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BEGIN:VEVENT
SUMMARY:Jie Xiao (Memorial University of Newfoundland)
DTSTART;VALUE=DATE-TIME:20220913T010000Z
DTEND;VALUE=DATE-TIME:20220913T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/1
DESCRIPTION:Title: Mean Hoelder-Lipschitz Potentials in Curved Campanato-R
adon Spaces\nby Jie Xiao (Memorial University of Newfoundland) as part
of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU
Gongguan Campus Mathematics Building.\n\nAbstract\nThis talk will present
L. Liu-J. Xiao's article: Math. Ann. 375(2019)1045-1077\, proving that f
or $s \\in (0\,1)$\, $\\alpha \\in (0\,n)$\, $\\beta \\in (0\,n]$\, \n\\[\
n1\\leq \\min\\{p\, q\\}\\le\\max\\{p\,q\\}<\\beta p(n-\\alpha p)^{-1}<\\i
nfty\n\\]\nand $\\lambda=q(np^{-1}-s-\\alpha)+n-\\beta$\, if $\\mu$ is a n
onnegative Radon measure on $\\mathbb R^n$ with the $\\beta$-dimensional u
pper curvature $|\\|\\mu|\\|_\\beta<\\infty$ then $I_\\alpha \\dot{\\varLa
mbda}_s^{p\,\\infty}$ (the mean Hoelder-Lipschitz potential space on $\\ma
thbb R^n$) embeds continuously into $\\mathcal{L}^{q\,\\lambda}_\\mu$ (the
curved Campanato-Radon space on $\\mathbb R^n$)\; and yet its converse is
still valid with $\\mu$ being admissible\, thereby discovering\nthe $\\ga
mma$-Hoelder-Lipschitz continuity of any duality solution to the $\\alpha$
-th Laplace equation $(-\\varDelta)^{\\frac\\alpha 2}u=\\mu$\nor the $[1\,
n/2)\\cap\\{1\,2...\,n\\}\\ni k$-th Hessian equation $F_k[u]=\\mu$ under a
suitable curvature $|\\||\\mu|\\||_\\beta<\\infty$.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Volberg (Michigan State University)
DTSTART;VALUE=DATE-TIME:20220920T010000Z
DTEND;VALUE=DATE-TIME:20220920T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/2
DESCRIPTION:Title: Dyadic rectangles\nby Alexander Volberg (Michigan S
tate University) as part of Nonlinear Analysis Seminar Series\n\nLecture h
eld in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract
\nWeighted Carleson embedding (weighted paraproduct estimates in another l
anguage) lies in the core of various harmonic analysis and PDE results. N
ot much is known about it in multi-parameter situation\, while one paramet
er is completely understood. I will formulate several new results on weigh
ted multi-parameter Carleson embedding on multi-trees and their corollarie
s as embeddings of Hilbert spaces of analytic functions on poly-discs.\n\n
I will also formulate corresponding Poincar\\'e inequalities on multi-tree
s and poly-discs. Some of those results are final\, but even embedding of
Hardy space on bi-disc is not completely described. My presentation is bas
ed on joint works with N. Arcozzi\, I. Holmes\, P. Mozolyako\, P. Zorin-K
ranich.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenka Slavikova (Charles University)
DTSTART;VALUE=DATE-TIME:20220927T070000Z
DTEND;VALUE=DATE-TIME:20220927T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/3
DESCRIPTION:Title: Classical multiplier theorems and their sharp variants<
/a>\nby Lenka Slavikova (Charles University) as part of Nonlinear Analysis
Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathe
matics Building.\n\nAbstract\nThe question of finding good sufficient cond
itions on a bounded function $m$ guaranteeing the $L^p$-boundedness of the
associated Fourier multiplier operator is a long-standing open problem in
harmonic analysis. In this talk\, I will recall the classical multiplier
theorems of H\\"ormander and Marcinkiewicz and present their sharp variant
s in which the multiplier belongs to a certain fractional Sobolev space. T
he talk is based in part on a joint work with L. Grafakos and M. Masty\\l
o.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Maggi (UT Austin)
DTSTART;VALUE=DATE-TIME:20221004T010000Z
DTEND;VALUE=DATE-TIME:20221004T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/4
DESCRIPTION:by Francesco Maggi (UT Austin) as part of Nonlinear Analysis S
eminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathema
tics Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jin-Cheng Jiang (National Tsing Hua University)
DTSTART;VALUE=DATE-TIME:20221018T070000Z
DTEND;VALUE=DATE-TIME:20221018T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/5
DESCRIPTION:Title: On the Cauchy problem for the cutoff Boltzmann equation
with small initial data\nby Jin-Cheng Jiang (National Tsing Hua Unive
rsity) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Roo
m M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nWe prove
the global existence of the non-negative unique mild\nsolution for the Ca
uchy problem of the cutoff Boltzmann equation for\nsoft potential model
−1<=γ<0 with the small initial data in three\ndimensional space. Thus o
ur result fixes the gap for the case γ=−1 in\nthree dimensional space i
n the authors' previous work where the estimate\nfor the loss term was imp
roperly used. The other gap there for the case\nγ=0 in two dimensional sp
ace is recently fixed by Chen\, Denlinger and\nPavlović. The initial data
f0 is non-negative\, small in weighted\nL3_{x\,v} and finite in weighted
L15/8_{x\,v}. We also show that the\nsolution scatters with respect to the
kinetic transport operator. The\nnovel contribution of this work lies in
the exploration of the symmetric\nproperty of the gain term in terms of we
ighted estimate. It is the key\ningredient for solving the model −1<γ<0
when applying the Strichartz\nestimates.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neal Bez (Saitama University)
DTSTART;VALUE=DATE-TIME:20221129T010000Z
DTEND;VALUE=DATE-TIME:20221129T033000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/6
DESCRIPTION:Title: An introduction to Strichartz estimates I\nby Neal
Bez (Saitama University) as part of Nonlinear Analysis Seminar Series\n\nL
ecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\n
Abstract\nThe aim of these lectures is to give a gentle introduction to St
richartz estimates\, with an emphasis on particular cases such as the line
ar Schr\\"odinger and wave equations. The associated dispersive estimates
play a highly important role in the theory of Strichartz estimates so I wi
ll begin in Lecture 1 by proving the required dispersive estimates.\n\nNex
t\, in Lecture 2\, I will prove the homogeneous Strichartz estimates in al
l admissible cases\, including the so-called Keel--Tao endpoint case. Buil
ding on the content of the first two lectures\, in Lecture 3\, I will disc
