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BEGIN:VEVENT
SUMMARY:Guofang Wei (plenary) (UC Santa Barbara)
DTSTART:20200803T230000Z
DTEND:20200804T001000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/1
DESCRIPTION:Title: Fundamental gap estimate in the hyperbolic spaces\nby Gu
ofang Wei (plenary) (UC Santa Barbara) as part of Eighth Pacific Rim Confe
rence in Mathematics\n\n\nAbstract\nIn their celebrated work\, B. Andrews
and J. Clutterbuck proved the fundamental gap conjecture the that differen
ce of first two eigenvalues of the Laplacian with Dirichlet boundary condi
tion on convex domain with diameter D in the Euclidean space is greater th
an or equal to $3\\pi^2/D^2$. In several joint works with X. Dai\, Z. He\,
S. Seto\, L. Wang (in various subsets)\, the estimate is generalized\, sh
owing the same lower bound holds for convex domains in the unit sphere. In
sharp contrast\, in recent joint work with T. Bourni\, J. Clutterbuck\, A
. Stancu\, X. Nguyen and V. Wheeler\, we prove that the product of the fun
damental gap with the square of the diameter can be arbitrarily small for
convex domains of any diameter in the hyperbolic spaces.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Sáez (Universidad Catolica de Chile)
DTSTART:20200804T002000Z
DTEND:20200804T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/2
DESCRIPTION:Title: Short-time existence for the network flow\nby Mariel Sá
ez (Universidad Catolica de Chile) as part of Eighth Pacific Rim Conferenc
e in Mathematics\n\n\nAbstract\nThe network flow is a system of parabolic
differential equations that describes the motion of a family of curves in
which each of them evolves under curve-shortening flow. This problem arise
s naturally in physical phenomena and its solutions present a rich variety
of behaviors. \nThe goal of this talk is to describe some properties of t
his geometric flow and to discuss an alternative proof of short-time exist
ence for non-regular initial conditions. The methods of our proof are base
d on techniques of geometric microlocal analysis that have been used to un
derstand parabolic problems on spaces with conic singularities. This is jo
int work with Jorge Lira\, Rafe Mazzeo\, and Alessandra Pluda.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hojoo Lee (Jeonbuk National University)
DTSTART:20200804T011000Z
DTEND:20200804T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/3
DESCRIPTION:Title: Minimal surfaces and flat structures\nby Hojoo Lee (Jeon
buk National University) as part of Eighth Pacific Rim Conference in Mathe
matics\n\n\nAbstract\nWe will introduce the flat structures on minimal sur
faces introduced by Chern and Ricci\, respectively.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Ebenfelt (UC San Diego)
DTSTART:20200805T002000Z
DTEND:20200805T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/4
DESCRIPTION:Title: Deformations and embeddings of compact strictly pseudoconvex
CR 3-manifolds\nby Peter Ebenfelt (UC San Diego) as part of Eighth Pa
cific Rim Conference in Mathematics\n\n\nAbstract\nA celebrated result of
Boutet de Monvel is that a compact strictly pseudoconvex CR manifold $M$ o
f dimension $2n+1$ is embeddable as a CR submanifold in $\\mathbb{C}^N$ \,
for some (potentially large) $N$\, provided $n\\geq 2$. The situation for
three-dimensional $M$ ($n=1$) is more subtle: "Most" such\, even real-an
alytic ones\, are not embeddable in this way. Much work has been done over
the years to characterize and describe the space of embeddable structures
. In this talk\, we shall consider the embeddability of families of deform
ations of a given embedded CR $3$-manifold\, and the structure of the spac
e of embeddable CR structures on $S^3$. We discuss a modified version of t
he Cheng-Lee slice theorem in which the embeddable deformations in the sli
ce can be explicitly characterized (in terms of spherical harmonics). We a
lso introduce a canonical family of embeddable deformations and correspond
ing embeddings starting with any infinitesimally embeddable deformation of
the unit sphere in $\\mathbb{C}^2$. The talk is based on joint work with
Sean Curry.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedram Hekmati (University of Auckland)
DTSTART:20200805T011000Z
DTEND:20200805T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/5
DESCRIPTION:Title: Holomorphic bundles on foliations\nby Pedram Hekmati (Un
iversity of Auckland) as part of Eighth Pacific Rim Conference in Mathemat
ics\n\n\nAbstract\nIt is well-known that the existence of Hermitian-Einste
in metrics on holomorphic bundles is intimately tied to the notion of stab
ility. In this talk I will discuss how this correspondence extends to the
setting of transverse holomorphic bundles on taut Riemannian foliations. I
will further elucidate the relation to higher dimensional instantons on S
asakian manifolds and mention some applications.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiko Matsumoto (Osaka University)
DTSTART:20200805T021000Z
DTEND:20200805T030000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/6
DESCRIPTION:Title: Asymptotically complex hyperbolic Einstein spaces and CR geo
metry\nby Yoshihiko Matsumoto (Osaka University) as part of Eighth Pac
ific Rim Conference in Mathematics\n\n\nAbstract\nThe correspondence betwe
en Poincaré-Einstein spaces and conformal \ngeometry of the boundaries at
infinity is actively pursued. Our subject is its lesser-known analog\, an
d yet also classical because it generalizes the study of invariant metrics
on bounded strictly pseudoconvex domains. I will discuss the existence ma
tter and construction of CR invariants through asymptotically complex hype
rbolic \nEinstein metrics.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiping Zhang (Chern Institute of Mathematics)
DTSTART:20200805T030000Z
DTEND:20200805T035000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/7
DESCRIPTION:Title: Positive scalar curvature on foliations\nby Weiping Zhan
g (Chern Institute of Mathematics) as part of Eighth Pacific Rim Conferenc
e in Mathematics\n\n\nAbstract\nA famous theorem of Lichnerowicz states th
at if a closed spin manifold carries a Riemannian metric of positive scala
r curvature\, then the $\\widehat{A}$-genus of the manifold vanishes. We w
ill describe various generalizations of this result\, as well as some othe
r classical results concerning positive scalar curvature\, to the case of
foliations. A typical example is Connes' theorem which states that if the
$\\widehat{A}$-genus of a compact foliated manifold with spin leaves does
not vanish\, then there is no metric with positive scalar curvature along
the leaves.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoichiro Mori (University of Pennsylvania)
DTSTART:20200804T002000Z
DTEND:20200804T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/8
DESCRIPTION:Title: Stability of planar fronts of the bidomain Allen-Cahn equati
on\nby Yoichiro Mori (University of Pennsylvania) as part of Eighth Pa
cific Rim Conference in Mathematics\n\n\nAbstract\nThe bidomain model is t
he standard model describing electrical activity of the heart. We discuss
the stability of planar front solutions of the bidomain equation with a bi
stable nonlinearity (the bidomain Allen‐Cahn equation) in two spatial di
mensions. In the bidomain Allen‐Cahn equation a Fourier multiplier opera
tor whose symbol is a positive homogeneous rational function of degree two
(the bidomain operator) takes the place of the Laplacian in the classical
Allen‐Cahn equation. Stability of the planar front may depend on the di
rection of propagation given the anisotropic nature of the bidomain operat
or. We establish various criteria for stability and instability of the pla
nar front in each direction of propagation. Our analysis reveals that plan
ar fronts can be unstable in the bidomain Allen‐Cahn equation in strikin
g contrast to the classical or anisotropic Allen‐Cahn equations. We iden
tify two types of instabilities\, one with respect to long‐wavelength pe
rturbations\, the other with respect to medium‐wavelength perturbations.
