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:20260404T095653Z UID:GNTRT/1 DESCRIPTION:Title: Some results and problems on the genericity of genuine representation s\nby Fan Gao (Zhejiang University) as part of Geometry\, Number Theor y and Representation Theory Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Maarten Solleveld (Radboud Universiteit) DTSTART:20210202T160000Z DTEND:20210202T170000Z DTSTAMP:20260404T095653Z UID:GNTRT/2 DESCRIPTION:Title: Bernstein Components and Hecke Algebras for $p$-adic Groups\nby M aarten Solleveld (Radboud Universiteit) as part of Geometry\, Number Theor y and Representation Theory Seminar\n\n\nAbstract\nSuppose that one has a supercuspidal representation of a Levi subgroup of some reductive \n$p$-ad ic group $G$. Bernstein associated to this a block $\\mathrm{Rep}(G)^s$ in the category of smooth $G$-representations. We address the question: what does $\\mathrm{Rep}(G)^s$ look like? Usually this is investigated with Bu shnell--Kutzko types\, but these are not always available. Instead\, we ap proach it via a progenerator of $\\mathrm{Rep}(G)^s.$ We will discuss the structure of the $G$\n-endomorphism algebra of such a progenerator in deta il. We will show that $\\mathrm{Rep}(G)^s$\nis "almost" equivalent with th e module category of an affine Hecke algebra -- a statement that will be m ade precise in several ways. In the end\, this leads to a classification o f the irreducible representations in $\\mathrm{Rep}(G)^s$ in terms of the complex torus and the finite group that are canonically associated to this Bernstein component.\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Kei Yuen Chan (Shanghai Center for Mathematical Sciences) DTSTART:20210210T010000Z DTEND:20210210T020000Z DTSTAMP:20260404T095653Z UID:GNTRT/3 DESCRIPTION:Title: Bernstein components for Whittaker models and branching laws\nby Kei Yuen Chan (Shanghai Center for Mathematical Sciences) as part of Geome try\, Number Theory and Representation Theory Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Siarhei Finski (Université Grenoble Alpes) DTSTART:20210223T170000Z DTEND:20210223T180000Z DTSTAMP:20260404T095653Z UID:GNTRT/4 DESCRIPTION:Title: On Riemann-Roch-Grothendieck theorem for punctured curves with hyperb olic singularities\nby Siarhei Finski (Université Grenoble Alpes) as part of Geometry\, Number Theory and Representation Theory Seminar\n\n\nAb stract\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 surfaces\, and more precisely of its determinant\, lies in the heart of ou r approach.\n\nWhen our result is applied directly to the moduli space of punctured 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 f irst Chern form of a Hermitian line bundle. This provides a generalisation of a result of Takhtajan-Zograf.\n\nWe will also explain how our results imply some bounds on the growth of Weil-Petersson form near the compactify ing divisor of the moduli space of punctured stable curves. This would per mit us to give a new approach to some well-known results of Wolpert on the Weil-Petersson geometry.\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis Eriksson (Chalmers University Technology) DTSTART:20210302T170000Z DTEND:20210302T180000Z DTSTAMP:20260404T095653Z UID:GNTRT/5 DESCRIPTION:Title: Genus one mirror symmetry\nby Dennis Eriksson (Chalmers Universit y Technology) as part of Geometry\, Number Theory and Representation Theor y Seminar\n\n\nAbstract\nMirror symmetry\, in a crude formulation\, is usu ally presented as a correspondence between curve counting on a Calabi-Yau variety X\, and some invariants extracted from a mirror family of Calabi-Y au varieties. After the physicists Bershadsky-Cecotti-Ooguri-Vafa\, this i s organised 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 talk\, I will give a general introduction to these problems based on joint work with Gerard Freixas and Christophe Mourougane. I will explain t he main ideas of the proof of the conjecture for Calabi-Yau hypersurfaces in projective space\, relying on the Riemann-Roch theorem in Arakelov geom etry. Our results generalise from dimension 3 to arbitrary dimensions prev ious work of Fang-Lu-Yoshikawa\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Changjian Su (University of Toronto) DTSTART:20210309T170000Z DTEND:20210309T180000Z DTSTAMP:20260404T095653Z UID:GNTRT/6 DESCRIPTION:Title: Motivic Chern classes of Schubert cells and applications\nby Chan gjian Su (University of Toronto) as part of Geometry\, Number Theory and R epresentation Theory Seminar\n\n\nAbstract\nThe motivic Chern classes are K-theoretic generalization of the MacPherson classes in homology. The moti vic Chern classes of Schubert cells have a Langlands dual description in t he Iwahori invariants of principal series representation of the p-adic Lan glands dual group. In joint works with Aluffi\, Mihalcea\, and Schurmann\, we use this relation to solve conjectures of Bump\, Nakasuji and Naruse a bout Casselman's basis\, and also relate the Euler characteristics of the motivic Chern classes to the Iwahori Whittaker functions.