uss the situation regarding inhomogeneous Strichartz estimates.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neal Bez (Saitama University)
DTSTART;VALUE=DATE-TIME:20221206T010000Z
DTEND;VALUE=DATE-TIME:20221206T033000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/7
DESCRIPTION:Title: An introduction to Strichartz estimates II\nby Neal
Bez (Saitama University) as part of Nonlinear Analysis Seminar Series\n\n
Lecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\
nAbstract\nThe aim of these lectures is to give a gentle introduction to S
trichartz estimates\, with an emphasis on particular cases such as the lin
ear Schr\\"odinger and wave equations. The associated dispersive estimates
play a highly important role in the theory of Strichartz estimates so I w
ill begin in Lecture 1 by proving the required dispersive estimates.\n\nNe
xt\, in Lecture 2\, I will prove the homogeneous Strichartz estimates in a
ll admissible cases\, including the so-called Keel--Tao endpoint case. Bui
lding on the content of the first two lectures\, in Lecture 3\, I will dis
cuss the situation regarding inhomogeneous Strichartz estimates.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neal Bez (Saitama University)
DTSTART;VALUE=DATE-TIME:20221213T010000Z
DTEND;VALUE=DATE-TIME:20221213T033000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/8
DESCRIPTION:Title: An introduction to Strichartz estimates III\nby Nea
l Bez (Saitama University) as part of Nonlinear Analysis Seminar Series\n\
nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n
\nAbstract\nThe aim of these lectures is to give a gentle introduction to
Strichartz estimates\, with an emphasis on particular cases such as the li
near Schr\\"odinger and wave equations. The associated dispersive estimate
s play a highly important role in the theory of Strichartz estimates so I
will begin in Lecture 1 by proving the required dispersive estimates.\n\nN
ext\, in Lecture 2\, I will prove the homogeneous Strichartz estimates in
all admissible cases\, including the so-called Keel--Tao endpoint case. Bu
ilding on the content of the first two lectures\, in Lecture 3\, I will di
scuss the situation regarding inhomogeneous Strichartz estimates.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lubos Pick (Charles University)
DTSTART;VALUE=DATE-TIME:20221108T070000Z
DTEND;VALUE=DATE-TIME:20221108T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/9
DESCRIPTION:Title: Optimality problems in Orlicz spaces\nby Lubos Pick
(Charles University) as part of Nonlinear Analysis Seminar Series\n\nLect
ure held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbs
tract\nWe prove a general principle\, called the principal alternative\, w
hich yields an easily verifiable necessary and sufficient condition for th
e existence or the non-existence of an optimal Orlicz space in a wide vari
ety of specific tasks including boundedness of operators. We show that the
key relation is the positioning of certain rearrangement-invariant space\
, characteristic for the task in question\, to its fundamental Orlicz spac
e. The main motivation stems from the imbalance between the expressivity\,
meaning the richness and versatility\, of certain class of function space
s\, and its accessibility\, i.e.\, its complexity and technical difficulty
. More precisely\, while an optimal rearrangement-invariant space in a giv
en task often exists\, it might be too complicated or too implicit to be o
f any practical value. Optimal Orlicz spaces\, on the other hand\, are sim
pler and more manageable for applications\, but they tend not to exist at
all. We apply the general abstract result to several specific tasks includ
ing continuity of Sobolev embeddings or boundedness of integral operators
such as the Hardy-Littlewood maximal operator and the Laplace transform. T
he proof of the principal alternative is based on relations of endpoint Lo
rentz spaces to unions or intersections of Orlicz spaces. This is a joint
work with Vít Musil (Brno) and Jakub Takáč (Warwick).\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tess Anderson (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20221025T010000Z
DTEND;VALUE=DATE-TIME:20221025T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/10
DESCRIPTION:Title: Analysis and number theory team up\nby Tess Anders
on (Carnegie Mellon University) as part of Nonlinear Analysis Seminar Seri
es\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Buildi
ng.\n\nAbstract\nWe discuss two ways that analysis and number theory have
recently teamed up\, using a back and forth interplay to make progress on
two different types of counting problems. First we will count equilateral
triangles in Euclidean space. Second we will determine how often a random
polynomial fails to have "full" Galois group. Though easy to state\, these
questions have generated a lot of interesting techniques through the year
s\, which we will glimpse during this talk.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolin Kreisbeck (Katholischen Universität Eichstätt - Ingolsta
dt)
DTSTART;VALUE=DATE-TIME:20221101T070000Z
DTEND;VALUE=DATE-TIME:20221101T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/11
DESCRIPTION:Title: Dealing with nonlocalities in variational functionals:
Convexity notions\, lower semicontinuity\, and relaxation\nby Carolin
Kreisbeck (Katholischen Universität Eichstätt - Ingolstadt) as part of
Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gon
gguan Campus Mathematics Building.\n\nAbstract\nNonlocal variational probl
ems arise in various applications\, such as continuum mechanics\, the theo
ry of phase transitions\, or image processing. Naturally\, the presence of
nonlocalities leads to new effects\, and the standard methods in the calc
ulus of variations\, which tend to rely intrinsically on localization argu
ments\, do not apply. In this talk\, we address questions arising from the
existence theory for three different classes of variational functionals:
integrals depending on Riesz fractional gradients\, double integrals\, and
double supremals - and find qualitatively very different results. Regardi
ng the characterization of weak lower semicontinuity\, it may be surprisin
g that quasiconvexity\, which is well-known from the classical local setti
ng\, also provides the correct convexity notion for the fractional integra
ls. Our proof relies on a translation mechanism that allows switching betw
