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BEGIN:VEVENT
SUMMARY:Guofang Wei (plenary) (UC Santa Barbara)
DTSTART:20200803T230000Z
DTEND:20200804T001000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/1
DESCRIPTION:Title: Fundamental gap estimate in the hyperbolic spaces\nby Guofang W
ei (plenary) (UC Santa Barbara) as part of Eighth Pacific Rim Conference i
n Mathematics\n\n\nAbstract\nIn their celebrated work\, B. Andrews and J.
Clutterbuck proved the fundamental gap conjecture the that difference of f
irst two eigenvalues of the Laplacian with Dirichlet boundary condition on
convex domain with diameter D in the Euclidean space is greater than or e
qual to $3\\pi^2/D^2$. In several joint works with X. Dai\, Z. He\, S. Set
o\, L. Wang (in various subsets)\, the estimate is generalized\, showing t
he same lower bound holds for convex domains in the unit sphere. In sharp
contrast\, in recent joint work with T. Bourni\, J. Clutterbuck\, A. Stanc
u\, X. Nguyen and V. Wheeler\, we prove that the product of the fundamenta
l gap with the square of the diameter can be arbitrarily small for convex
domains of any diameter in the hyperbolic spaces.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Sáez (Universidad Catolica de Chile)
DTSTART:20200804T002000Z
DTEND:20200804T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/2
DESCRIPTION:Title: Short-time existence for the network flow\nby Mariel Sáez (Uni
versidad Catolica de Chile) as part of Eighth Pacific Rim Conference in Ma
thematics\n\n\nAbstract\nThe network flow is a system of parabolic differe
ntial equations that describes the motion of a family of curves in which e
ach of them evolves under curve-shortening flow. This problem arises natur
ally in physical phenomena and its solutions present a rich variety of beh
aviors. \nThe goal of this talk is to describe some properties of this geo
metric flow and to discuss an alternative proof of short-time existence fo
r non-regular initial conditions. The methods of our proof are based on te
chniques of geometric microlocal analysis that have been used to understan
d parabolic problems on spaces with conic singularities. This is joint wor
k with Jorge Lira\, Rafe Mazzeo\, and Alessandra Pluda.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hojoo Lee (Jeonbuk National University)
DTSTART:20200804T011000Z
DTEND:20200804T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/3
DESCRIPTION:Title: Minimal surfaces and flat structures\nby Hojoo Lee (Jeonbuk Nat
ional University) as part of Eighth Pacific Rim Conference in Mathematics\
n\n\nAbstract\nWe will introduce the flat structures on minimal surfaces i
ntroduced by Chern and Ricci\, respectively.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Ebenfelt (UC San Diego)
DTSTART:20200805T002000Z
DTEND:20200805T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/4
DESCRIPTION:Title: Deformations and embeddings of compact strictly pseudoconvex CR 3-m
anifolds\nby Peter Ebenfelt (UC San Diego) as part of Eighth Pacific R
im Conference in Mathematics\n\n\nAbstract\nA celebrated result of Boutet
de Monvel is that a compact strictly pseudoconvex CR manifold $M$ of dimen
sion $2n+1$ is embeddable as a CR submanifold in $\\mathbb{C}^N$ \, for so
me (potentially large) $N$\, provided $n\\geq 2$. The situation for three-
dimensional $M$ ($n=1$) is more subtle: "Most" such\, even real-analytic
ones\, are not embeddable in this way. Much work has been done over the ye
ars to characterize and describe the space of embeddable structures. In th
is talk\, we shall consider the embeddability of families of deformations
of a given embedded CR $3$-manifold\, and the structure of the space of em
beddable CR structures on $S^3$. We discuss a modified version of the Chen
g-Lee slice theorem in which the embeddable deformations in the slice can
be explicitly characterized (in terms of spherical harmonics). We also int
roduce a canonical family of embeddable deformations and corresponding emb
eddings starting with any infinitesimally embeddable deformation of the un
it sphere in $\\mathbb{C}^2$. The talk is based on joint work with Sean Cu
rry.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedram Hekmati (University of Auckland)
DTSTART:20200805T011000Z
DTEND:20200805T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/5
DESCRIPTION:Title: Holomorphic bundles on foliations\nby Pedram Hekmati (Universit
y of Auckland) as part of Eighth Pacific Rim Conference in Mathematics\n\n
\nAbstract\nIt is well-known that the existence of Hermitian-Einstein metr
ics on holomorphic bundles is intimately tied to the notion of stability.
In this talk I will discuss how this correspondence extends to the setting
of transverse holomorphic bundles on taut Riemannian foliations. I will f
urther elucidate the relation to higher dimensional instantons on Sasakian
manifolds and mention some applications.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiko Matsumoto (Osaka University)
DTSTART:20200805T021000Z
DTEND:20200805T030000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/6
DESCRIPTION:Title: Asymptotically complex hyperbolic Einstein spaces and CR geometry\nby Yoshihiko Matsumoto (Osaka University) as part of Eighth Pacific Ri
m Conference in Mathematics\n\n\nAbstract\nThe correspondence between Poin
caré-Einstein spaces and conformal \ngeometry of the boundaries at infini
ty is actively pursued. Our subject is its lesser-known analog\, and yet a
lso classical because it generalizes the study of invariant metrics on bou
nded strictly pseudoconvex domains. I will discuss the existence matter an
d construction of CR invariants through asymptotically complex hyperbolic
\nEinstein metrics.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiping Zhang (Chern Institute of Mathematics)
DTSTART:20200805T030000Z
DTEND:20200805T035000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/7
DESCRIPTION:Title: Positive scalar curvature on foliations\nby Weiping Zhang (Cher
n Institute of Mathematics) as part of Eighth Pacific Rim Conference in Ma
thematics\n\n\nAbstract\nA famous theorem of Lichnerowicz states that if a
closed spin manifold carries a Riemannian metric of positive scalar curva
ture\, then the $\\widehat{A}$-genus of the manifold vanishes. We will des
cribe various generalizations of this result\, as well as some other class
ical results concerning positive scalar curvature\, to the case of foliat
ions. A typical example is Connes' theorem which states that if the $\\wid
ehat{A}$-genus of a compact foliated manifold with spin leaves does not va
nish\, then there is no metric with positive scalar curvature along the le
aves.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoichiro Mori (University of Pennsylvania)
DTSTART:20200804T002000Z
DTEND:20200804T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/8
DESCRIPTION:Title: Stability of planar fronts of the bidomain Allen-Cahn equation\
nby Yoichiro Mori (University of Pennsylvania) as part of Eighth Pacific R
im Conference in Mathematics\n\n\nAbstract\nThe bidomain model is the stan
dard model describing electrical activity of the heart. We discuss the sta
bility of planar front solutions of the bidomain equation with a bistable
nonlinearity (the bidomain Allen‐Cahn equation) in two spatial dimension
s. In the bidomain Allen‐Cahn equation a Fourier multiplier operator who
se symbol is a positive homogeneous rational function of degree two (the b
idomain operator) takes the place of the Laplacian in the classical Allen
‐Cahn equation. Stability of the planar front may depend on the directio
n of propagation given the anisotropic nature of the bidomain operator. We
establish various criteria for stability and instability of the planar fr
ont in each direction of propagation. Our analysis reveals that planar fro
nts can be unstable in the bidomain Allen‐Cahn equation in striking cont
rast to the classical or anisotropic Allen‐Cahn equations. We identify t
wo types of instabilities\, one with respect to long‐wavelength perturba
tions\, the other with respect to medium‐wavelength perturbations. Inter
estingly\, whether the front is stable or unstable under long‐wavelength
perturbations does not depend on the bistable nonlinearity and is fully d
etermined by the convexity properties of a suitably defined Frank diagram.