\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Ip (Hong Kong University of Science and Technology) DTSTART:20210316T150000Z DTEND:20210316T160000Z DTSTAMP:20260404T095653Z UID:GNTRT/7 DESCRIPTION:Title: Parabolic Positive Representations of $\\mathcal{U}_q(\\mathfrak{g}_\ \mathbb{R})$\nby Ivan Ip (Hong Kong University of Science and Technolo gy) as part of Geometry\, Number Theory and Representation Theory Seminar\ n\n\nAbstract\nWe construct a new family of irreducible representations of $\\mathcal{U}_q(\\mathfrak{g}_\\mathbb{R})$ and its modular double by qua ntizing the classical parabolic induction corresponding to arbitrary parab olic subgroups\, such that the generators of $\\mathcal{U}_q(\\mathfrak{g} _\\mathbb{R})$ act by positive self-adjoint operators on a Hilbert space. This generalizes the well-established positive representations introduced by [Frenkel-Ip] which correspond to induction by the minimal parabolic (i. e. Borel) 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 es tablish the properties of its central characters and universal $\\mathcal{ R}$ operator. We construct a positive version of the evaluation module of the affine quantum group\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Auguste Hébert (Institut de Mathématiques Elie Cartan Nancy) DTSTART:20210323T160000Z DTEND:20210323T170000Z DTSTAMP:20260404T095653Z UID:GNTRT/8 DESCRIPTION:Title: Principal series representations of Iwahori-Hecke algebras for Kac-Mo ody groups over local fields\nby Auguste Hébert (Institut de Mathéma tiques Elie Cartan Nancy) as part of Geometry\, Number Theory and Represen tation 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. Princip al series representations of H\, introduced by Matsumoto at the end of 197 0's\, are important in the representation theory of H. Every irreducible r epresentation of H is the quotient of and can be embedded in some principa l series representation of H and thus studying these representations enabl es to get information on the irreducible representations of H. S.Kato prov ided an irreducibility criterion for these representations in the beginnin g of the 1980's.\n\nKac-Moody groups are interesting infinite dimensional generalizations of reductive groups. Their study over non-Archimedean loca l field began in 1995 with the works of Garland. Let G be a split Kac-Mood y group (à la Tits) over a non-Archimedean local field. Braverman\, Kazhd an and Patnaik and Bardy-Panse\, Gaussent and Rousseau associated an Iwaho ri-Hecke algebra to G in 2014. I recently defined principal series represe ntations of these algebras. In this talk\, I will talk of these representa tions\, of a generalization of Kato's irreducibility criterion for these r epresentations and of how they decompose when they are reducible.\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Punya Satpathy (U. Michigan) DTSTART:20210330T150000Z DTEND:20210330T160000Z DTSTAMP:20260404T095653Z UID:GNTRT/9 DESCRIPTION:Title: Scattering theory on Locally Symmetric Spaces\nby Punya Satpathy (U. Michigan) as part of Geometry\, Number Theory and Representation Theor y Seminar\n\n\nAbstract\nIn 1976\, Victor Guillemin published a paper disc ussing geometric scattering theory\, in which he related the Lax-Phillips Scattering matrices (associated to a noncompact hyperbolic surface with cu sps) and the sojourn times associated to a set of geodesics which run to i nfinity in either direction.\nLater\, the work of Guillemin was generalize d to locally symmetric spaces by Lizhen Ji and Maciej Zworski. In the case of a $\\Q$-rank one locally symmetric space $\\Gamma \\backslash X$\, the y constructed a class of scattering geodesics which move to infinity in bo th directions and are distance minimizing near both infinities. An associa ted sojourn time was defined for such a scattering geodesic\, which is th e time it spends in a fixed compact region. One of their main results was that the frequencies of oscillation coming from the singularities of the F ourier transforms of scattering matrices on $\\Gamma \\backslash X$ occur at sojourn times of scattering geodesics on the locally symmetric space. \ n\nIn this talk I will review the work of Guillemin\, Ji and Zworski as we ll as discuss the work from my doctoral dissertation on analogous results for higher rank locally symmetric spaces. In particular\, I will describe higher dimensional analogues of scattering geodesics called $\\textbf{Scat tering Flat}$ and study these flats in the case of the locally symmetric s pace given by the quotient\n$SL(3\,\\mathbb{Z}) \\backslash SL(3\,\\mathbb {R}) / SO(3)$. A parametrization space is discussed for such scattering fl ats as well as an associated vector valued parameter (bearing similarities to sojourn times) called $\\textbf{sojourn vector}$ and these are related to the frequency of oscillations of the associated scattering matrices co ming from the minimal parabolic subgroups of $\\text{SL}(3\,\\mathbb{R})$. The key technique is the factorization of higher rank scattering matrices .