een classical and fractional gradients. In the case of double supremals\,
we show that the natural guess of separate level convexity fails in the ve
ctorial case\, and introduce the new Cartesian level convexity. As for rel
axation\, we discuss the central issue of why one cannot expect these nonl
ocal functionals\, in contrast to their local counterparts\, to be structu
re-preserving. This is based on joint work with Antonella Ritorto\, Hidde
Schönberger (both KU Eichstätt-Ingolstadt)\, and Elvira Zappale (Sapienz
a University of Rome).\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luz Roncal (Basque Center for Applied Mathematics)
DTSTART;VALUE=DATE-TIME:20221122T070000Z
DTEND;VALUE=DATE-TIME:20221122T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/12
DESCRIPTION:Title: Unique continuation for fractional discrete elliptic e
quations\nby Luz Roncal (Basque Center for Applied Mathematics) as par
t of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTN
U Gongguan Campus Mathematics Building.\n\nAbstract\nIn this talk we will
describe several qualitative and quantitative unique continuation properti
es for the fractional discrete Laplacian. We will show that\, in contrast
to the fractional continuous Laplacian\, global unique continuation fails
to hold in general for fractional discrete elliptic equations.\n\nWe will
also discuss quantitative versions of unique continuation which illustrate
how the properties in the continuous setting may be recovered if exponent
ially small (in terms of the lattice size) correction factors are added.\n
\nJoint work with Aingeru Fernández-Bertolin and Angkana Rüland.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serena Dipierro (University of Western Australia)
DTSTART;VALUE=DATE-TIME:20230411T070000Z
DTEND;VALUE=DATE-TIME:20230411T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/13
DESCRIPTION:Title: The Bernstein technique for integro-differential equat
ions\nby Serena Dipierro (University of Western Australia) as part of
Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gon
gguan Campus Mathematics Building.\n\nAbstract\nIn this talk we discuss ho
w to extend the classical Bernstein technique to the setting of integro-di
fferential operators. As a consequence of this\, we are able to provide fi
rst and one-sided second derivative estimates for solutions to fractional
equations. Our method is robust enough to be applied to some Pucci-type ex
tremal equations and to obstacle problems for fractional operators.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María J. Carro (Universidad Complutense de Madrid)
DTSTART;VALUE=DATE-TIME:20230418T070000Z
DTEND;VALUE=DATE-TIME:20230418T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/14
DESCRIPTION:Title: Solving the Dirichlet and the Neumann problem at the e
nd-point\nby María J. Carro (Universidad Complutense de Madrid) as pa
rt of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NT
NU Gongguan Campus Mathematics Building.\n\nAbstract\nIn 1980 C. Kenig pro
ved that for every Lipschitz domain $\\Omega$ in the plane there exists $1
\\le p_0<2$ so that the Dirichlet problem has a solution for every $f\\in
L^p(ds)$ and every $p\\in (p_0\, \\infty)$. Moreover\, if $p_0>1$\, the re
sult is false for $p\\le p_0$. The goal of this talk is to analyze what ha
ppen at the endpoint $p_0$\; that is\, we want to look for spaces $X\\subs
et L^{p_0}$ so that the Dirichlet problem has a solution for every $f\\in
X$. These spaces $X$ will be either a Lorentz space $L^{p_0\,1} (ds)$ or
some Orlicz space of logarithmic type. Similar results will be presented f
or the Neumann problem. This is a joint work with Virginia Naibo and Carme
n Ortiz-Caraballo.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Campbell (Charles University)
DTSTART;VALUE=DATE-TIME:20230307T070000Z
DTEND;VALUE=DATE-TIME:20230307T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/15
DESCRIPTION:Title: Injectivity in second-gradient Nonlinear Elasticity\nby Daniel Campbell (Charles University) as part of Nonlinear Analysis S
eminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathema
tics Building.\n\nAbstract\nWe study injectivity for models of Nonlinear E
lasticity that involve the second gradient. We assume that $\\Omega\\subse
t\\mathbb{R}^n$ is a domain\, $f\\in W^{2\,q}(\\Omega\,\\mathbb{R}^n)$ sat
isfies $|J_f|^{-a}\\in L^1$ and that $f$ equals a given homeomorphism on $
\\partial \\Omega$. Under suitable conditions on $q$ and $a$ we show that
$f$ must be a homeomorphism. As a main new tool we find an optimal conditi
on for $a$ and $q$ that imply that $\\mathcal{H}^{n-1}(\\{J_f=0\\})=0$ and
hence $J_f$ cannot change sign. We further specify in dependence of $q$ a
nd $a$ the maximal Hausdorff dimension $d$ of the critical set $\\{J_f=0\\
}$. The sharpness of our conditions for $d$ is demonstrated by constructin
g respective counterexamples.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keng Hao Ooi (National Central University)
DTSTART;VALUE=DATE-TIME:20230314T070000Z
DTEND;VALUE=DATE-TIME:20230314T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/16
DESCRIPTION:Title: Harmonic Analysis in Nonlinear Potential Theory\nb
y Keng Hao Ooi (National Central University) as part of Nonlinear Analysis
Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathe
matics Building.\n\nAbstract\nIn this talk I will introduce a type of Sobo
lev multiplier which appears naturally in many super critical nonlinear PD
Es. We will briefly study the preduals of the Sobolev multplier spaces an
d the boundedness of Hardy-Littlewood maximal operators on such spaces. F
urthermore\, the boundedness of maximal operators on the spaces of Choquet
integrals associated with capacities will also be addressed. The main to
ols in tackling these problems rely on classical harmonic analysis and non
linear potential theory.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominic Breit (TU Clausthal)
DTSTART;VALUE=DATE-TIME:20230328T070000Z
DTEND;VALUE=DATE-TIME:20230328T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/17
DESCRIPTION:Title: Inclusion relations among fractional Orlicz-Sobolev sp
aces and a Littlewood-Paley characterization\nby Dominic Breit (TU Cla
usthal) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Ro
om M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nOptimal
embeddings among fractional Orlicz-Sobolev spaces with different smoothne