Interestingly\, whether the front is stable or unstable under long‐wave
length perturbations does not depend on the bistable nonlinearity and is f
ully determined by the convexity properties of a suitably defined Frank di
agram. On the other hand\, stability under intermediate‐wavelength pertu
rbations does depend on the choice of bistable nonlinearity. Intermediate
‐wavelength instabilities can occur even when the Frank diagram is conve
x\, so long as the bidomain operator does not reduce to the Laplacian. We
shall also give a remarkable example in which the planar front is unstable
in all directions. Time permitting\, I will also discuss properties of th
e bidomain FitzHugh Nagumo equations. This is joint work with Hiroshi Mata
no\, Mitsunori Nara and Koya Sakakibara.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong-Jung Kim (KAIST)
DTSTART:20200804T011000Z
DTEND:20200804T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/9
DESCRIPTION:Title: Can you tell how effective a COVID-19 prevention scheme is a
t elementary schools?\nby Yong-Jung Kim (KAIST) as part of Eighth Paci
fic Rim Conference in Mathematics\n\n\nAbstract\nWe focus on the fact that
the basic reproduction number $R_0$ is decided by the pattern of social c
ontacts. We claim that finding a social contact pattern which is affordabl
e and of small enough $R_0$ is the key to preventing COVID-19 from spreadi
ng. Recently\, the Ministry of Education of the Republic of Korea has issu
ed new school operating policies due to COVID-19 pandemic. Schools have de
veloped new ways to run schools to comply with the new policies\, which re
sulted in new contact patterns in schools. We compute $R_0$ corresponding
to such patterns and conclude that reducing the class size and the inter-c
lass contact rate is the best way to lower $R_0$ in elementary and seconda
ry schools.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihong Du (plenary) (University of New England)
DTSTART:20200804T021000Z
DTEND:20200804T032000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/10
DESCRIPTION:Title: Propagation\, diffusion and free boundaries\nby Yihong
Du (plenary) (University of New England) as part of Eighth Pacific Rim Con
ference in Mathematics\n\n\nAbstract\nIn this talk I will discuss some of
the mathematical theories on nonlinear partial differential equations moti
vated by the desire of providing better models for various propagation phe
nomena. The talk will start with classical works of Fisher\, Kolmogorov-Pe
trovskii-Piskunov and Aronson-Weinberger\, and then focus on recent result
s on free boundary models with local as well as nonlocal diffusion\, which
are variations of the models in the classical works.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Ward (University of British Columbia)
DTSTART:20200805T011000Z
DTEND:20200805T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/11
DESCRIPTION:Title: Synchrony and oscillatory dynamics for a 2-D PDE-ODE model
of diffusion-sensing with small signaling compartments\nby Michael War
d (University of British Columbia) as part of Eighth Pacific Rim Conferenc
e in Mathematics\n\n\nAbstract\nWe analyze a class of cell-bulk coupled PD
E-ODE models\, motivated by quorum and diffusion sensing phenomena in micr
obial systems\, that characterize communication between localized spatiall
y segregated dynamically active signaling compartments or "cells'' that ha
ve a permeable boundary. In this model\, the cells are disks of a common r
adius $\\varepsilon \\ll 1$ and they are spatially coupled through a passi
ve extracellular bulk diffusion field with diffusivity $D$ in a bounded 2-
D domain. Each cell secretes a signaling chemical into the bulk region at
a constant rate and receives a feedback of the bulk chemical from the enti
re collection of cells. This global feedback\, which activates signaling p
athways within the cells\, modifies the intracellular dynamics according t
o the external environment. The cell secretion and global feedback are reg
ulated by permeability parameters across the cell membrane. For arbitrary
reaction-kinetics within each cell\, the method of matched asymptotic exp
ansions is used in the limit $\\varepsilon\\ll 1$ of small cell radius to
construct steady-state solutions of the PDE-ODE model\, and to derive a gl
obally coupled nonlinear matrix eigenvalue problem (GCEP) that characteriz
es the linear stability properties of the steady-states. The analysis and
computation of the nullspace of the GCEP as parameters are varied is centr
al to the linear stability analysis. In the limit of large bulk diffusivit
y $D={D_0/\\nu}\\gg 1$\, where $\\nu\\equiv {-1/\\log\\varepsilon}$\, an a
symptotic analysis of the PDE-ODE model leads to a limiting ODE system for
the spatial average of the concentration in the bulk region that is coupl
ed to the intracellular dynamics within the cells. Results from the linea
r stability theory and ODE dynamics are illustrated for Sel'kov reaction-k
inetics\, where the kinetic parameters are chosen so that each cell is qui
escent when uncoupled from the bulk medium. For various specific spatial c
onfigurations of cells\, the linear stability theory is used to construct
phase diagrams in parameter space characterizing where a switch-like emerg
ence of intracellular oscillations can occur through a Hopf bifurcation. T
he effect of the membrane permeability parameters\, the reaction-kinetic p
arameters\, the bulk diffusivity\, and the spatial configuration of cells
on both the emergence and synchronization of the oscillatory intracellular
dynamics\, as mediated by the bulk diffusion field\, is analyzed in detai
l. The linear stability theory is validated from full numerical simulation
s of the PDE-ODE system\, and from the reduced ODE model when $D$ is large
.\nJoint with Sarafa Iyaniwura (UBC)\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihisa Morita (Ryukoku University)
DTSTART:20200805T020000Z
DTEND:20200805T025000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/12
DESCRIPTION:Title: Segregation pattern in a mathematical model of cell polarit
y\nby Yoshihisa Morita (Ryukoku University) as part of Eighth Pacific
Rim Conference in Mathematics\n\n\nAbstract\nAsymmetric cell division is o
ne of the fundamental processes to create cell diversity in the early stag
e of embryonic development. We deal with polarity models describing the PA
R polarity formation in the asymmetric cell division of a C. elegans embry
o. We employee a bulk-surface diffusion model together with a simpler mode
l to exhibit the long time behavior of the polarity formation of a bulk-su
rface cell. Moreover\, we rigorously prove the existence of stable noncons
tant solutions of the simpler equations in a parameter regime and explore
how the boundary position of polarity domain is determined. This talk is o
wing to a recent joint work with S. Seirin-Lee (Hiroshima University).\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiun-Chuan Chen (National Taiwan University)
DTSTART:20200805T030000Z
DTEND:20200805T035000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/13
DESCRIPTION:Title: Travelling wave solutions of the 3-species Lotka-Volterra c
ompetition system with diffusion\nby Chiun-Chuan Chen (National Taiwan
University) as part of Eighth Pacific Rim Conference in Mathematics\n\n\n
Abstract\nOne of the central issues in mathematical ecology is to understa
nd how coexistence of many species is possible. This talk is concerned wit
h the problem of whether competition among species helps to sustain their
coexistence. We first focus on the existence of a special type of non-mono
