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BEGIN:VEVENT
SUMMARY:Fan Gao (Zhejiang University)
DTSTART;VALUE=DATE-TIME:20210127T010000Z
DTEND;VALUE=DATE-TIME:20210127T020000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210202T160000Z
DTEND;VALUE=DATE-TIME:20210202T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210210T010000Z
DTEND;VALUE=DATE-TIME:20210210T020000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210223T170000Z
DTEND;VALUE=DATE-TIME:20210223T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210302T170000Z
DTEND;VALUE=DATE-TIME:20210302T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210309T170000Z
DTEND;VALUE=DATE-TIME:20210309T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210316T150000Z
DTEND;VALUE=DATE-TIME:20210316T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210323T160000Z
DTEND;VALUE=DATE-TIME:20210323T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210330T150000Z
DTEND;VALUE=DATE-TIME:20210330T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210407T000000Z
DTEND;VALUE=DATE-TIME:20210407T010000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210413T160000Z
DTEND;VALUE=DATE-TIME:20210413T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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;VALUE=DATE-TIME:20210420T160000Z
DTEND;VALUE=DATE-TIME:20210420T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T112622Z
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
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