On the other hand\, stability under intermediate‐wavelength perturbatio
ns does depend on the choice of bistable nonlinearity. Intermediate‐wave
length instabilities can occur even when the Frank diagram is convex\, so
long as the bidomain operator does not reduce to the Laplacian. We shall a
lso give a remarkable example in which the planar front is unstable in all
directions. Time permitting\, I will also discuss properties of the bidom
ain FitzHugh Nagumo equations. This is joint work with Hiroshi Matano\, Mi
tsunori Nara and Koya Sakakibara.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong-Jung Kim (KAIST)
DTSTART:20200804T011000Z
DTEND:20200804T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/9
DESCRIPTION:Title: Can you tell how effective a COVID-19 prevention scheme is at eleme
ntary schools?\nby Yong-Jung Kim (KAIST) as part of Eighth Pacific Rim
Conference in Mathematics\n\n\nAbstract\nWe focus on the fact that the ba
sic reproduction number $R_0$ is decided by the pattern of social contacts
. We claim that finding a social contact pattern which is affordable and o
f small enough $R_0$ is the key to preventing COVID-19 from spreading. Rec
ently\, the Ministry of Education of the Republic of Korea has issued new
school operating policies due to COVID-19 pandemic. Schools have developed
new ways to run schools to comply with the new policies\, which resulted
in new contact patterns in schools. We compute $R_0$ corresponding to such
patterns and conclude that reducing the class size and the inter-class co
ntact rate is the best way to lower $R_0$ in elementary and secondary scho
ols.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihong Du (plenary) (University of New England)
DTSTART:20200804T021000Z
DTEND:20200804T032000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/10
DESCRIPTION:Title: Propagation\, diffusion and free boundaries\nby Yihong Du (ple
nary) (University of New England) as part of Eighth Pacific Rim Conference
in Mathematics\n\n\nAbstract\nIn this talk I will discuss some of the mat
hematical theories on nonlinear partial differential equations motivated b
y the desire of providing better models for various propagation phenomena.
The talk will start with classical works of Fisher\, Kolmogorov-Petrovski
i-Piskunov and Aronson-Weinberger\, and then focus on recent results on fr
ee boundary models with local as well as nonlocal diffusion\, which are va
riations of the models in the classical works.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Ward (University of British Columbia)
DTSTART:20200805T011000Z
DTEND:20200805T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/11
DESCRIPTION:Title: Synchrony and oscillatory dynamics for a 2-D PDE-ODE model of diff
usion-sensing with small signaling compartments\nby Michael Ward (Univ
ersity of British Columbia) as part of Eighth Pacific Rim Conference in Ma
thematics\n\n\nAbstract\nWe analyze a class of cell-bulk coupled PDE-ODE m
odels\, motivated by quorum and diffusion sensing phenomena in microbial s
ystems\, that characterize communication between localized spatially segre
gated dynamically active signaling compartments or "cells'' that have a pe
rmeable boundary. In this model\, the cells are disks of a common radius $
\\varepsilon \\ll 1$ and they are spatially coupled through a passive extr
acellular bulk diffusion field with diffusivity $D$ in a bounded 2-D domai
n. Each cell secretes a signaling chemical into the bulk region at a const
ant rate and receives a feedback of the bulk chemical from the entire coll
ection of cells. This global feedback\, which activates signaling pathways
within the cells\, modifies the intracellular dynamics according to the e
xternal environment. The cell secretion and global feedback are regulated
by permeability parameters across the cell membrane. For arbitrary reacti
on-kinetics within each cell\, the method of matched asymptotic expansions
is used in the limit $\\varepsilon\\ll 1$ of small cell radius to constru
ct steady-state solutions of the PDE-ODE model\, and to derive a globally
coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the
linear stability properties of the steady-states. The analysis and computa
tion of the nullspace of the GCEP as parameters are varied is central to t
he linear stability analysis. In the limit of large bulk diffusivity $D={D
_0/\\nu}\\gg 1$\, where $\\nu\\equiv {-1/\\log\\varepsilon}$\, an asymptot
ic analysis of the PDE-ODE model leads to a limiting ODE system for the sp
atial average of the concentration in the bulk region that is coupled to t
he intracellular dynamics within the cells. Results from the linear stabi
lity theory and ODE dynamics are illustrated for Sel'kov reaction-kinetics
\, where the kinetic parameters are chosen so that each cell is quiescent
when uncoupled from the bulk medium. For various specific spatial configur
ations of cells\, the linear stability theory is used to construct phase d
iagrams in parameter space characterizing where a switch-like emergence of
intracellular oscillations can occur through a Hopf bifurcation. The effe
ct of the membrane permeability parameters\, the reaction-kinetic paramete
rs\, the bulk diffusivity\, and the spatial configuration of cells on both
the emergence and synchronization of the oscillatory intracellular dynami
cs\, as mediated by the bulk diffusion field\, is analyzed in detail. The
linear stability theory is validated from full numerical simulations of th
e PDE-ODE system\, and from the reduced ODE model when $D$ is large.\nJoin
t with Sarafa Iyaniwura (UBC)\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihisa Morita (Ryukoku University)
DTSTART:20200805T020000Z
DTEND:20200805T025000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/12
DESCRIPTION:Title: Segregation pattern in a mathematical model of cell polarity\n
by Yoshihisa Morita (Ryukoku University) as part of Eighth Pacific Rim Con
ference in Mathematics\n\n\nAbstract\nAsymmetric cell division is one of t
he fundamental processes to create cell diversity in the early stage of em
bryonic development. We deal with polarity models describing the PAR polar
ity formation in the asymmetric cell division of a C. elegans embryo. We e
mployee a bulk-surface diffusion model together with a simpler model to ex
hibit the long time behavior of the polarity formation of a bulk-surface c
ell. Moreover\, we rigorously prove the existence of stable nonconstant so
lutions of the simpler equations in a parameter regime and explore how the
boundary position of polarity domain is determined. This talk is owing to
a recent joint work with S. Seirin-Lee (Hiroshima University).\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiun-Chuan Chen (National Taiwan University)
DTSTART:20200805T030000Z
DTEND:20200805T035000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/13
DESCRIPTION:Title: Travelling wave solutions of the 3-species Lotka-Volterra competit
ion system with diffusion\nby Chiun-Chuan Chen (National Taiwan Univer
sity) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstrac
t\nOne of the central issues in mathematical ecology is to understand how
coexistence of many species is possible. This talk is concerned with the p
roblem of whether competition among species helps to sustain their coexist