ss are characterized. The equivalence of their Gagliardo-Slobodeckij norms
to norms defined via Littlewood-Paley decompostions\, via oscillations\,
or via Besov type difference quotients is also established. These equivale
nces\, of independent interest\, are a key tool in the proof of the releva
nt embeddings. \nThis is joint work with Andrea Cianchi\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Ghosh (TIFR Centre For Applicable Mathematics)
DTSTART;VALUE=DATE-TIME:20230425T070000Z
DTEND;VALUE=DATE-TIME:20230425T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/18
DESCRIPTION:Title: On bilinear Stein-Weiss inequality\nby Abhishek Gh
osh (TIFR Centre For Applicable Mathematics) as part of Nonlinear Analysis
Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathe
matics Building.\n\nAbstract\nIn this talk\, we discuss some bilinear frac
tional integral operators introduced by Kenig and Stein. Also\, the Stein-
Weiss inequality and its bilinear analogues will be addressed in Euclidean
space and beyond. This is a joint work with Rajesh K. Singh.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catalin Carstea (National Yang Ming Chiao Tung University)
DTSTART;VALUE=DATE-TIME:20230321T070000Z
DTEND;VALUE=DATE-TIME:20230321T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/19
DESCRIPTION:Title: An inverse problem for the porous medium equation\
nby Catalin Carstea (National Yang Ming Chiao Tung University) as part of
Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gon
gguan Campus Mathematics Building.\n\nAbstract\nThe porous medium equation
is a degenerate parabolic type quasilinear equation that models\, for exa
mple\, the flow of a gas through a porous medium. In this talk I will pres
ent recent results on uniqueness in the inverse boundary value problem fo
r this equation. These are the first such results to be obtained for a deg
enerate parabolic equation. The talk is based on work with T. Ghosh & G. N
akamura and T. Ghosh & G. Uhlmann.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Kh. Balci (Universität Bielefeld)
DTSTART;VALUE=DATE-TIME:20230516T070000Z
DTEND;VALUE=DATE-TIME:20230516T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/20
DESCRIPTION:Title: Behind the regularity: variational problems with energ
y gaps\nby Anna Kh. Balci (Universität Bielefeld) as part of Nonlinea
r Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Ca
mpus Mathematics Building.\n\nAbstract\nWe study different problems with
energy gaps: local and nonlocal double potential\, variable exponent and w
eights models. We design the general procedure to construct new examples o
f energy gaps and present the numerical scheme that converges to the glob
al minimiser of the problem. The talk is based on several joint projects
with Lars Diening\, Michail Surnachev\, Johanness Srorn and Christoph Ortn
er.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qing Han (Notre Dame)
DTSTART;VALUE=DATE-TIME:20230607T060000Z
DTEND;VALUE=DATE-TIME:20230607T070000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/21
DESCRIPTION:Title: A Concise Boundary Regularity for the Uniformly Degene
rate Elliptic Equations\nby Qing Han (Notre Dame) as part of Nonlinear
Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Cam
pus Mathematics Building.\n\nAbstract\nUniformly degenerate elliptic equat
ions appear frequently in many geometric problems. Solutions may exhibit s
ingular behaviors near the boundary where the degeneracy occurs. Usually\,
behaviors of solutions near the boundary are described through expansions
. In this talk\, we identify a precise singular term as an additional inde
pendent self-variable and establish a concise boundary regularity.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tien Nguyen (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20230912T070000Z
DTEND;VALUE=DATE-TIME:20230912T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/22
DESCRIPTION:Title: Singularities in the Keller-Segel system\nby Tien
Nguyen (National Taiwan University) as part of Nonlinear Analysis Seminar
Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Bu
ilding.\n\nAbstract\nThe talk presents constructions of blowup solutions t
o the Keller-Segel system in $\\mathbb{R}^d$.\n\n\n$d = 2$ ($L^1$-critical
): There exist finite time single blowup solutions that are of Type II wit
h finite mass. Blowup rates are quantized according to a discrete spectrum
of a linearized operator around the rescaled stationary solution in the s
elf-similar setting. There is also \\textit{multiple collapsing blowup sol
utions} formed by a collision of multiple single solutions with self-simil
arity that provides a brand new mechanism of singularity formation.\n\n\n$
d \\geq 3$ ($L^1$-supercritical): For $d \\geq 3$\, there exist finite tim
e blowup solutions having the form of collapsing-ring which consists of an
imploding\, smoothed-out shock wave moving towards the origin to form a D
irac mass at the singularity. For $d = 3\,4 $\, we found blowup solutions
with infinite mass that are asymptotically self-similar with a log correct
ion to their profile. \n\n\nThe constructions rely on a spectral approach
for multiple-scale problems\, renormalization technique\, and refined ener
gy estimates. The talk is based on a series of joint works with C. Collot
(Paris Cergy)\, T. Ghoul (NYU Abu Dhabi)\, N. Nouaili (Paris Dauphine)\, N
. Masmoudi (NYU) and H. Zaag (Paris Nord).\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Cianchi (Universita' di Firenze)
DTSTART;VALUE=DATE-TIME:20231003T070000Z
DTEND;VALUE=DATE-TIME:20231003T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/24
DESCRIPTION:Title: Local boundedness of minimizers under unbalanced Orlic
z growth conditions\nby Andrea Cianchi (Universita' di Firenze) as par
t of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTN
U Gongguan Campus Mathematics Building.\n\nAbstract\nLocal minimizers of i
ntegral functionals of the calculus of variations are analyzed under growt
h conditions dictated by different lower and upper bounds for the integran
d. Growths \n of non-necessarily power-type are allowed. The local bounde
dness of the relevant minimizers is established under a suitable balance b
etween the lower and the upper bounds. Classical minimizers\, as well as q
uasi-minimizers are included in our discussion. Functionals subject to so-
called $p\,q$-growth conditions are embraced as special cases and the corr