tone traveling waves of the 3-species system and introduce some related re
sults in recent years. Then we show that this type of waves provides new c
lues about the problem of coexistence.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ofer Zeitouni (plenary) (Weizmann Institute of Science)
DTSTART:20200804T150000Z
DTEND:20200804T161000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/14
DESCRIPTION:Title: Stability and instability of spectrum for small random pert
urbations of structured non-normal matrices\nby Ofer Zeitouni (plenary
) (Weizmann Institute of Science) as part of Eighth Pacific Rim Conference
in Mathematics\n\n\nAbstract\nWe discuss the spectrum of high dimensional
non-normal matrices under small noisy perturbations. That spectrum can be
extremely unstable\, as the maximal nilpotent matrix $J_N$ with $J_N(i\,j
)=1$ iff $j=i+1$ demonstrates. Numerical analysts studied worst case pert
urbations\, using the notion of pseudo-spectrum. Our focus is on finding t
he locus of most eigenvalues (limits of density of states)\, as well as st
udying stray eigenvalues ("outliers")\, in the case where the unperturbed
matrix is either Toeplitz or twisted Toeplitz. I will describe the backgro
und\, show some fun and intriguing simulations\, and present some theorems
and work in progress concerning eigenvectors. No background will be assum
ed. The talk is based on joint works with Anirban Basak\, Elliot Paquette\
, and Martin Vogel.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Dembo (Stanford University)
DTSTART:20200804T162000Z
DTEND:20200804T171000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/15
DESCRIPTION:Title: Universality for diffusions interacting through a random ma
trix\nby Amir Dembo (Stanford University) as part of Eighth Pacific Ri
m Conference in Mathematics\n\n\nAbstract\nConsider a system of $N$ stocha
stic differential equations interacting through an $N$-dimensional\nmatrix
$J$ of independent random entries (starting at an initial state whose law
is independent of $J$).\nWe show that the trajectories of a large class o
f observables which are averaged over the\n$N$ coordinates of the solution
\, are universal. That is\, for a fixed time interval the limit of such ob
servables as $N$ grows\, essentially depends only on the first two moments
of the marginal\ndistributions of entries of $J$.\n\nConcrete settings fo
r which such universality holds include aging in\nthe spherical Sherringto
n-Kirkpatrick spin-glass and Langevin dynamics\nfor a certain collection o
f Hopfield networks.\n\nThis talk is based on joint works with Reza Gheiss
ari\, and with Eyal Lubetzky and Ofer Zeitouni.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Remenik (Universidad de Chile)
DTSTART:20200804T172000Z
DTEND:20200804T181000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/16
DESCRIPTION:Title: Non-intersecting Brownian motions with outliers\, KPZ fluct
uations and random matrices\nby Daniel Remenik (Universidad de Chile)
as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nA w
ell known result implies that the rescaled maximal height of a system of $
N$ non-intersecting Brownian bridges starting and ending at the origin con
verges\, as $N$ goes to infinity\, to the Tracy-Widom GOE random variable
from random matrix theory. In this talk I will focus on the same question
in case where the top $m$ paths start and end at arbitrary locations. I wi
ll present several related results about the distribution of the limiting
maximal height for this system\, which provides a deformation of the Tracy
-Widom GOE distribution: it can be expressed through a Fredholm determinan
t formula and in terms of Painlevé transcendents\; it is connected with t
he fluctuations of models in the KPZ universality class with a particular
initial condition\; and it is connected with two PDEs\, the KdV equation a
nd an equation derived by Bloemendal and Virág for spiked random matrices
. Based on joint work with Karl Liechty and Gia Bao Nguyen.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Chatterjee (Stanford University)
DTSTART:20200805T002000Z
DTEND:20200805T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/17
DESCRIPTION:Title: Mass gap implies quark confinement\nby Sourav Chatterje
e (Stanford University) as part of Eighth Pacific Rim Conference in Mathem
atics\n\n\nAbstract\nThe confinement of quarks is one of the enduring myst
eries of modern physics. I will present a rigorous result that shows that
if a pure lattice gauge theory at some given coupling strength has exponen
tial decay of correlations under arbitrary boundary conditions\, and the g
auge group is a compact connected matrix Lie group with a nontrivial cente
r\, then the theory is confining. This gives mathematical justification fo
r a longstanding belief in physics about the mechanism behind confinement\
, which roughly says that confinement is the result of strong coupling beh
avior plus center symmetry. The proof is almost entirely based in probabil
ity theory\, making extensive use of the idea of coupling probability meas
ures.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Sauermann (Stanford University)
DTSTART:20200805T012000Z
DTEND:20200805T021000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/18
DESCRIPTION:Title: On the extension complexity of random polytopes\nby Lis
a Sauermann (Stanford University) as part of Eighth Pacific Rim Conference
in Mathematics\n\n\nAbstract\nSometimes\, it is possible to represent a c
omplicated polytope as a projection of a much simpler polytope. To quantif
y this phenomenon\, the extension complexity of a polytope $P$ is defined
to be the minimum number of facets in a (possibly higher-dimensional) poly
tope from which $P$ can be obtained as a (linear) projection. In this talk
\, we discuss some results on the extension complexity of random polytopes
. For a fixed dimension $d$\, we consider random $d$-dimensional polytopes
obtained as the convex hull of independent random points either in the un
it ball ball or on the unit sphere. In both cases\, we prove that the exte
nsion complexity is typically on the order of the square root of number of
vertices of the polytope. Joint work with Matthew Kwan and Yufei Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Insuk Seo (Seoul National University)
DTSTART:20200805T022000Z
DTEND:20200805T031000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/19
DESCRIPTION:Title: Metastable interacting particle systems\nby Insuk Seo (
Seoul National University) as part of Eighth Pacific Rim Conference in Mat
hematics\n\n\nAbstract\nIn this talk\, we discuss interacting particles sy
stems exhibiting a phenomenon known as the condensation of particles. For
these systems\, particles tend to be condensed at a site because of either
sticky or attracting interacting mechanism. A fundamental question for th
ese systems is to describe the behavior of the movement of the condensed s
ite as a suitable scaling limit. We introduce recent results regarding thi
s problem for the zero-range process and the inclusion process. This talk
is based on joint works with S. Kim\, C. Landim and D. Marcondes.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Donaldson (plenary) (Stony Brook University and Imperial Col
lege\, London)
DTSTART:20200807T230000Z
DTEND:20200808T001000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/20
DESCRIPTION:Title: $G_{2}$-geometry and complex variables (NEW TIME)\nby S
imon Donaldson (plenary) (Stony Brook University and Imperial College\, Lo
ndon) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstrac
t\nThe setting for this talk is the study of 7-dimensional manifolds with