ence. We first focus on the existence of a special type of non-monotone tr
aveling waves of the 3-species system and introduce some related results i
n recent years. Then we show that this type of waves provides new clues ab
out the problem of coexistence.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ofer Zeitouni (plenary) (Weizmann Institute of Science)
DTSTART:20200804T150000Z
DTEND:20200804T161000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/14
DESCRIPTION:Title: Stability and instability of spectrum for small random perturbatio
ns of structured non-normal matrices\nby Ofer Zeitouni (plenary) (Weiz
mann Institute of Science) as part of Eighth Pacific Rim Conference in Mat
hematics\n\n\nAbstract\nWe discuss the spectrum of high dimensional non-no
rmal matrices under small noisy perturbations. That spectrum can be extrem
ely unstable\, as the maximal nilpotent matrix $J_N$ with $J_N(i\,j)=1$ if
f $j=i+1$ demonstrates. Numerical analysts studied worst case perturbatio
ns\, using the notion of pseudo-spectrum. Our focus is on finding the locu
s of most eigenvalues (limits of density of states)\, as well as studying
stray eigenvalues ("outliers")\, in the case where the unperturbed matrix
is either Toeplitz or twisted Toeplitz. I will describe the background\, s
how some fun and intriguing simulations\, and present some theorems and wo
rk in progress concerning eigenvectors. No background will be assumed. The
talk is based on joint works with Anirban Basak\, Elliot Paquette\, and M
artin Vogel.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Dembo (Stanford University)
DTSTART:20200804T162000Z
DTEND:20200804T171000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/15
DESCRIPTION:Title: Universality for diffusions interacting through a random matrix\nby Amir Dembo (Stanford University) as part of Eighth Pacific Rim Confe
rence in Mathematics\n\n\nAbstract\nConsider a system of $N$ stochastic di
fferential equations interacting through an $N$-dimensional\nmatrix $J$ of
independent random entries (starting at an initial state whose law is ind
ependent of $J$).\nWe show that the trajectories of a large class of obser
vables which are averaged over the\n$N$ coordinates of the solution\, are
universal. That is\, for a fixed time interval the limit of such observabl
es as $N$ grows\, essentially depends only on the first two moments of the
marginal\ndistributions of entries of $J$.\n\nConcrete settings for which
such universality holds include aging in\nthe spherical Sherrington-Kirkp
atrick spin-glass and Langevin dynamics\nfor a certain collection of Hopfi
eld networks.\n\nThis talk is based on joint works with Reza Gheissari\, a
nd with Eyal Lubetzky and Ofer Zeitouni.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Remenik (Universidad de Chile)
DTSTART:20200804T172000Z
DTEND:20200804T181000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/16
DESCRIPTION:Title: Non-intersecting Brownian motions with outliers\, KPZ fluctuations
and random matrices\nby Daniel Remenik (Universidad de Chile) as part
of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nA well kno
wn result implies that the rescaled maximal height of a system of $N$ non-
intersecting Brownian bridges starting and ending at the origin converges\
, as $N$ goes to infinity\, to the Tracy-Widom GOE random variable from ra
ndom 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 will pres
ent 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 determinant formu
la and in terms of Painlevé transcendents\; it is connected with the fluc
tuations of models in the KPZ universality class with a particular initial
condition\; and it is connected with two PDEs\, the KdV equation and an e
quation derived by Bloemendal and Virág for spiked random matrices. Based
on joint work with Karl Liechty and Gia Bao Nguyen.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sourav Chatterjee (Stanford University)
DTSTART:20200805T002000Z
DTEND:20200805T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/17
DESCRIPTION:Title: Mass gap implies quark confinement\nby Sourav Chatterjee (Stan
ford University) as part of Eighth Pacific Rim Conference in Mathematics\n
\n\nAbstract\nThe confinement of quarks is one of the enduring mysteries o
f modern physics. I will present a rigorous result that shows that if a pu
re lattice gauge theory at some given coupling strength has exponential de
cay of correlations under arbitrary boundary conditions\, and the gauge gr
oup is a compact connected matrix Lie group with a nontrivial center\, the
n the theory is confining. This gives mathematical justification for a lon
gstanding belief in physics about the mechanism behind confinement\, which
roughly says that confinement is the result of strong coupling behavior p
lus center symmetry. The proof is almost entirely based in probability the
ory\, making extensive use of the idea of coupling probability measures.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Sauermann (Stanford University)
DTSTART:20200805T012000Z
DTEND:20200805T021000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/18
DESCRIPTION:Title: On the extension complexity of random polytopes\nby Lisa Sauer
mann (Stanford University) as part of Eighth Pacific Rim Conference in Mat
hematics\n\n\nAbstract\nSometimes\, it is possible to represent a complica
ted polytope as a projection of a much simpler polytope. To quantify this
phenomenon\, the extension complexity of a polytope $P$ is defined to be t
he minimum number of facets in a (possibly higher-dimensional) polytope fr
om which $P$ can be obtained as a (linear) projection. In this talk\, we d
iscuss some results on the extension complexity of random polytopes. For a
fixed dimension $d$\, we consider random $d$-dimensional polytopes obtain
ed as the convex hull of independent random points either in the unit ball
ball or on the unit sphere. In both cases\, we prove that the extension c
omplexity is typically on the order of the square root of number of vertic
es of the polytope. Joint work with Matthew Kwan and Yufei Zhao.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Insuk Seo (Seoul National University)
DTSTART:20200805T022000Z
DTEND:20200805T031000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/19
DESCRIPTION:Title: Metastable interacting particle systems\nby Insuk Seo (Seoul N
ational University) as part of Eighth Pacific Rim Conference in Mathematic
s\n\n\nAbstract\nIn this talk\, we discuss interacting particles systems e
xhibiting a phenomenon known as the condensation of particles. For these s
ystems\, particles tend to be condensed at a site because of either sticky
or attracting interacting mechanism. A fundamental question for these sys
tems is to describe the behavior of the movement of the condensed site as
a suitable scaling limit. We introduce recent results regarding this probl
em for the zero-range process and the inclusion process. This talk is base
d on joint works with S. Kim\, C. Landim and D. Marcondes.\n
LOCATION:https://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:20260422T212859Z
UID:pacificrim2020/20
DESCRIPTION:Title: $G_{2}$-geometry and complex variables (NEW TIME)\nby Simon Do
naldson (plenary) (Stony Brook University and Imperial College\, London) a
s part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nThe