esponding sharp results available in the literature are recovered.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Manfredi (University of Pittsburgh)
DTSTART;VALUE=DATE-TIME:20231017T010000Z
DTEND;VALUE=DATE-TIME:20231017T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/25
DESCRIPTION:Title: On Viscosity Solutions to the Non-Homogeneous Infinite
Laplace Equation\nby Juan Manfredi (University of Pittsburgh) as part
of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU
Gongguan Campus Mathematics Building.\n\nAbstract\nWe will revisit the Th
eorem on Sums and use it to study viscosity solutions of non-homogeneous
equations involving the infinite Laplacian in Euclidean Space\, Riemannian
manifolds\, and Carnot Groups.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zdeněk Mihula (Czech Technical University in Prague)
DTSTART;VALUE=DATE-TIME:20230919T070000Z
DTEND;VALUE=DATE-TIME:20230919T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/26
DESCRIPTION:Title: Optimal Sobolev inequalities in the hyperbolic space\nby Zdeněk Mihula (Czech Technical University in Prague) as part of No
nlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongg
uan Campus Mathematics Building.\n\nAbstract\nIn this talk\, we consider a
(higher order) Sobolev inequality for the Laplace--Beltrami operator in t
he ball model of the hyperbolic space $\\mathbb{H}^n$\, and we look for fu
nction spaces that are in a sense optimal in the inequality. The inequalit
y in question is\n$$\\|u\\|_{Y(\\mathbb{H}^n)} \\leq C \\|\\nabla_g^m u\\|
_{X(\\mathbb{H}^n)} \\quad \\text{for every $u\\in V_0^m X(\\mathbb{H}^n)$
}\;$$\nhere $$\\nabla_g^m = \n\\begin{cases}\n\\Delta_g^{\\frac{m}{2}} \\q
uad &\\text{if $m$ is even}\,\\\\\n\\nabla_g\\Delta_g^{\\lfloor \\frac{m}{
2} \\rfloor} \\quad &\\text{if $m$ is odd}\,\n\\end{cases}\n$$\nwhere $\\D
elta_g$ is the Laplace--Beltrami operator and $\\nabla_g$ is the hyperboli
c gradient\; $X(\\mathbb{H}^n)$ and $Y(\\mathbb{H}^n)$ are rearrangement-i
nvariant spaces\, and $V_0^m X(\\mathbb{H}^n)$ is a suitable $m$th order S
obolev space. For a given rearrangement-invariant space $X(\\mathbb{H}^n)$
\, we will describe the optimal (i.e.\, with the strongest norm) rearrange
ment-invariant space $Y(\\mathbb{H}^n)$ on the left-hand side.\n\nWe first
discuss the general description(s) of the optimal space. Then we turn our
attention to some concrete examples. Namely\, when $X$ is $L^1$\, $L^\\fr
ac{n}{m}$\, or an exponential Orlicz space ``near $L^\\infty$''. Even in t
hese simple cases\, the inequalities that we obtain seems to be missing in
the literature (especially\, when $m\\geq3$).\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rami Ayoush (Universitreiy of Warsaw)
DTSTART;VALUE=DATE-TIME:20231128T070000Z
DTEND;VALUE=DATE-TIME:20231128T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/27
DESCRIPTION:Title: On finite configurations in the spectra of singular me
asures\nby Rami Ayoush (Universitreiy of Warsaw) as part of Nonlinear
Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Camp
us Mathematics Building.\n\nAbstract\nDuring the talk I will discuss appli
cations of elementary additive combinatorics to dimensional estimates of P
DE- and Fourier-constrained measures. My main tool will be a simple certai
nty principle of the following form: a set $S ⊂ \\mathbb{R}^N$ contains
a given finite linear pattern if $S$ is a spectrum of a sufficiently singu
lar measure.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cody Stockdale (Clemson University)
DTSTART;VALUE=DATE-TIME:20230926T010000Z
DTEND;VALUE=DATE-TIME:20230926T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/28
DESCRIPTION:Title: A different approach to endpoint weak-type estimates f
or Calderón-Zygmund operators\nby Cody Stockdale (Clemson University)
as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210
in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nThe weak-type
$(1\,1)$ estimate for Calderón-Zygmund operators is fundamental in harmon
ic analysis. We investigate weak-type inequalities for Calderón-Zygmund s
ingular integral operators using the Calderón-Zygmund decomposition and i
deas inspired by Nazarov\, Treil\, and Volberg. We discuss applications of
these techniques in the Euclidean setting\, in weighted settings\, for mu
ltilinear operators\, for operators with weakened smoothness assumptions\,
and in studying the dimensional dependence of the Riesz transforms.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armin Schikorra (University of Pittsburgh)
DTSTART;VALUE=DATE-TIME:20231114T010000Z
DTEND;VALUE=DATE-TIME:20231114T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/29
DESCRIPTION:Title: On s-Stability of W^{s\,n/s}-minimizing maps between s
pheres in homotopy classes\nby Armin Schikorra (University of Pittsbur
gh) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M
210 in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nWe consider
maps between spheres S^n to S^\\ell that minimize the\nSobolev-space ener
gy W^{s\,n/s} for some s \\in (0\,1) in given homotopy\nclass.\nThe basic
question is: in which homotopy class does a minimizer exist?\nThis is a no
ntrivial question since the energy under consideration is\nconformally inv
ariant and bubbles can form.\nSacks-Uhlenbeck theory tells us that minimiz
ers exist in a set of\nhomotopy classes that generates the whole homotopy
group\n\\pi_{n}(\\S^\\ell). In some situations explicit examples are known
if\nn/s = 2 or s=1.\n\nIn our talk we are interested in the stability of
the above question\nin dependence of s. We can show that as s varies local
ly\, the set of\nhomotopy classes in which minimizers exists can be chosen
stable. We\nalso discuss that the minimum W^{s\,n/s}-energy in homotopy c
lasses is\ncontinuously depending on s.\n\nJoint work with K. Mazowiecka (
U Warsaw)\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felipe Hernandez (MIT)
DTSTART;VALUE=DATE-TIME:20231024T010000Z
DTEND;VALUE=DATE-TIME:20231024T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/30
DESCRIPTION:Title: Uncertainty principles for Wigner functions\nby Fe
lipe Hernandez (MIT) as part of Nonlinear Analysis Seminar Series\n\nLectu
re held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbst
ract\nThe Wigner function of a quantum state is a way of describing the ph
ase space distribution of a quantum particle. The uncertainty principle f