torsion free $G_{2}$-structures. While these are not complex manifolds the
re are many interactions with complex geometry and the talk will survey so
me of these. Topics that will be discussed include "$G_{2}$-cobordisms" be
tween Calabi-Yau 3-folds\; Kovalev’s twisted connected sum construction
which involves of Fano or semi-Fano 3-folds and the adiabatic limits of $G
_{2}$-geometry on manifolds with $K3$-fibrations.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiki Oshima (Osaka University)
DTSTART:20200805T002000Z
DTEND:20200805T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/21
DESCRIPTION:Title: Collapsing of Ricci-flat Kahler metrics and compactificatio
ns of moduli spaces\nby Yoshiki Oshima (Osaka University) as part of E
ighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nCertain locally
Hermitian symmetric spaces parameterize complex algebraic varieties\, suc
h as polarized abelian varieties and K3 surfaces through periods.\nIn this
talk\, we will see that one of Satake compactifications of locally symmet
ric spaces\, which is different from the Baily-Borel compactification\, pa
rameterizes limits of canonical (Ricci-flat) metrics on abelian varieties
or K3 surfaces. This in particular involves parameterization of "tropical"
varieties by locally symmetric spaces and confirms a conjecture of Kontse
vich-Soibelman in the case of K3 surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mao Sheng (University of Science and Technology of China)
DTSTART:20200805T011000Z
DTEND:20200805T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/22
DESCRIPTION:Title: De Rham decomposition theorem with intersection condition\nby Mao Sheng (University of Science and Technology of China) as part o
f Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nDeligne-Illu
sie proved that the Frobenius pushforward of the de Rham complex is decomp
osable in the derived category under suitable conditions. It is called the
de Rham decomposition theorem\, that is the key for an algebraic proof of
the $E_1$ degeneration of the Hodge to de Rham spectral sequence over the
field of complex numbers. In their nonabelian Hodge theory in positive ch
aracteristic\, Ogus-Vologodsky established the de Rham decomposition theor
em with coefficients\, that generalizes Deligne-Illusie's result in a far
reaching way. In my talk\, I shall report a further generalization of Ogus
-Vologodsky's decomposition theorem\, that takes care of an intersection c
ondition at infinity. This work was motivated by Gabber's purity theorem f
or perverse sheaves\, and Zucker\, Cattani-Kaplan-Schmid and Kashiwara-Kaw
ai's works on intersection cohomologies of variations of Hodge structure.
This is a joint work with Zebao Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoyuki Hisamoto (Tokyo Metropolitan University)
DTSTART:20200806T030000Z
DTEND:20200806T035000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/23
DESCRIPTION:Title: Optimal lower bound of the Calabi type functionals\nby
Tomoyuki Hisamoto (Tokyo Metropolitan University) as part of Eighth Pacifi
c Rim Conference in Mathematics\n\n\nAbstract\nCalabi functional is define
d as the $L^2$ norm of the scalar curvature and conjecturally its lower bo
und is achieved by a sequence of the normalized Donaldson-Futaki invariant
s. It is naturally related to the limit behavior of the Calabi flow. \nFor
the Fano manifolds the problem can be reformulated in terms of the Ricci
curvature potential. We prove in this situation that the lower bound of th
e Ricci-Calabi functional is achieved by a sequence of the normalized D-in
variants\, taking the multiplier ideal sheaves of the appropriate geometri
c flow. \nThe same argument can be applied to the Dervan-Székelyhidi's lo
wer bound of the entropy functional.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaokui Yang (Chinese Academy of Sciences)
DTSTART:20200806T040000Z
DTEND:20200806T045000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/24
DESCRIPTION:Title: RC-positivity and geometry of complex manifolds\nby Xia
okui Yang (Chinese Academy of Sciences) as part of Eighth Pacific Rim Conf
erence in Mathematics\n\n\nAbstract\nIn this presentation\, we discuss som
e recent progress on the geometry of compact manifolds with RC-positive ta
ngent bundles\, including an affirmative answer to an open problem of S.T.
Yau on rational connectedness of compact Kahler manifolds with positive h
olomorphic sectional curvature\, and new Liouville type theorems for holom
orphic maps and harmonic maps. Several open problems related to the theory
of RC-positivity will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radu Laza (Stony Brook University)
DTSTART:20200806T050000Z
DTEND:20200806T055000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/25
DESCRIPTION:Title: Remarks on degenerations of Hyperkaehler and Calabi-Yau man
ifolds\nby Radu Laza (Stony Brook University) as part of Eighth Pacifi
c Rim Conference in Mathematics\n\n\nAbstract\nDue to Kulikov theorem and
its applications\, one has a good understanding of the degenerations of K3
surfaces and consequently some understanding of compactifications for mod
uli of K3 surfaces. In this talk\, I will discuss some aspects of higher d
imensional analogues of these results. Most of the results will concern Hy
perkaehler manifolds\, where the picture is quite similar to that for K3 s
urfaces. I will close with some ideas on how to deal with the more subtle
Calabi-Yau case.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Sideris (UC Santa Barbara)
DTSTART:20200806T002000Z
DTEND:20200806T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/27
DESCRIPTION:Title: The affine motion of 2d incompressible ideal fluids surroun
ded by vacuum\nby Thomas Sideris (UC Santa Barbara) as part of Eighth
Pacific Rim Conference in Mathematics\n\n\nAbstract\nThe equations of affi
ne motion for a 2D incompressible ideal fluid surrounded\nby vacuum reduce
to a globally solvable Hamiltonian system of ordinary differential\nequat
ions for the deformation gradient constrained to $SL(2\,R)$. The evolution
of the fluid domain is described by a family of ellipses of fixed area. W
e shall provide a complete description of the dynamic behavior of these do
mains for perfect fluids and for magnetically conducting fluids. For perfe
ct fluids\, the displacement generically becomes unbounded as time tends t
o infinity\, and for magnetically conducting fluids\, solutions remain bou
nded and are generically quasi-periodic.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baoxiang Wang (Peking University)
DTSTART:20200806T011000Z
DTEND:20200806T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/28
DESCRIPTION:Title: Navier-Stokes Equation in Super-Critical Spaces $E^s_{p\,q}
$\nby Baoxiang Wang (Peking University) as part of Eighth Pacific Rim
Conference in Mathematics\n\n\nAbstract\nIn this paper we develop a new wa
y to study the global existence and uniqueness for the Navier-Stokes equat
ion (NS) and consider the initial data in a class of modulation spaces $E^
s_{p\,q}$ with exponentially decaying weights $(s<0\, \\ 1< p\,q<\\infty)$
for which the norms are defined by\n$$\n\\|f\\|_{E^s_{p\,q}} = \\left(\\s
um_{k\\in \\mathbb{Z}^d} 2^{s|k|q}\\|\\mathscr{F}^{-1} \\chi_{k+[0\,1]^d}\
\mathscr{F} f\\|^q_p \\right)^{1/q}.\n$$\nThe space $E^s_{p\,q}$ is a rath
er rough function space and cannot be treated as a subspace of tempered di
stributions. For example\, we have the embedding $H^{\\sigma}\\subset E^s_
{2\,1}$ for any $\\sigma<0$ and $s<0$. It is known that $H^\\sigma$ ($\\si
gma< d/2-1$) is a super-critical space of NS\, it follows that $ E^s_{2\,1