setting for this talk is the study of 7-dimensional manifolds with torsion
free $G_{2}$-structures. While these are not complex manifolds there are
many interactions with complex geometry and the talk will survey some of t
hese. Topics that will be discussed include "$G_{2}$-cobordisms" between C
alabi-Yau 3-folds\; Kovalev’s twisted connected sum construction which i
nvolves of Fano or semi-Fano 3-folds and the adiabatic limits of $G_{2}$-g
eometry on manifolds with $K3$-fibrations.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshiki Oshima (Osaka University)
DTSTART:20200805T002000Z
DTEND:20200805T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/21
DESCRIPTION:Title: Collapsing of Ricci-flat Kahler metrics and compactifications of m
oduli spaces\nby Yoshiki Oshima (Osaka University) as part of Eighth P
acific Rim Conference in Mathematics\n\n\nAbstract\nCertain locally Hermit
ian symmetric spaces parameterize complex algebraic varieties\, such as po
larized abelian varieties and K3 surfaces through periods.\nIn this talk\,
we will see that one of Satake compactifications of locally symmetric spa
ces\, which is different from the Baily-Borel compactification\, parameter
izes limits of canonical (Ricci-flat) metrics on abelian varieties or K3 s
urfaces. This in particular involves parameterization of "tropical" variet
ies by locally symmetric spaces and confirms a conjecture of Kontsevich-So
ibelman in the case of K3 surfaces.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mao Sheng (University of Science and Technology of China)
DTSTART:20200805T011000Z
DTEND:20200805T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/22
DESCRIPTION:Title: De Rham decomposition theorem with intersection condition\nby
Mao Sheng (University of Science and Technology of China) as part of Eight
h Pacific Rim Conference in Mathematics\n\n\nAbstract\nDeligne-Illusie pro
ved that the Frobenius pushforward of the de Rham complex is decomposable
in the derived category under suitable conditions. It is called the de Rha
m 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 character
istic\, Ogus-Vologodsky established the de Rham decomposition theorem with
coefficients\, that generalizes Deligne-Illusie's result in a far reachin
g way. In my talk\, I shall report a further generalization of Ogus-Vologo
dsky's decomposition theorem\, that takes care of an intersection conditio
n at infinity. This work was motivated by Gabber's purity theorem for perv
erse sheaves\, and Zucker\, Cattani-Kaplan-Schmid and Kashiwara-Kawai's wo
rks on intersection cohomologies of variations of Hodge structure. This is
a joint work with Zebao Zhang.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoyuki Hisamoto (Tokyo Metropolitan University)
DTSTART:20200806T030000Z
DTEND:20200806T035000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/23
DESCRIPTION:Title: Optimal lower bound of the Calabi type functionals\nby Tomoyuk
i Hisamoto (Tokyo Metropolitan University) as part of Eighth Pacific Rim C
onference in Mathematics\n\n\nAbstract\nCalabi functional is defined as th
e $L^2$ norm of the scalar curvature and conjecturally its lower bound is
achieved by a sequence of the normalized Donaldson-Futaki invariants. It i
s naturally related to the limit behavior of the Calabi flow. \nFor the Fa
no manifolds the problem can be reformulated in terms of the Ricci curvatu
re potential. We prove in this situation that the lower bound of the Ricci
-Calabi functional is achieved by a sequence of the normalized D-invariant
s\, taking the multiplier ideal sheaves of the appropriate geometric flow.
\nThe same argument can be applied to the Dervan-Székelyhidi's lower bou
nd of the entropy functional.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaokui Yang (Chinese Academy of Sciences)
DTSTART:20200806T040000Z
DTEND:20200806T045000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/24
DESCRIPTION:Title: RC-positivity and geometry of complex manifolds\nby Xiaokui Ya
ng (Chinese Academy of Sciences) as part of Eighth Pacific Rim Conference
in Mathematics\n\n\nAbstract\nIn this presentation\, we discuss some recen
t progress on the geometry of compact manifolds with RC-positive tangent b
undles\, including an affirmative answer to an open problem of S.T. Yau on
rational connectedness of compact Kahler manifolds with positive holomorp
hic sectional curvature\, and new Liouville type theorems for holomorphic
maps and harmonic maps. Several open problems related to the theory of RC-
positivity will also be discussed.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radu Laza (Stony Brook University)
DTSTART:20200806T050000Z
DTEND:20200806T055000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/25
DESCRIPTION:Title: Remarks on degenerations of Hyperkaehler and Calabi-Yau manifolds<
/a>\nby Radu Laza (Stony Brook University) as part of Eighth Pacific Rim C
onference in Mathematics\n\n\nAbstract\nDue to Kulikov theorem and its app
lications\, one has a good understanding of the degenerations of K3 surfac
es and consequently some understanding of compactifications for moduli of
K3 surfaces. In this talk\, I will discuss some aspects of higher dimensio
nal analogues of these results. Most of the results will concern Hyperkaeh
ler manifolds\, where the picture is quite similar to that for K3 surfaces
. I will close with some ideas on how to deal with the more subtle Calabi-
Yau case.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Sideris (UC Santa Barbara)
DTSTART:20200806T002000Z
DTEND:20200806T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/27
DESCRIPTION:Title: The affine motion of 2d incompressible ideal fluids surrounded by
vacuum\nby Thomas Sideris (UC Santa Barbara) as part of Eighth Pacific
Rim Conference in Mathematics\n\n\nAbstract\nThe equations of affine moti
on for a 2D incompressible ideal fluid surrounded\nby vacuum reduce to a g
lobally solvable Hamiltonian system of ordinary differential\nequations fo
r the deformation gradient constrained to $SL(2\,R)$. The evolution of the
fluid domain is described by a family of ellipses of fixed area. We shall
provide a complete description of the dynamic behavior of these domains f
or perfect fluids and for magnetically conducting fluids. For perfect flui
ds\, the displacement generically becomes unbounded as time tends to infin
ity\, and for magnetically conducting fluids\, solutions remain bounded an
d are generically quasi-periodic.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baoxiang Wang (Peking University)
DTSTART:20200806T011000Z
DTEND:20200806T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/28
DESCRIPTION:Title: Navier-Stokes Equation in Super-Critical Spaces $E^s_{p\,q}$\n
by Baoxiang Wang (Peking University) as part of Eighth Pacific Rim Confere
nce in Mathematics\n\n\nAbstract\nIn this paper we develop a new way to st
udy the global existence and uniqueness for the Navier-Stokes equation (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 wh
ich the norms are defined by\n$$\n\\|f\\|_{E^s_{p\,q}} = \\left(\\sum_{k\\
in \\mathbb{Z}^d} 2^{s|k|q}\\|\\mathscr{F}^{-1} \\chi_{k+[0\,1]^d}\\mathsc
r{F} f\\|^q_p \\right)^{1/q}.\n$$\nThe space $E^s_{p\,q}$ is a rather roug
h function space and cannot be treated as a subspace of tempered distribut