rom Fourier analysis places some restriction on the allowable decay of a W
igner function. In this talk I will give an introduction to the Wigner fu
nction and show that rapidly decaying Wigner functions must also be Schwar
tz\, which can also be interpreted as a type of uncertainty principle. Th
is is based on joint work with Jess Riedel.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Alberico (CNR - IAC)
DTSTART;VALUE=DATE-TIME:20231121T070000Z
DTEND;VALUE=DATE-TIME:20231121T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/31
DESCRIPTION:Title: Optimal embeddings for fractional Orlicz-Sobolev space
s\nby Angela Alberico (CNR - IAC) as part of Nonlinear Analysis Semina
r Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics
Building.\n\nAbstract\nThe optimal target space is exhibited for embedding
s of fractional-order Orlicz-Sobolev spaces.\nBoth the subcritical and the
supercritical regimes are considered.\nIn the former case\, the smallest
possible Orlicz target space is detected. In the latter\,\n the relevant O
rlicz-Sobolev spaces are shown to be embedded into the space of bounded\nc
ontinuous functions in $\\mathbb R^n$. Moreover\, their\n optimal modulus
of continuity is exhibited.\nThese results are the subject of a series of
joint papers with Andrea Cianchi\, Lubos Pick and Lenka\nSlavikova.\n\n\nA
.Alberico\, A.Cianchi\, L.Pick and L.Slavikova\,\nFractional Orlicz-Sobol
ev embeddings\,\n J. de Mathematiqués Pures et Appliquées\,
149 (2021).\n\n\nA.Alberico\, A.Cianchi\, L.Pick and L.Slavikova\,\n
Boundedness of functions in fractional Orlicz-Sobolev spaces\,\n
Nonlinear Analysis\, 230 (2023).\n\n\n A.Alberico\, A.Cianchi
\, L.Pick and L.Slavikova\,\nOn the Modulus of Continuity of fractional Or
licz-Sobolev functions\,\n in progress.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Hajłasz (University of Pittsburgh)
DTSTART;VALUE=DATE-TIME:20231205T010000Z
DTEND;VALUE=DATE-TIME:20231205T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/32
DESCRIPTION:Title: Approximation of mappings with derivatives of low rank
\nby Piotr Hajłasz (University of Pittsburgh) as part of Nonlinear An
alysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus
Mathematics Building.\n\nAbstract\nMy talk is based on two recent joint p
apers with Paweł Goldstein.\n\n\nJacek Gałęski in 2017\, in the context
of his research in geometric measure theory\, formulated the following co
njecture:\n\nConjecture.\nLet $1\\leq m< n$ be integers and let $\\Omega\\
subset\\mathbb{R}^n$ be open. If $f\\in C^1(\\Omega\,\\mathbb{R}^n)$ satis
fies $\\operatorname{rank} Df\\leq m$ everywhere in $\\Omega$\, then $f$ c
an be uniformly approximated by smooth mappings $g\\in C^\\infty(\\Omega\,
\\mathbb{R}^n)$ such that $\\operatorname{rank} Dg\\leq m$ everywhere in $
\\Omega$.\n\nOne can also modify the conjecture and ask about a local appr
oximation: smooth approximation in a neighborhood of any point.\nThese are
very natural problems with possible applications to PDEs and Calculus of
Variations. However\, the problems are difficult\, because standard approx
imation techniques like the one based on convolution do not preserve the r
ank of the derivative. It is a highly nonlinear constraint\, difficult to
deal with.\n\nIn 2018 Goldstein and Hajłasz obtained infinitely many coun
terexamples to this conjecture. Here is one:\n\nExample.\nThere is $f\\in
C^1(\\mathbb{R}^5\,\\mathbb{R}^5)$ with $\\operatorname{rank} Df\\leq 3$ t
hat cannot be locally and uniformly approximated by mappings\n$g\\in C^2(\
\mathbb{R}^5\,\\mathbb{R}^5)$ satisfying $\\operatorname{rank} Dg\\leq 3$.
\n\nThis example is a special case of a much more general result and the c
onstruction heavily depends on algebraic topology including the homotopy g
roups of spheres and the Freudenthal suspension theorem.\n\nMore recently
Goldstein and Hajłasz proved the conjecture in the positive in the case w
hen $m=1$. The proof is based this time on methods of analysis on metric s
paces and in particular on factorization of a mapping through metric trees
.\n\nThe method of factorization through metric trees used in the proof of
the conjecture when $m=1$ is very different and completely unrelated to t
he methods of algebraic topology used in the construction of counterexampl
es. However\, quite surprisingly\, both techniques have originally been us
ed by Wenger and Young as tools for study of Lipschitz homotopy groups of
the Heisenberg group\, a problem that seems completely unrelated to proble
ms discussed in this talk.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Raita (Georgetown University)
DTSTART;VALUE=DATE-TIME:20231107T010000Z
DTEND;VALUE=DATE-TIME:20231107T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/33
DESCRIPTION:Title: Limiting linear $L^1$ estimates near the boundary\
nby Bogdan Raita (Georgetown University) as part of Nonlinear Analysis Sem
inar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathemati
cs Building.\n\nAbstract\nWe identify necessary and sufficient conditions
on $k$th order linear differential operators $\\mathbb{A}$ in terms of a f
ixed halfspace $H\\subset\\mathbb{R}^n$ such that the Gagliardo--Nirenberg
--Sobolev inequality\n $$\n \\|D^{k-1}u\\|_{\\mathrm{L}^{\\frac{n}{n-1}}
(H)}\\leq c\\|\\mathbb{A} u\\|_{\\mathrm{L}^1(H)}\\quad\\text{for }u\\in\\
mathrm{C}^\\infty_c (\\mathbb{R}^{n}\,V)\n $$\n holds. This comes as a c
onsequence of sharp trace theorems on $\\partial H$. Strong estimates on l
ower order derivatives are the best possible due to the failure of Calder\
\'on--Zygmund theory in $L^1$.\n\nJoint work with Franz Gmeineder and Jean
Van Schaftingen.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Cruz-Uribe (University of Alabama)
DTSTART;VALUE=DATE-TIME:20231212T070000Z
DTEND;VALUE=DATE-TIME:20231212T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/34
DESCRIPTION:Title: Weighted norm inequalities for multiplier weak-type in
equalities\nby David Cruz-Uribe (University of Alabama) as part of Non
linear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gonggu
an Campus Mathematics Building.\n\nAbstract\nIn this talk we will consider
a version of weak-type inequalities we\nrefer to as {\\em multiplier weak
-type inequalities}. Given a weight\n$w$ and $1\\leq p<\\infty$\, the $(
p\,p)$ multiplier weak-type inequality\nfor an operator $T$ is of the form
\n\\[ |\\{ x\\in {\\mathbb{R}^n} : |w^{\\frac{1}{p}}(x)T(w^{-\\frac{1}{p}}
f)(x)|> t\\}|\n \\leq \\frac{C}{t^p} \\int_{\\mathbb{R}^n} |f(x)|^p\\\,dx