}$ ($s<0$) is also super-critical for NS.\nWe show that NS has a unique gl
obal mild solution if the initial data belong to $E^s_{2\,1}$ ($s<0$) and
their Fourier transforms are supported in $ \\mathbb{R}^d_I:= \\{\\xi\\in
\\mathbb{R}^d: \\ \\xi_i \\geq 0\, \\\, i=1\,...\,d\\}$. Similar results h
old for the initial data in $E^s_{r\,1}$ with $2< r \\leq d$. Our results
imply that NS has a unique global solution if the initial value $u_0$ is i
n $L^2$ with ${\\rm supp} \\\, \\widehat{u}_0 \\\, \\subset \\mathbb{R}^d_
I$. This is a joint work with Professors H. G. Feichtinger\, K. Gröchenig
and Dr. Kuijie Li.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Glen Wheeler (University of Wollongong)
DTSTART:20200806T021000Z
DTEND:20200806T030000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/29
DESCRIPTION:Title: On Chen's Flow\nby Glen Wheeler (University of Wollongo
ng) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\
nIn this talk we give survey what is currently known for Chen’s flow\, a
nd discuss some very recent results. Chen’s flow is the biharmonic heat
flow for immersions\, where the velocity is given by the rough Laplacian o
f the mean curvature vector. This operator is known as Chen’s biharmonic
operator and the solutions to the elliptic problem are called biharmonic
submanifolds. The flow itself is very similar to the mean curvature flow (
this is essentially the content of Chen’s conjecture)\, however proving
this requires quite different strategies compared to the mean curvature fl
ow. We focus on results available in low dimensions – curves\, surfaces\
, and 4-manifolds. We provide characterisations of finite-time singulariti
es and global analysis. The case of curves is particularly challenging. He
re we identify a new shrinker (the Lemniscate of Bernoulli) and use some n
ew observations to push through the analysis. Some numerics is also presen
ted. The work reported on in the talk is in collaboration with Yann Bernar
d\, Matthew Cooper\, and Valentina-Mira Wheeler.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Senjo Shimizu (Kyoto University)
DTSTART:20200806T030000Z
DTEND:20200806T035000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/30
DESCRIPTION:Title: Maximal $L^1$-regularity for parabolic boundary value probl
ems with inhomogeneous data in the half-space\nby Senjo Shimizu (Kyoto
University) as part of Eighth Pacific Rim Conference in Mathematics\n\n\n
Abstract\nEnd-point maximal $L^1$-regularity for the parabolic initial bou
ndary\nvalue problem is considered. For a parabolic boundary value problem
\nwith inhomogeneous Dirichlet and Neumann data\, maximal $L^1$-regularity
\nfor the initial boundary value problem is established in time end-point\
ncase upon the Besov space $\\dot B_{p\,1}^0(\\mathbb{R}^n_+)$ with\n$1< p
< \\infty$.\nWe utilize a method of harmonic analysis\,\nin particular\, t
he almost orthogonal properties between the boundary\npotentials of the Di
richlet and the Neumann boundary data and the\nLittlewood-Paley dyadic dec
omposition of unity in the Besov and\nthe Lizorkin-Triebel spaces.\nThis i
s a joint work with Prof. Takayoshi Ogawa (Tohoku University).\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ailana Fraser (University of British Columbia)
DTSTART:20200806T002000Z
DTEND:20200806T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/31
DESCRIPTION:Title: Higher eigenvalue optimization\nby Ailana Fraser (Unive
rsity of British Columbia) as part of Eighth Pacific Rim Conference in Mat
hematics\n\n\nAbstract\nWhen we choose a metric on a manifold we determine
the spectrum of the Laplace operator. Thus an eigenvalue may be considere
d as a functional on the space of metrics. For example the first eigenvalu
e would be the fundamental vibrational frequency. In some cases the normal
ized eigenvalues are bounded independent of the metric. In such cases it m
akes sense to attempt to find critical points in the space of metrics. In
this talk we will discuss some results on higher eigenvalue optimization f
or surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Viaclovsky (UC Irvine)
DTSTART:20200806T011000Z
DTEND:20200806T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/32
DESCRIPTION:Title: Gravitational instantons and K3 surfaces\nby Jeff Viacl
ovsky (UC Irvine) as part of Eighth Pacific Rim Conference in Mathematics\
n\n\nAbstract\nThere are many interesting examples of complete non-compact
Ricci-flat metrics in dimension 4\, which are referred to as ALE\, ALF\,
ALG\, ALH gravitational instantons. In this talk\, I will describe some ex
amples of these geometries\, and other types called ALG$^*$ and ALH$^*$. A
ll of the above types of gravitational instantons arise as bubbles for seq
uences of Ricci-flat metrics on K3 surfaces\, and are therefore important
for understanding the behavior of Calabi-Yau metrics near the boundary of
the moduli space. I will describe some general aspects of this type of deg
eneration\, and some recent work on degenerations of Ricci-flat metrics on
elliptic K3 surfaces in which case ALG and ALG$^*$ bubbles can arise.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsuyoshi Kato (Kyoto University)
DTSTART:20200806T021000Z
DTEND:20200806T030000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/33
DESCRIPTION:Title: $L^2$ harmonic theory and Seiberg-Witten Bauer-Furuta theor
y on non-compact complete Riemannian 4-manifolds\nby Tsuyoshi Kato (Ky
oto University) as part of Eighth Pacific Rim Conference in Mathematics\n\
n\nAbstract\nI will talk on some fusion of a topic on Singer conjecture in
$L^2$ harmonic theory with Seiberg-Witten Bauer-Furuta theory on non-comp
act complete Riemannian 4-manifolds. We explain their analytic settings\,
certain results and questions.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Bamler (plenary) (UC Berkeley)
DTSTART:20200806T230000Z
DTEND:20200807T001000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/34
DESCRIPTION:Title: Uniqueness of Weak Solutions to the Ricci Flow and Topologi
cal Applications\nby Richard Bamler (plenary) (UC Berkeley) as part of
Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nIn this talk
I will survey recent work with Kleiner in which we verify two topological
conjectures using Ricci flow. First\, we classify the diffeomorphism group
of every 3-dimensional spherical space form up to homotopy. This proves t
he Generalized Smale Conjecture and gives an alternative proof of the Smal
e Conjecture\, which was originally due to Hatcher. Second\, we show that
the space of metrics with positive scalar curvature on every 3-manifold is
either contractible or empty. This completes work initiated by Marques.\n
\nOur proof is based on a new uniqueness theorem for singular Ricci flows\
, which I have previously obtained with Kleiner. Singular Ricci flows were
inspired by Perelman’s proof of the Poincaré and Geometrization Conjec
tures\, which relied on a flow in which singularities were removed by a ce
rtain surgery construction. Since this surgery construction depended on va
rious auxiliary parameters\, the resulting flow was not uniquely determine
d by its initial data. Perelman therefore conjectured that there must be a
canonical\, weak Ricci flow that automatically "flows through its singula
rities" at an infinitesimal scale. Our work on the uniqueness of singular
Ricci flows gives an affirmative answer to Perelman's conjecture and allow
s the study of continuous families of singular Ricci flows leading to the
topological applications mentioned above. More details and historical back
ground will be given in the talk.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shinichiroh Matsuo (Nagoya University)