ions. For example\, we have the embedding $H^{\\sigma}\\subset E^s_{2\,1}$
for any $\\sigma<0$ and $s<0$. It is known that $H^\\sigma$ ($\\sigma< d/
2-1$) 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 global mi
ld solution if the initial data belong to $E^s_{2\,1}$ ($s<0$) and their F
ourier transforms are supported in $ \\mathbb{R}^d_I:= \\{\\xi\\in \\mathb
b{R}^d: \\ \\xi_i \\geq 0\, \\\, i=1\,...\,d\\}$. Similar results hold for
the initial data in $E^s_{r\,1}$ with $2< r \\leq d$. Our results imply t
hat NS has a unique global solution if the initial value $u_0$ is in $L^2$
with ${\\rm supp} \\\, \\widehat{u}_0 \\\, \\subset \\mathbb{R}^d_I$. Thi
s is a joint work with Professors H. G. Feichtinger\, K. Gröchenig and Dr
. Kuijie Li.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Glen Wheeler (University of Wollongong)
DTSTART:20200806T021000Z
DTEND:20200806T030000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/29
DESCRIPTION:Title: On Chen's Flow\nby Glen Wheeler (University of Wollongong) as
part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nIn thi
s talk we give survey what is currently known for Chen’s flow\, and disc
uss some very recent results. Chen’s flow is the biharmonic heat flow fo
r immersions\, where the velocity is given by the rough Laplacian of the m
ean curvature vector. This operator is known as Chen’s biharmonic operat
or and the solutions to the elliptic problem are called biharmonic submani
folds. The flow itself is very similar to the mean curvature flow (this is
essentially the content of Chen’s conjecture)\, however proving this re
quires quite different strategies compared to the mean curvature flow. We
focus on results available in low dimensions – curves\, surfaces\, and 4
-manifolds. We provide characterisations of finite-time singularities and
global analysis. The case of curves is particularly challenging. Here we i
dentify a new shrinker (the Lemniscate of Bernoulli) and use some new obse
rvations to push through the analysis. Some numerics is also presented. Th
e work reported on in the talk is in collaboration with Yann Bernard\, Mat
thew Cooper\, and Valentina-Mira Wheeler.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Senjo Shimizu (Kyoto University)
DTSTART:20200806T030000Z
DTEND:20200806T035000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/30
DESCRIPTION:Title: Maximal $L^1$-regularity for parabolic boundary value problems wit
h inhomogeneous data in the half-space\nby Senjo Shimizu (Kyoto Univer
sity) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstrac
t\nEnd-point maximal $L^1$-regularity for the parabolic initial boundary\n
value problem is considered. For a parabolic boundary value problem\nwith
inhomogeneous Dirichlet and Neumann data\, maximal $L^1$-regularity\nfor t
he initial boundary value problem is established in time end-point\ncase u
pon the Besov space $\\dot B_{p\,1}^0(\\mathbb{R}^n_+)$ with\n$1< p< \\inf
ty$.\nWe utilize a method of harmonic analysis\,\nin particular\, the almo
st orthogonal properties between the boundary\npotentials of the Dirichlet
and the Neumann boundary data and the\nLittlewood-Paley dyadic decomposit
ion of unity in the Besov and\nthe Lizorkin-Triebel spaces.\nThis is a joi
nt work with Prof. Takayoshi Ogawa (Tohoku University).\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ailana Fraser (University of British Columbia)
DTSTART:20200806T002000Z
DTEND:20200806T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/31
DESCRIPTION:Title: Higher eigenvalue optimization\nby Ailana Fraser (University o
f British Columbia) as part of Eighth Pacific Rim Conference in Mathematic
s\n\n\nAbstract\nWhen we choose a metric on a manifold we determine the sp
ectrum of the Laplace operator. Thus an eigenvalue may be considered as a
functional on the space of metrics. For example the first eigenvalue would
be the fundamental vibrational frequency. In some cases the normalized ei
genvalues are bounded independent of the metric. In such cases it makes se
nse to attempt to find critical points in the space of metrics. In this ta
lk we will discuss some results on higher eigenvalue optimization for surf
aces.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Viaclovsky (UC Irvine)
DTSTART:20200806T011000Z
DTEND:20200806T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/32
DESCRIPTION:Title: Gravitational instantons and K3 surfaces\nby Jeff Viaclovsky (
UC Irvine) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAb
stract\nThere are many interesting examples of complete non-compact Ricci-
flat metrics in dimension 4\, which are referred to as ALE\, ALF\, ALG\, A
LH gravitational instantons. In this talk\, I will describe some examples
of these geometries\, and other types called ALG$^*$ and ALH$^*$. All of t
he above types of gravitational instantons arise as bubbles for sequences
of Ricci-flat metrics on K3 surfaces\, and are therefore important for und
erstanding the behavior of Calabi-Yau metrics near the boundary of the mod
uli space. I will describe some general aspects of this type of degenerati
on\, and some recent work on degenerations of Ricci-flat metrics on ellipt
ic K3 surfaces in which case ALG and ALG$^*$ bubbles can arise.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsuyoshi Kato (Kyoto University)
DTSTART:20200806T021000Z
DTEND:20200806T030000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/33
DESCRIPTION:Title: $L^2$ harmonic theory and Seiberg-Witten Bauer-Furuta theory on no
n-compact complete Riemannian 4-manifolds\nby Tsuyoshi Kato (Kyoto Uni
versity) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbst
ract\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-compact com
plete Riemannian 4-manifolds. We explain their analytic settings\, certain
results and questions.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Bamler (plenary) (UC Berkeley)
DTSTART:20200806T230000Z
DTEND:20200807T001000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/34
DESCRIPTION:Title: Uniqueness of Weak Solutions to the Ricci Flow and Topological App
lications\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 conject
ures using Ricci flow. First\, we classify the diffeomorphism group of eve
ry 3-dimensional spherical space form up to homotopy. This proves the Gene
ralized Smale Conjecture and gives an alternative proof of the Smale Conje
cture\, which was originally due to Hatcher. Second\, we show that the spa
ce of metrics with positive scalar curvature on every 3-manifold is either
contractible or empty. This completes work initiated by Marques.\n\nOur p
roof is based on a new uniqueness theorem for singular Ricci flows\, which
I have previously obtained with Kleiner. Singular Ricci flows were inspir
ed by Perelman’s proof of the Poincaré and Geometrization Conjectures\,
which relied on a flow in which singularities were removed by a certain s
urgery construction. Since this surgery construction depended on various a
uxiliary parameters\, the resulting flow was not uniquely determined by it
s initial data. Perelman therefore conjectured that there must be a canoni
cal\, weak Ricci flow that automatically "flows through its singularities"
at an infinitesimal scale. Our work on the uniqueness of singular Ricci f
lows gives an affirmative answer to Perelman's conjecture and allows the s