. \\]\nThese inequalities follow from the a strong $(p\,p)$ inequality of
the\nform\n\\[ \\int_{\\mathbb{R}^n} |Tf(x)|^pw(x)\\\,dx \\leq C \\int_{\
\mathbb{R}^n} |f(x)|^pw(x)\\\,dx \\]\nby mapping $f\\mapsto w^{-\\frac{1}{
p}}f$ and applying Chebyshev's\ninequality. These inequalities were first
considered by Muckenhoupt\nand Wheeden (1977) for the maximal operator an
d the Hilbert transform\non the real line. They showed that such inequali
ties hold if $w$ is a\nMuckenhoupt $A_p$ weight\, but gave examples to sho
w that the class of\nweights is strictly larger for these operators. Thei
r $A_p$ results\nwere extended to all dimensions and all Calder\\'on-Zygmu
nd integral\noperators by myself\, Martell\, and Perez (2005). They have
attracted\nrenewed attention since they were shown to be the right way of\
ngeneralizing weak-type inequalities to the setting of matrix weights\n(DC
U\, Isralowitz\, Moen\, Pott\, Rivera-Rios\, 2020).\n\nIn this talk\, we w
ill consider the problem of quantitative estimates\,\nin terms of the $A_p
$ characteristic\, for maximal operators and\nsingular integrals. Our res
ults extend those gotten in 2020 in the\ncase $p=1$ to all $1\\leq p<\\inf
ty$. We also show that our proofs can\nbe adapted to prove quantitative
estimates for matrix weighted\ninequalities. Finally\, we prove the analo
gous results for the\nfractional integral/Riesz potential in both the scal
ar and matrix\nweighted cases. These results are completely new\, as even
qualitative\nresults for fractional integrals were not known.\n\n\\bigski
p\n\nThis talk is joint work with Brandon Sweeting\, the University of Ala
bama.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Anastasia Molchanova (University of Vienna)
DTSTART;VALUE=DATE-TIME:20240319T070000Z
DTEND;VALUE=DATE-TIME:20240319T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/35
DESCRIPTION:Title: Limits of Sobolev Homeomorphisms in Nonlinear Elastici
ty\nby Dr. Anastasia Molchanova (University of Vienna) as part of Nonl
inear Analysis Seminar Series\n\nLecture held in Room 509\, Cosmology Buil
ding\, National Taiwan University.\n\nAbstract\nLimits of Sobolev homeomor
phisms naturally appear in geometric function theory\, calculus of variati
ons\, and continuum mechanics. In this talk\, we discuss essential propert
ies of mappings essential for elastic deformations\, focusing on aspects s
uch as continuity\, injectivity\, and differentiability\, as well as Lusin
's $(N)$- and $(N^{-1})$-conditions.\nWe consider variational problems of
nonlinear elasticity\, where admissible deformations are given by limits o
f Sobolev homeomorphisms\, and prove the existence of minimizers.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. MingQing Xiao (Southern Illinois University)
DTSTART;VALUE=DATE-TIME:20240312T010000Z
DTEND;VALUE=DATE-TIME:20240312T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/36
DESCRIPTION:Title: Low Rank Approximation of Multi-Dimensional Data Set f
or Completion\nby Dr. MingQing Xiao (Southern Illinois University) as
part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M212 in
NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nLarge datasets oft
en manifest naturally as multi-dimensional arrays\, commonly referred to a
s tensors. These tensors may represent diverse phenomena\, from sensor mea
surements in scientific experiments to user behavior in recommendation sys
tems. However\, real-world data is rarely perfect\, and incomplete entries
are common due to various reasons such as sensor failures\, missing obser
vations\, or privacy constraints. In this talk\, we introduce a new noncon
vex regularization approach\, which can better capture the low-rank charac
teristics than the convex approach for data completion. A minimization alg
orithm\, associated with the augmented Lagrangian multipliers and the nonc
onvex regularizer\, will be presented.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Fulton Gonzalez (Tufts University)
DTSTART;VALUE=DATE-TIME:20240326T073000Z
DTEND;VALUE=DATE-TIME:20240326T083000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/37
DESCRIPTION:Title: The Snapshot Problem for the Wave Equation\nby Dr.
Fulton Gonzalez (Tufts University) as part of Nonlinear Analysis Seminar
Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Bu
ilding.\n\nAbstract\nBy definition\, a wave is a $C^\\infty$ solution $u(x
\,t)$ of the wave equation on $\\mathbb{R}^n$\, and a snapshot of the wave
$u$ at time $t$ is the function $u_t$ on $\\mathbb{R}^n$ given by $u_t(x
)=u(x\,t)$. We show that there are infinitely many waves with given $C^\\
infty$ snapshots $f_0$ and $f_1$ at times $t=0$ and $t=1$ respectively\, b
ut that all such waves have the same snapshots at integer times. We prese
nt necessary and sufficient conditions for the existence and uniqueness of
a wave $u$ to have three given snapshots at three different times\, and w
e show how this leads to problems in Diophantine approximations and "small
denominators"\, which dates back to the early study of the $n$-body probl
em in $\\mathbb{R}^3$. We consider generalizations to the Euler-Poisson-Da
rboux equation and to modified wave equations on spheres and symmetric spa
ces\, as well as some open questions. \n\n \nJoint with J. Christensen (Co
lgate)\, J. Wang (N. China Inst. of Science & Technology)\, and T. Kakehi
(Tsukuba).\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Oscar Dominguez Bonilla (Cunef Universidad)
DTSTART;VALUE=DATE-TIME:20240402T070000Z
DTEND;VALUE=DATE-TIME:20240402T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/38
DESCRIPTION:Title: Affine fractional Moser-Trudinger and Morrey inequalit
ies\nby Dr. Oscar Dominguez Bonilla (Cunef Universidad) as part of Non
linear Analysis Seminar Series\n\nLecture held in Room 509\, Cosmology Bui
lding\, National Taiwan University.\n\nAbstract\nIn this talk we establish
affine versions of fractional Moser-Trudinger and Morrey inequalities. Th
ese new inequalities are stronger than the affine Moser-Trudinger and Morr
ey inequalities due to Cianchi-Lutwak-Yang-Zhang and complement the affine
fractional Sobolev inequalities of Haddad-Ludwig. This is a joint work wi
th Y. Li\, S. Tikhonov\, D. Yang\, and W. Yuan.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Prasun Roychowdhury (National Center for Theoretical Sciences
Taiwan)
DTSTART;VALUE=DATE-TIME:20240416T070000Z