DTSTART:20200807T011000Z
DTEND:20200807T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/36
DESCRIPTION:Title: The Atiyah-Patodi-Singer index and domain-wall fermion Dira
c operators\nby Shinichiroh Matsuo (Nagoya University) as part of Eigh
th Pacific Rim Conference in Mathematics\n\n\nAbstract\nWe introduce a mat
hematician-friendly formulation of the physicist-friendly derivation of th
e Atiyah-Patodi-Singer index.\n\nIn a previous work\, motivated by the stu
dy of lattice gauge theory\, we derived a formula expressing the Atiyah-Pa
todi-Singer index in terms of the eta invariant of "domain-wall fermion Di
rac operators" when the base manifold is a flat 4-dimensional torus. Now w
e generalise this formula to any even dimensional closed Riemannian manifo
lds\, and prove it mathematically rigorously. Our proof uses a Witten loca
lisation argument combined with a devised embedding into a cylinder of one
dimension higher. Our viewpoint sheds some new light on the interplay amo
ng the Atiyah-Patodi-Singer boundary condition\, domain-wall fermions\, an
d edge modes.\n\nThis talk is based on a joint work with H. Fukaya\, M. Fu
ruta\, T. Onogi\, S. Yamaguchi\, and M. Yamashita: arXiv:1910.01987.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Cristofaro-Gardiner (UC Santa Cruz)
DTSTART:20200806T150000Z
DTEND:20200806T155000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/37
DESCRIPTION:Title: The simplicity conjecture\nby Dan Cristofaro-Gardiner (
UC Santa Cruz) as part of Eighth Pacific Rim Conference in Mathematics\n\n
\nAbstract\nIn the 60s and 70s\, there was a flurry of activity concerning
the question of whether or not various subgroups of homeomorphism groups
of manifolds are simple\, with beautiful contributions by Fathi\, Kirby\,
Mather\, Thurston\, and many others. A funnily stubborn case that remaine
d open was the case of area-preserving homeomorphisms of surfaces. For ex
ample\, for balls of dimension at least 3\, the relevant group was shown t
o be simple by work of Fathi in 1980\; but\, the answer in the two-dimens
ional case\, asked in the 70s\, was not known. I will explain recent join
t work proving that the group of compactly supported area preserving homeo
morphisms of the two-disc is in fact not a simple group\; this answers the
"Simplicity Conjecture" in the affirmative. Our proof uses new spectral i
nvariants\, defined via periodic Floer homology\, that I will introduce: t
hese recover the Calabi invariant of monotone twists.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ko Honda (UCLA)
DTSTART:20200806T160000Z
DTEND:20200806T165000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/38
DESCRIPTION:Title: Convex hypersurface theory in higher-dimensional contact to
pology\nby Ko Honda (UCLA) as part of Eighth Pacific Rim Conference in
Mathematics\n\n\nAbstract\nConvex surface theory and bypasses are extreme
ly powerful tools for analyzing contact 3-manifolds. In particular they ha
ve been successfully applied to many classification problems. After briefl
y reviewing convex surface theory in dimension three\, we explain how to g
eneralize many of their properties to higher dimensions. This is joint wor
k with Yang Huang.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleny Ionel (Stanford University)
DTSTART:20200806T170000Z
DTEND:20200806T175000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/39
DESCRIPTION:Title: Thin compactifications and Relative Fundamental Classes
\nby Eleny Ionel (Stanford University) as part of Eighth Pacific Rim Confe
rence in Mathematics\n\n\nAbstract\nFamilies of moduli spaces in symplecti
c Gromov-Witten theory and gauge theory are often manifolds that have "thi
n" compactifications\, in the sense that the boundary of the generic fiber
has codimension at least two. In this talk we discuss a notion of a relat
ive fundamental class for such thinly compactified families. It associates
to each fiber\, regardless whether it is regular or not\, an element in i
ts Cech homology in a way that is consistent along paths. The invariants d
efined by relative fundamental classes agree with those defined by pseudo-
cycles\, and the relative fundamental class is equal to the virtual fundam
ental class defined by Pardon via implicit atlases in all cases when both
are defined. We give some examples of this construction\, discuss some of
its properties\, and its benefits. This talk is based on joint work with T
om Parker.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Eliashberg (plenary) (Stanford University)
DTSTART:20200806T180000Z
DTEND:20200806T191000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/40
DESCRIPTION:Title: The program of arborealization\nby Yakov Eliashberg (pl
enary) (Stanford University) as part of Eighth Pacific Rim Conference in M
athematics\n\n\nAbstract\nWeinstein symplectic manifolds is one of the bas
ic objects in symplectic topology\, similar to Stein complex manifolds in
the high-dimensional complex analysis. The arborealization program initiat
ed by David Nadler aims to describe Weinstein manifolds as cotangent bundl
es of\ncomplexes\, called arboreal spaces\, which are more general than sm
ooth manifolds\, and yet have simple standard local chart description. Thi
s allows to state symplectic topological questions about Weinstein manifol
ds as problems in differential topology of arboreal spaces. In the talk I'
ll describe the program and its current status.\nThis is a joint work with
Daniel Alvarez-Gavela and David Nadler.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hector Pasten (Pontificia Universidad Catolica de Chile)
DTSTART:20200806T002000Z
DTEND:20200806T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/41
DESCRIPTION:Title: Hilbert's tenth problem for rings of integers of certain nu
mber fields of degree six\nby Hector Pasten (Pontificia Universidad Ca
tolica de Chile) as part of Eighth Pacific Rim Conference in Mathematics\n
\n\nAbstract\nHilbert's tenth problem asked for an algorithm to decide sol
vability of Diophantine equations over the integers. The work of Davis\, P
utnam\, Robinson\, and Matijasevich showed that the requested algorithm do
es not exist. It is conjectured that the natural extension of the problem
to the ring of integers of every number field also has a negative solution
\, but the problem remains open in general. I'll sketch a proof of this co
njecture in certain cases of degree six\, by a new method based on Iwasawa
theory and Heegner points. This is joint work with Natalia Garcia-Fritz.\
n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoichi Mieda (University of Tokyo)
DTSTART:20200806T011000Z
DTEND:20200806T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/42
DESCRIPTION:Title: Local Saito-Kurokawa $A$-packets and $l$-adic cohomology of
Rapoport-Zink tower for $GSp(4)$\nby Yoichi Mieda (University of Toky
o) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\n
The Rapoport-Zink tower for $GSp(4)$ is a $p$-adic local counterpart of th
e Siegel threefold.\nIts l-adic cohomology is naturally equipped with acti
ons of three groups: the Weil group of $Q_p$\, $GSp_4(Q_p)$\, and an inner
form $J(Q_p)$ of $GSp_4(Q_p)$. As in the case of $GL(n)$\, it is expected
that the cohomology is strongly related with the local Langlands correspo
ndence. However\, the situation is much more complicated than $GL(n)$ case
\; for example\, a supercuspidal representation appears in the cohomology
outside the middle degree.\nIn this talk\, I will focus on a certain class
of non-tempered $A$-packets of $J(Q_p)$\, called the Saito-Kurokawa type.