tudy of continuous families of singular Ricci flows leading to the topolog
ical applications mentioned above. More details and historical background
will be given in the talk.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shinichiroh Matsuo (Nagoya University)
DTSTART:20200807T011000Z
DTEND:20200807T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/36
DESCRIPTION:Title: The Atiyah-Patodi-Singer index and domain-wall fermion Dirac opera
tors\nby Shinichiroh Matsuo (Nagoya University) as part of Eighth Paci
fic Rim Conference in Mathematics\n\n\nAbstract\nWe introduce a mathematic
ian-friendly formulation of the physicist-friendly derivation of the Atiya
h-Patodi-Singer index.\n\nIn a previous work\, motivated by the study of l
attice gauge theory\, we derived a formula expressing the Atiyah-Patodi-Si
nger index in terms of the eta invariant of "domain-wall fermion Dirac ope
rators" when the base manifold is a flat 4-dimensional torus. Now we gener
alise this formula to any even dimensional closed Riemannian manifolds\, a
nd prove it mathematically rigorously. Our proof uses a Witten localisatio
n argument combined with a devised embedding into a cylinder of one dimens
ion higher. Our viewpoint sheds some new light on the interplay among the
Atiyah-Patodi-Singer boundary condition\, domain-wall fermions\, and edge
modes.\n\nThis talk is based on a joint work with H. Fukaya\, M. Furuta\,
T. Onogi\, S. Yamaguchi\, and M. Yamashita: arXiv:1910.01987.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Cristofaro-Gardiner (UC Santa Cruz)
DTSTART:20200806T150000Z
DTEND:20200806T155000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/37
DESCRIPTION:Title: The simplicity conjecture\nby Dan Cristofaro-Gardiner (UC Sant
a Cruz) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstr
act\nIn the 60s and 70s\, there was a flurry of activity concerning the qu
estion of whether or not various subgroups of homeomorphism groups of mani
folds are simple\, with beautiful contributions by Fathi\, Kirby\, Mather\
, Thurston\, and many others. A funnily stubborn case that remained open
was the case of area-preserving homeomorphisms of surfaces. For example\,
for balls of dimension at least 3\, the relevant group was shown to be si
mple by work of Fathi in 1980\; but\, the answer in the two-dimensional c
ase\, asked in the 70s\, was not known. I will explain recent joint work
proving that the group of compactly supported area preserving homeomorphis
ms of the two-disc is in fact not a simple group\; this answers the "Simpl
icity Conjecture" in the affirmative. Our proof uses new spectral invarian
ts\, defined via periodic Floer homology\, that I will introduce: these re
cover the Calabi invariant of monotone twists.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ko Honda (UCLA)
DTSTART:20200806T160000Z
DTEND:20200806T165000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/38
DESCRIPTION:Title: Convex hypersurface theory in higher-dimensional contact topology<
/a>\nby Ko Honda (UCLA) as part of Eighth Pacific Rim Conference in Mathem
atics\n\n\nAbstract\nConvex surface theory and bypasses are extremely powe
rful tools for analyzing contact 3-manifolds. In particular they have been
successfully applied to many classification problems. After briefly revie
wing convex surface theory in dimension three\, we explain how to generali
ze many of their properties to higher dimensions. This is joint work with
Yang Huang.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleny Ionel (Stanford University)
DTSTART:20200806T170000Z
DTEND:20200806T175000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/39
DESCRIPTION:Title: Thin compactifications and Relative Fundamental Classes\nby El
eny Ionel (Stanford University) as part of Eighth Pacific Rim Conference i
n Mathematics\n\n\nAbstract\nFamilies of moduli spaces in symplectic Gromo
v-Witten theory and gauge theory are often manifolds that have "thin" comp
actifications\, in the sense that the boundary of the generic fiber has co
dimension at least two. In this talk we discuss a notion of a relative fun
damental class for such thinly compactified families. It associates to eac
h fiber\, regardless whether it is regular or not\, an element in its Cech
homology in a way that is consistent along paths. The invariants defined
by relative fundamental classes agree with those defined by pseudo-cycles\
, and the relative fundamental class is equal to the virtual fundamental c
lass defined by Pardon via implicit atlases in all cases when both are def
ined. We give some examples of this construction\, discuss some of its pro
perties\, and its benefits. This talk is based on joint work with Tom Park
er.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yakov Eliashberg (plenary) (Stanford University)
DTSTART:20200806T180000Z
DTEND:20200806T191000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/40
DESCRIPTION:Title: The program of arborealization\nby Yakov Eliashberg (plenary)
(Stanford University) as part of Eighth Pacific Rim Conference in Mathemat
ics\n\n\nAbstract\nWeinstein symplectic manifolds is one of the basic obje
cts in symplectic topology\, similar to Stein complex manifolds in the hig
h-dimensional complex analysis. The arborealization program initiated by D
avid Nadler aims to describe Weinstein manifolds as cotangent bundles of\n
complexes\, called arboreal spaces\, which are more general than smooth ma
nifolds\, and yet have simple standard local chart description. This allow
s to state symplectic topological questions about Weinstein manifolds as p
roblems in differential topology of arboreal spaces. In the talk I'll desc
ribe the program and its current status.\nThis is a joint work with Daniel
Alvarez-Gavela and David Nadler.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hector Pasten (Pontificia Universidad Catolica de Chile)
DTSTART:20200806T002000Z
DTEND:20200806T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/41
DESCRIPTION:Title: Hilbert's tenth problem for rings of integers of certain number fi
elds of degree six\nby Hector Pasten (Pontificia Universidad Catolica
de Chile) as part of Eighth Pacific Rim Conference in Mathematics\n\n\nAbs
tract\nHilbert's tenth problem asked for an algorithm to decide solvabilit
y of Diophantine equations over the integers. The work of Davis\, Putnam\,
Robinson\, and Matijasevich showed that the requested algorithm does 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 conjectur
e 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://researchseminars.org/talk/pacificrim2020/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoichi Mieda (University of Tokyo)
DTSTART:20200806T011000Z
DTEND:20200806T020000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/42
DESCRIPTION:Title: Local Saito-Kurokawa $A$-packets and $l$-adic cohomology of Rapopo
rt-Zink tower for $GSp(4)$\nby Yoichi Mieda (University of Tokyo) as p
art of Eighth Pacific Rim Conference in Mathematics\n\n\nAbstract\nThe Rap
oport-Zink tower for $GSp(4)$ is a $p$-adic local counterpart of the Siege
l threefold.\nIts l-adic cohomology is naturally equipped with actions 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 t
he cohomology is strongly related with the local Langlands correspondence.