\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuanqing Cai (Kanazawa University) DTSTART:20210407T000000Z DTEND:20210407T010000Z DTSTAMP:20260404T095653Z UID:GNTRT/10 DESCRIPTION:Title: Doubling integrals for Brylinski-Deligne extensions of classical gro ups\nby Yuanqing Cai (Kanazawa University) as part of Geometry\, Numbe r Theory and Representation Theory Seminar\n\n\nAbstract\nIn the 1980s\, P iatetski-Shapiro and Rallis discovered a family of\nRankin-Selberg integra ls for the classical groups that did not rely on\nWhittaker models. This i s the so-called doubling method. It grew out of\nRallis' work on the inner products of theta lifts -- the Rallis inner\nproduct formula.\n\nRecently \, a family of global integrals that represent the tensor product\nL-funct ions for classical groups (joint with Friedberg\, Ginzburg\, and\nKaplan) and the tensor product L-functions for covers of symplectic\ngroups (Kapla n) was discovered. These can be viewed as generalizations\nof the doubling method. In this talk\, we explain how to develop the\ndoubling integrals for Brylinski-Deligne extensions of connected\nclassical groups. This give s a family of Eulerian global integrals for\nthis class of non-linear exte nsions.\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Siddharth Sankaran (U. Manitoba) DTSTART:20210413T160000Z DTEND:20210413T170000Z DTSTAMP:20260404T095653Z UID:GNTRT/11 DESCRIPTION:Title: Green forms\, special cycles and modular forms.\nby Siddharth Sa nkaran (U. Manitoba) as part of Geometry\, Number Theory and Representatio n Theory Seminar\n\n\nAbstract\nShimura varieties attached to orthogonal g roups (of which modular curves are examples) are interesting objects of st udy for many reasons\, not least of which is the fact that they possess an abundance of “special” cycles. These cycles are at the centre of a co njectural program proposed by Kudla\; roughly speaking\, Kudla’s conject ures suggest that upon passing to an (arithmetic) Chow group\, the special cycles behave like the Fourier coefficients of automorphic forms. These c onjectures also include more precise identities\; for example\, the arithm etic Siegel-Weil formula relates arithmetic heights of special cycles to d erivatives of Eisenstein series. In this talk\, I’ll describe a construc tion (in joint work with Luis Garcia) of Green currents for these cycles\, which are an essential ingredient in the “Archimedean” part of the st ory\; I’ll also sketch a few applications of this construction to Kudla ’s conjectures.\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Shamgar Gurevich (U. Wisconsin\, Madison) DTSTART:20210420T160000Z DTEND:20210420T170000Z DTSTAMP:20260404T095653Z UID:GNTRT/12 DESCRIPTION:Title: Harmonic Analysis on GL_n over Finite Fields\nby Shamgar Gurevic h (U. Wisconsin\, Madison) as part of Geometry\, Number Theory and Represe ntation Theory Seminar\n\n\nAbstract\nThere are many formulas that express interesting properties of a finite group \n$G$ in terms of sums over its characters. For estimating these sums\, one of the most salient quantities to understand is the character ratio $\\mathrm{Trace}(\\rho(g))/ \\dim(\\ rho)$ for an irreducible representation $\\rho$ of $G$ and an element $g \ \in G.$ For example\, Diaconis and Shahshahani stated a formula of the men tioned type for analyzing certain random walks on $G.$ Recently\, we disco vered that for classical groups $G$ over finite fields there is a natural invariant of representations that provides strong information on the chara cter ratio. We call this invariant rank. \n\nRank suggests a new organizat ion of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s “philosophy of cusp forms”\, which is (since the 60s) the main organization principle\, and is based on the ( huge collection) of “Large” representations. \n\nThis talk will discus s the notion of rank for the group GLn over finite fields\, demonstrate ho w it controls the character ratio\, and explain how one can apply the resu lts to verify mixing time and rate for random walks. \n\nThis is joint wor k with Roger Howe (Yale and Texas A&M). The numerics for this work was car ried with Steve Goldstein (Madison) and John Cannon (Sydney).\n LOCATION:https://stable.researchseminars.org/talk/GNTRT/12/ END:VEVENT END:VCALENDAR