\nUnder the assumption that the $A$-packet contains a supercuspidal repres
entation with trivial central character\,\nI will determine how the $A$-pa
cket contributes to the cohomology of the Rapoport-Zink tower for $GSp(4)$
.\nThis is a joint work with Tetsushi Ito.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheng-Chiang Tsai (Stanford University)
DTSTART:20200806T021000Z
DTEND:20200806T030000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/43
DESCRIPTION:Title: Uniform bounds of orbital integrals\nby Cheng-Chiang Ts
ai (Stanford University) as part of Eighth Pacific Rim Conference in Mathe
matics\n\n\nAbstract\nIn this talk\, we aim to give a survey about availab
le and expected results on uniform bounds of orbital integrals. Interestin
gly\, both the heuristic and method comes from the geometry of so-called a
ffine Springer fiber\, and in particular the expectation that this fibrati
on (between infinite-dimensional varieties) is "semi-small." We will put a
n emphasis on this connection.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen-Wei Li (Peking University)
DTSTART:20200806T030000Z
DTEND:20200806T035000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/44
DESCRIPTION:Title: Stable trace formula for metaplectic groups\nby Wen-Wei
Li (Peking University) as part of Eighth Pacific Rim Conference in Mathem
atics\n\n\nAbstract\nA theory of endoscopy for the metaplectic covering of
symplectic groups was proposed by the author almost 10 years ago\, and th
e elliptic part of the Arthur-Selberg trace formula has been stabilized si
nce then. I will give an overview of the stabilization of the full trace f
ormula for these coverings\, which is indispensable for global application
s. This is largely inspired by the prior works of Arthur and Moeglin-Walds
purger for linear reductive groups. This is a work in stable progress.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Eischen (University of Oregon)
DTSTART:20200807T002000Z
DTEND:20200807T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/45
DESCRIPTION:Title: $p$-adic aspects of $L$-functions and automorphic forms
\nby Ellen Eischen (University of Oregon) as part of Eighth Pacific Rim Co
nference in Mathematics\n\n\nAbstract\nI will discuss recent developments
for $p$-adic aspects of $L$-functions and automorphic forms\, especially i
n the setting of unitary groups. With a viewpoint that encompasses several
settings\,\nincluding modular forms (GL$_2$) and automorphic forms on hig
her rank (namely\, unitary and symplectic) groups\, I will\ngive a recipe
for constructing $p$-adic $L$-functions that relies strongly on the behavi
or of associated automorphic forms. Recent\ndevelopments will be put in th
e context of more familiar constructions of Serre\, Katz\, and Hida. I wil
l also describe some challenges unique to the higher rank setting\, as wel
l as recent attempts to overcome them.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Yamana (Osaka City University)
DTSTART:20200807T011000Z
DTEND:20200807T020000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/46
DESCRIPTION:Title: Base change and central values of triple product L-series\nby Shunsuke Yamana (Osaka City University) as part of Eighth Pacific R
im Conference in Mathematics\n\n\nAbstract\nLet $\\pi_i$ be an irreducible
cuspidal automorphic representation of $GL(2\,A)$ with central character
$\\omega_i$\, where $A$ is an adele ring of a number field. When the produ
ct $\\omega_1\\omega_2\\omega_3$ is the trivial character of $A^*$\, Atsus
hi Ichino proved a formula for the central value $L(1/2\,\\pi_1\\times\\pi
_2\\times\\pi_3)$ of the triple product $L$-series in terms of global tril
inear forms that appear in Jacquet's conjecture. I will extend this formul
a to the case when $\\omega_1\\omega_2\\omega_3$ is a quadratic character.