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 representatio
n with trivial central character\,\nI will determine how the $A$-packet co
ntributes to the cohomology of the Rapoport-Zink tower for $GSp(4)$.\nThis
is a joint work with Tetsushi Ito.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheng-Chiang Tsai (Stanford University)
DTSTART:20200806T021000Z
DTEND:20200806T030000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/43
DESCRIPTION:Title: Uniform bounds of orbital integrals\nby Cheng-Chiang Tsai (Sta
nford University) as part of Eighth Pacific Rim Conference in Mathematics\
n\n\nAbstract\nIn this talk\, we aim to give a survey about available and
expected results on uniform bounds of orbital integrals. Interestingly\, b
oth the heuristic and method comes from the geometry of so-called affine S
pringer fiber\, and in particular the expectation that this fibration (bet
ween infinite-dimensional varieties) is "semi-small." We will put an empha
sis on this connection.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen-Wei Li (Peking University)
DTSTART:20200806T030000Z
DTEND:20200806T035000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/44
DESCRIPTION:Title: Stable trace formula for metaplectic groups\nby Wen-Wei Li (Pe
king University) as part of Eighth Pacific Rim Conference in Mathematics\n
\n\nAbstract\nA theory of endoscopy for the metaplectic covering of symple
ctic groups was proposed by the author almost 10 years ago\, and the ellip
tic part of the Arthur-Selberg trace formula has been stabilized since the
n. I will give an overview of the stabilization of the full trace formula
for these coverings\, which is indispensable for global applications. This
is largely inspired by the prior works of Arthur and Moeglin-Waldspurger
for linear reductive groups. This is a work in stable progress.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Eischen (University of Oregon)
DTSTART:20200807T002000Z
DTEND:20200807T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/45
DESCRIPTION:Title: $p$-adic aspects of $L$-functions and automorphic forms\nby El
len Eischen (University of Oregon) as part of Eighth Pacific Rim Conferenc
e in Mathematics\n\n\nAbstract\nI will discuss recent developments for $p$
-adic aspects of $L$-functions and automorphic forms\, especially in the s
etting of unitary groups. With a viewpoint that encompasses several settin
gs\,\nincluding modular forms (GL$_2$) and automorphic forms on higher ran
k (namely\, unitary and symplectic) groups\, I will\ngive a recipe for con
structing $p$-adic $L$-functions that relies strongly on the behavior of a
ssociated automorphic forms. Recent\ndevelopments will be put in the conte
xt of more familiar constructions of Serre\, Katz\, and Hida. I will also
describe some challenges unique to the higher rank setting\, as well as re
cent attempts to overcome them.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Yamana (Osaka City University)
DTSTART:20200807T011000Z
DTEND:20200807T020000Z
DTSTAMP:20260422T212859Z
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 Rim Conf
erence in Mathematics\n\n\nAbstract\nLet $\\pi_i$ be an irreducible cuspid
al automorphic representation of $GL(2\,A)$ with central character $\\omeg
a_i$\, where $A$ is an adele ring of a number field. When the product $\\o
mega_1\\omega_2\\omega_3$ is the trivial character of $A^*$\, Atsushi Ichi
no proved a formula for the central value $L(1/2\,\\pi_1\\times\\pi_2\\tim
es\\pi_3)$ of the triple product $L$-series in terms of global trilinear f
orms that appear in Jacquet's conjecture. I will extend this formula to th
e case when $\\omega_1\\omega_2\\omega_3$ is a quadratic character. This i
s a joint work with Ming-Lun Hsieh.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takeshi Saito (plenary) (University of Tokyo)
DTSTART:20200807T021000Z
DTEND:20200807T032000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/47
DESCRIPTION:Title: Wild ramification and the cotangent bundle in mixed characteristic
\nby Takeshi Saito (plenary) (University of Tokyo) as part of Eighth P
acific Rim Conference in Mathematics\n\n\nAbstract\nThe analogy between th
e wild ramification in arithmetic geometry and the irregular singularity o
f partial differential equations has attracted interests of mathematicians
. For a $D$-module on a complex manifold\, its singular support is defined
on the cotangent bundle. An algebraic variant over a field of positive ch
aracteristic is recently introduced by Beilinson. I will discuss an analog
ue in mixed characteristic case.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (Institute for Advanced Study)
DTSTART:20200811T160000Z
DTEND:20200811T165000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/48
DESCRIPTION:Title: Incidence estimates with application to Fourier analysis\nby H
ong Wang (Institute for Advanced Study) as part of Eighth Pacific Rim Conf
erence in Mathematics\n\n\nAbstract\nWe are going to discuss some incidenc
e problems between points and tubes. Then we discuss how they are related
to problems in Fourier analysis. This includes joint work with Larry Guth\
, Noam Solomon\, and with Ciprian Demeter\, L. Guth.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polona Durcik (Chapman University)
DTSTART:20200811T170000Z
DTEND:20200811T175000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/49
DESCRIPTION:Title: Singular integrals and patterns in the Euclidean space\nby Pol
ona Durcik (Chapman University) as part of Eighth Pacific Rim Conference i
n Mathematics\n\n\nAbstract\nWe give an overview of some recent results on
point configurations in large subsets of the Euclidean space and discuss
their connection with multilinear singular integrals.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Christ (plenary) (UC Berkeley)
DTSTART:20200810T180000Z
DTEND:20200810T191000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/50
DESCRIPTION:Title: Oscillation and frustration in multilinear inequalities\nby Mi
chael Christ (plenary) (UC Berkeley) as part of Eighth Pacific Rim Confere
nce in Mathematics\n\n\nAbstract\nMultilinear functionals\, and inequaliti
es governing them\, arise\nin various contexts in harmonic analysis (in co
nnection with\nFourier restriction)\, in partial differential equations (n
onlinear\ninteractions) and in additive combinatorics (existence of certai
n patterns\nin sets of appropriately bounded density). This talk will focu
s\non an inequality that quantifies a weak convergence theorem\nof Joly\,
Métivier\, and Rauch (1995) concerning threefold products\,\nand on relat
ed inequalities for trilinear expressions involving\nhighly oscillatory fa
ctors.\nSublevel set inequalities\, which quantify\nthe impossibility of e
