fourier coefficients of automorphic forms. These conjectu res also include more precise identities\; for example\, the arithmetic Si egel-Weil formula relates arithmetic heights of special cycles to derivati ves of Eisenstein series. In this talk\, I’ll describe a construction (i n joint work with Luis Garcia) of Green currents for these cycles\, which are an essential ingredient in the “Archimedean” part of the story\; I ’ll also sketch a few applications of this construction to Kudla’s con jectures.\n LOCATION:https://researchseminars.org/talk/GNTRT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Shamgar Gurevich (U. Wisconsin\, Madison) DTSTART:20210420T160000Z DTEND:20210420T170000Z DTSTAMP:20260422T212709Z UID:GNTRT/12 DESCRIPTION:Title: H armonic Analysis on GL_n over Finite Fields\nby Shamgar Gurevich (U. W isconsin\, Madison) as part of Geometry\, Number Theory and Representation Theory Seminar\n\n\nAbstract\nThere are many formulas that express intere sting properties of a finite group \n$G$ in terms of sums over its charact ers. For estimating these sums\, one of the most salient quantities to und erstand is the character ratio $\\mathrm{Trace}(\\rho(g))/ \\dim(\\rho)$ f or an irreducible representation $\\rho$ of $G$ and an element $g \\in G.$ For example\, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on $G.$ Recently\, we discovered t hat for classical groups $G$ over finite fields there is a natural invaria nt of representations that provides strong information on the character ra tio. We call this invariant rank. \n\nRank suggests a new organization of representations based on the very few “Small” ones. This stands in con trast to Harish-Chandra’s “philosophy of cusp forms”\, which is (sin ce the 60s) the main organization principle\, and is based on the (huge co llection) of “Large” representations. \n\nThis talk will discuss the n otion of rank for the group GLn over finite fields\, demonstrate how it co ntrols the character ratio\, and explain how one can apply the results to verify mixing time and rate for random walks. \n\nThis is joint work with Roger Howe (Yale and Texas A&M). The numerics for this work was carried wi th Steve Goldstein (Madison) and John Cannon (Sydney).\n LOCATION:https://researchseminars.org/talk/GNTRT/12/ END:VEVENT END:VCALENDAR