This is a joint work with Ming-Lun Hsieh.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takeshi Saito (plenary) (University of Tokyo)
DTSTART:20200807T021000Z
DTEND:20200807T032000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/47
DESCRIPTION:Title: Wild ramification and the cotangent bundle in mixed charact
eristic\nby Takeshi Saito (plenary) (University of Tokyo) as part of E
ighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nThe analogy bet
ween the wild ramification in arithmetic geometry and the irregular singul
arity of partial differential equations has attracted interests of mathema
ticians. For a $D$-module on a complex manifold\, its singular support is
defined on the cotangent bundle. An algebraic variant over a field of posi
tive characteristic is recently introduced by Beilinson. I will discuss an
analogue in mixed characteristic case.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (Institute for Advanced Study)
DTSTART:20200811T160000Z
DTEND:20200811T165000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/48
DESCRIPTION:Title: Incidence estimates with application to Fourier analysis\nby Hong Wang (Institute for Advanced Study) as part of Eighth Pacific R
im Conference in Mathematics\n\n\nAbstract\nWe are going to discuss some i
ncidence problems between points and tubes. Then we discuss how they are r
elated to problems in Fourier analysis. This includes joint work with Larr
y Guth\, Noam Solomon\, and with Ciprian Demeter\, L. Guth.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polona Durcik (Chapman University)
DTSTART:20200811T170000Z
DTEND:20200811T175000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/49
DESCRIPTION:Title: Singular integrals and patterns in the Euclidean space\
nby Polona Durcik (Chapman University) as part of Eighth Pacific Rim Confe
rence in Mathematics\n\n\nAbstract\nWe give an overview of some recent res
ults on point configurations in large subsets of the Euclidean space and d
iscuss their connection with multilinear singular integrals.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Christ (plenary) (UC Berkeley)
DTSTART:20200810T180000Z
DTEND:20200810T191000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/50
DESCRIPTION:Title: Oscillation and frustration in multilinear inequalities
\nby Michael Christ (plenary) (UC Berkeley) as part of Eighth Pacific Rim
Conference in Mathematics\n\n\nAbstract\nMultilinear functionals\, and ine
qualities governing them\, arise\nin various contexts in harmonic analysis
(in connection with\nFourier restriction)\, in partial differential equat
ions (nonlinear\ninteractions) and in additive combinatorics (existence of
certain patterns\nin sets of appropriately bounded density). This talk wi
ll focus\non an inequality that quantifies a weak convergence theorem\nof
Joly\, Métivier\, and Rauch (1995) concerning threefold products\,\nand o
n related inequalities for trilinear expressions involving\nhighly oscilla
tory factors.\nSublevel set inequalities\, which quantify\nthe impossibili
ty of exactly solving certain systems of linear functional\nequations (the
frustration of the title)\, are a central element of the analysis.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zane Li (Indiana University\, Bloomington)
DTSTART:20200810T160000Z
DTEND:20200810T165000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/51
DESCRIPTION:Title: Connections between decoupling and efficient congruencing\nby Zane Li (Indiana University\, Bloomington) as part of Eighth Pacifi
c Rim Conference in Mathematics\n\n\nAbstract\nThere are two different loo
king proofs of Vinogradov's Mean Value Theorem. One was Bourgain-Demeter-G
uth's proof via $l^2$ decoupling of the moment curve using harmonic analys
is methods and another was Wooley's proof via nested efficient congruencin
g using number theoretic methods. We will illustrate the main ideas of how
an efficient congruencing proof can be translated into a decoupling proof
in the case of $l^2$ decoupling for the parabola. We will also mention ho
w to use these ideas to give a new proof of $l^2$ decoupling for the momen
t curve. This talk is based off joint work with Shaoming Guo\, Po-Lam Yung
and Pavel Zorin-Kranich.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chun-Kit Lai (San Francisco State University)
DTSTART:20200810T170000Z
DTEND:20200810T175000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/52
DESCRIPTION:Title: Fourier bases and Fourier frames for singular measures\
nby Chun-Kit Lai (San Francisco State University) as part of Eighth Pacifi
c Rim Conference in Mathematics\n\n\nAbstract\nA measure is called a frame
-spectral measures if we can find a countable set of exponential functions
$\\{e^{2\\pi i \\lambda x}:\\lambda\\in \\Lambda\\}$ such that it forms a
frame in $L^2(\\mu)$. i.e.\n$$\n\\|f\\|_{\\mu}^2 \\asymp \\sum_{\\lambda\
\in \\Lambda} |\\langle f\,e_{\\lambda}\\rangle_{\\mu}|^2.\n$$\nFrames are
natural generalization of orthonormal basis. It is known that some singul
ar measures also admit a Fourier frames. However\, it is still largely unk
nown which singular measures are frame-spectral. In this talk\, we will ex
plore some of the recent progresses about this problem.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kornélia Héra (University of Chicago)
DTSTART:20200811T180000Z
DTEND:20200811T185000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/53
DESCRIPTION:Title: Hausdorff dimension of unions of affine subspaces and relat
ed problems\nby Kornélia Héra (University of Chicago) as part of Eig
hth Pacific Rim Conference in Mathematics\n\n\nAbstract\nWe consider the q
uestion of how large a union of affine subspaces must be depending on the
family of affine subspaces constituting the union. In the famous Kakeya pr
oblem one considers lines in every direction. Here the position of the lin
es or higher-dimensional affine subspaces is more general\, and accordingl
y the expected dimension bound is different. We prove that the union of an
y $s$-dimensional family of $k$-dimensional affine subspaces is at least $
[k + s/(k+1)]$-dimensional\, and is exactly $(k + s)$-dimensional if $s$ i
s at most 1.\nPartially based on joint work with Tamás Keleti and András
Máthé.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhi Jang (University of Southern California)
DTSTART:20200811T000000Z
DTEND:20200811T005000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/54
DESCRIPTION:Title: Dynamics of Newtonian stars\nby Juhi Jang (University o
f Southern California) as part of Eighth Pacific Rim Conference in Mathema
tics\n\n\nAbstract\nThe gravitational Euler-Poisson system is a classical
fluid model describing the motion of self-gravitating gaseous Newton stars
. We discuss some recent results on expanding\, collapsing and rotating st
ar solutions of the Euler-Poisson system.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volker Schlue (University of Melbourne)
DTSTART:20200811T010000Z
DTEND:20200811T015000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/55
DESCRIPTION:Title: Expanding black hole cosmologies\nby Volker Schlue (Uni
versity of Melbourne) as part of Eighth Pacific Rim Conference in Mathemat
ics\n\n\nAbstract\nIn general relativity\, the Kerr de Sitter family of so
lutions to Einstein’s equations with positive cosmological constant are
a model of a black hole in the expanding universe. In this talk\, I will f
ocus on the stability problem for the expanding region of the spacetime\,
which can be formulated as a characteristic initial value problem to the f
uture of the cosmological horizons of the black hole. Unlike in the stabil
ity of Kerr or Kerr de Sitter black hole exteriors\, the solution in the c
osmological region does not globally converge to an explicit family of sol
utions\, but displays genuine asymptotic degrees of freedom. I will descri
be my work on the decay of the conformal Weyl curvature in this setting\,
and discuss the global construction of optical functions in de Sitter\, wh
ich are relevant for my approach to this problem in double null gauge.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pin Yu (Tsinghua University)
DTSTART:20200811T020000Z
DTEND:20200811T025000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/56
DESCRIPTION:Title: On the rigidity from infinity for nonlinear Alfven waves\nby Pin Yu (Tsinghua University) as part of Eighth Pacific Rim Conferenc
e in Mathematics\n\n\nAbstract\nThe Alfven waves are fundamental wave phen
omena in magnetized plasmas and the dynamics of Alfven waves are governed
by a system of nonlinear partial differential equations called the MHD sys
tem. In the talk\, we will focus on the rigidity aspects of the scattering
problem for the MHD equations: We prove that the Alfven waves must vanish
if their scattering fields vanish at infinities. The proof is based on a
careful study of the null structure and a family of weighted energy estima
tes.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Trudinger (CANCELLED) (Australian National University)
DTSTART:20200827T000000Z
DTEND:20200827T011000Z
DTSTAMP:20260404T094911Z
UID:pacificrim2020/57
DESCRIPTION:Title: Generated Jacobian Equations\; convexity\, geometric optics
and optimal transportation (CANCELLED)\nby Neil Trudinger (CANCELLED)
(Australian National University) as part of Eighth Pacific Rim Conference
in Mathematics\n\n\nAbstract\nGenerated Jacobian equations were originall
y introduced as an extension of Monge-Ampère type equations in optimal tr
ansportation to embrace near field geometric optics. In this talk we prese
nt some of the basic theory\, including the associated convexity theory of
generating functions and recent work on the resultant classical solvabil
ity of the associated boundary value problems.\n
LOCATION:https://stable.researchseminars.org/talk/pacificrim2020/57/
END:VEVENT
END:VCALENDAR