xactly solving certain systems of linear functional\nequations (the frustr
ation of the title)\, are a central element of the analysis.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zane Li (Indiana University\, Bloomington)
DTSTART:20200810T160000Z
DTEND:20200810T165000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/51
DESCRIPTION:Title: Connections between decoupling and efficient congruencing\nby
Zane Li (Indiana University\, Bloomington) as part of Eighth Pacific Rim C
onference in Mathematics\n\n\nAbstract\nThere are two different looking pr
oofs of Vinogradov's Mean Value Theorem. One was Bourgain-Demeter-Guth's p
roof via $l^2$ decoupling of the moment curve using harmonic analysis meth
ods and another was Wooley's proof via nested efficient congruencing using
number theoretic methods. We will illustrate the main ideas of how an eff
icient congruencing proof can be translated into a decoupling proof in the
case of $l^2$ decoupling for the parabola. We will also mention how to us
e these ideas to give a new proof of $l^2$ decoupling for the moment curve
. This talk is based off joint work with Shaoming Guo\, Po-Lam Yung and Pa
vel Zorin-Kranich.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chun-Kit Lai (San Francisco State University)
DTSTART:20200810T170000Z
DTEND:20200810T175000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/52
DESCRIPTION:Title: Fourier bases and Fourier frames for singular measures\nby Chu
n-Kit Lai (San Francisco State University) as part of Eighth Pacific Rim C
onference in Mathematics\n\n\nAbstract\nA measure is called a frame-spectr
al 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$$\n\\|f\\|_{\\mu}^2 \\asymp \\sum_{\\lambda\\in \\L
ambda} |\\langle f\,e_{\\lambda}\\rangle_{\\mu}|^2.\n$$\nFrames are natura
l generalization of orthonormal basis. It is known that some singular meas
ures also admit a Fourier frames. However\, it is still largely unknown wh
ich singular measures are frame-spectral. In this talk\, we will explore s
ome of the recent progresses about this problem.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kornélia Héra (University of Chicago)
DTSTART:20200811T180000Z
DTEND:20200811T185000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/53
DESCRIPTION:Title: Hausdorff dimension of unions of affine subspaces and related prob
lems\nby Kornélia Héra (University of Chicago) as part of Eighth Pac
ific Rim Conference in Mathematics\n\n\nAbstract\nWe consider the question
of how large a union of affine subspaces must be depending on the family
of affine subspaces constituting the union. In the famous Kakeya problem o
ne considers lines in every direction. Here the position of the lines or h
igher-dimensional affine subspaces is more general\, and accordingly the e
xpected dimension bound is different. We prove that the union of any $s$-d
imensional family of $k$-dimensional affine subspaces is at least $[k + s/
(k+1)]$-dimensional\, and is exactly $(k + s)$-dimensional if $s$ is at mo
st 1.\nPartially based on joint work with Tamás Keleti and András Máth
é.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhi Jang (University of Southern California)
DTSTART:20200811T000000Z
DTEND:20200811T005000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/54
DESCRIPTION:Title: Dynamics of Newtonian stars\nby Juhi Jang (University of South
ern California) as part of Eighth Pacific Rim Conference in Mathematics\n\
n\nAbstract\nThe gravitational Euler-Poisson system is a classical fluid m
odel describing the motion of self-gravitating gaseous Newton stars. We di
scuss some recent results on expanding\, collapsing and rotating star solu
tions of the Euler-Poisson system.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volker Schlue (University of Melbourne)
DTSTART:20200811T010000Z
DTEND:20200811T015000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/55
DESCRIPTION:Title: Expanding black hole cosmologies\nby Volker Schlue (University
of Melbourne) as part of Eighth Pacific Rim Conference in Mathematics\n\n
\nAbstract\nIn general relativity\, the Kerr de Sitter family of solutions
to Einstein’s equations with positive cosmological constant are a model
of a black hole in the expanding universe. In this talk\, I will focus on
the stability problem for the expanding region of the spacetime\, which c
an be formulated as a characteristic initial value problem to the future o
f the cosmological horizons of the black hole. Unlike in the stability of
Kerr or Kerr de Sitter black hole exteriors\, the solution in the cosmolog
ical region does not globally converge to an explicit family of solutions\
, but displays genuine asymptotic degrees of freedom. I will describe my w
ork on the decay of the conformal Weyl curvature in this setting\, and dis
cuss the global construction of optical functions in de Sitter\, which are
relevant for my approach to this problem in double null gauge.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pin Yu (Tsinghua University)
DTSTART:20200811T020000Z
DTEND:20200811T025000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/56
DESCRIPTION:Title: On the rigidity from infinity for nonlinear Alfven waves\nby P
in Yu (Tsinghua University) as part of Eighth Pacific Rim Conference in Ma
thematics\n\n\nAbstract\nThe Alfven waves are fundamental wave phenomena i
n magnetized plasmas and the dynamics of Alfven waves are governed by a sy
stem of nonlinear partial differential equations called the MHD system. In
the talk\, we will focus on the rigidity aspects of the scattering proble
m for the MHD equations: We prove that the Alfven waves must vanish if the
ir scattering fields vanish at infinities. The proof is based on a careful
study of the null structure and a family of weighted energy estimates.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Trudinger (CANCELLED) (Australian National University)
DTSTART:20200827T000000Z
DTEND:20200827T011000Z
DTSTAMP:20260422T212859Z
UID:pacificrim2020/57
DESCRIPTION:Title: Generated Jacobian Equations\; convexity\, geometric optics and op
timal transportation (CANCELLED)\nby Neil Trudinger (CANCELLED) (Austr
alian National University) as part of Eighth Pacific Rim Conference in Mat
hematics\n\n\nAbstract\nGenerated Jacobian equations were originally intro
duced as an extension of Monge-Ampère type equations in optimal transport
ation to embrace near field geometric optics. In this talk we present some
of the basic theory\, including the associated convexity theory of genera
ting functions and recent work on the resultant classical solvability of
the associated boundary value problems.\n
LOCATION:https://researchseminars.org/talk/pacificrim2020/57/
END:VEVENT
END:VCALENDAR