DTEND;VALUE=DATE-TIME:20240416T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/40
DESCRIPTION:Title: Classification of radial solutions to $-\\Delta_g u =
e^u$ on Riemannian models\nby Dr. Prasun Roychowdhury (National Center
for Theoretical Sciences Taiwan) as part of Nonlinear Analysis Seminar Se
ries\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Buil
ding.\n\nAbstract\nThe talk is devoted to the complete classification with
respect to asymptotic behaviour\, stability\, and intersections propertie
s of radial smooth solutions to the equation $-\\Delta_g u=e^u$ on Riemann
ian model manifolds $(M\,g)$ in dimension $N\\ge 2$. Our assumptions inclu
de Riemannian manifolds with sectional curvatures bounded or unbounded fro
m below. Intersection and stability properties of radial solutions are inf
luenced by the dimension $N$ in the sense that two different kinds of beha
viour occur when $2\\le N\\le 9$ or $N\\ge 10$\, respectively. The crucial
role of these dimensions in classifying solutions is well-known in Euclid
ean space\; here the analysis highlights new properties of solutions that
cannot be observed in the flat case. This is based on a joint work with El
vise Berchio\, Alberto Ferrero\, and Debdip Ganguly.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Robin Neumayer (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20240611T010000Z
DTEND;VALUE=DATE-TIME:20240611T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/41
DESCRIPTION:Title: The Saint-Venant inequality and quantitative resolvent
estimates for the Dirichlet Laplacian\nby Dr. Robin Neumayer (Carnegi
e Mellon University) as part of Nonlinear Analysis Seminar Series\n\nLectu
re held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\nAbst
ract\nAmong all cylindrical beams of a given cross-sectional area\, those
with circular cross sections are the most resistant to twisting forces. Th
e general dimensional analogue of this fact is the Saint-Venant inequality
\, which says that balls have the largest torsional rigidity among subsets
of Euclidean space with a fixed volume. We discuss recent results showing
that for a given set $E$\, the gap in the Saint-Venant inequality quantit
atively controls the $L^2$ difference between solutions of the Poisson equ
ation on $E$ and on the nearest ball\, for any Holder continuous right-han
d side. We additionally prove quantitative closeness of all eigenfunctions
of the Dirichlet Laplacian. This talk is based on joint work with Mark Al
len and Dennis Kriventsov.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Cody Stockdale (Clemson University)
DTSTART;VALUE=DATE-TIME:20240528T070000Z
DTEND;VALUE=DATE-TIME:20240528T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/42
DESCRIPTION:Title: On the theory of compact Calderón-Zygmund operators\nby Dr. Cody Stockdale (Clemson University) as part of Nonlinear Analys
is Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mat
hematics Building.\n\nAbstract\nWe present new developments in the theory
of compact Calderón-Zygmund operators. In particular\, we give a new form
ulation of the $T1$ theorem for compactness of CZ operators\, which\, comp
ared to existing compactness criteria\, more closely resembles David and J
ourné’s classical $T1$ theorem for boundedness and follows from a simpl
er argument. Our methods generalize to treat a class of "localized" operat
ors on a Hilbert space -- we apply this abstraction to characterize the co
mpact pseudodifferential operators on $L^2(\\mathbb{R}^n)$. Additionally\,
we discuss the extension of compact CZ theory to weighted Lebesgue spaces
via sparse domination methods. \n\nThis talk is based on joint works with
Mishko Mitkovski\, Paco Villarroya\, Cody Waters\, and Brett Wick.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ji Li (Macquarie University)
DTSTART;VALUE=DATE-TIME:20240423T073000Z
DTEND;VALUE=DATE-TIME:20240423T083000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/44
DESCRIPTION:Title: Schatten Properties of Calderon–Zygmund Singular Int
egral Commutator on stratified Lie groups\nby Ji Li (Macquarie Univers
ity) as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room
515 in NCTS in NTU.\n\nAbstract\nSchatten class estimates of the commutato
r of Riesz transform in $\\mathbb R^n$ link to the quantised derivative of
A. Connes. A general setting for quantised calculus is a spectral triple
$(\\mathcal A\,\\mathcal H\,D)$\, which consists of a Hilbert space $\\mat
hcal H$\, a pre-$C^*$-algebra $\\mathcal A $\, represented faithfully on $
\\mathcal H$ and a self-adjoint operator $D$ acting on $\\mathcal H$ such
that every $a\\in A$ maps the domain of $D$ into itself and the commutator
$[D\,a] = Da-aD$ extends from the domain of $D$ to a bounded linear endom
orphism of $\\mathcal H$. Here\, the quantised differential $\\qd a$ of $a
\\in \\mathcal A$ is defined to be the bounded operator ${\\rm i} [{\\rm
sgn}(D)\,a]$\, ${\\rm i}^2=-1$. \n\nWe provide full characterisation of th
e Schatten properties of $[M_b\,T]$\, the commutator of Calder\\'{o}n--Zy
gmund singular integral $T$ with symbol $b$ $(M_bf(x):=b(x)f(x))$ on strat
ified Lie groups $\\mathcal G$. We show that\, when $p$ is larger than the
homogeneous dimension $\\mathbb Q$ of $\\mathcal G$\, the Schatten $\\mat
hcal L_p$ norm of the commutator is equivalent to the Besov semi-norm $B_{
p}^{\\mathbb Q/p}$ of the function $b$\; but when $p\\leq \\mathbb Q$\, th
e commutator belongs to $\\mathcal L_p$ if and only if $b$ is a constant.
For the endpoint case at the critical index $p=\\mathbb Q$\, we further sh
ow that the Schatten $\\mathcal L_{\\mathbb Q\,\\infty}$ norm of the commu
tator is equivalent to the Sobolev norm $\\dot{W}^{1\,\\mathbb Q}$ of $b$.
Our method at the endpoint case differs from existing methods of Fourier
transforms or trace formula for Euclidean spaces or Heisenberg groups\, re
spectively.\n\nThis talk is based on my recent work joint with Xiao Xiong
and Fulin Yang.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. You Wei-Chen (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20240430T070000Z
DTEND;VALUE=DATE-TIME:20240430T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/45
DESCRIPTION:Title: A self-improving property of Riesz potentials in BMO\nby Dr. You Wei-Chen (National Taiwan University) as part of Nonlinear
Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Camp
us Mathematics Building.\n\nAbstract\nIn this talk\, we introduce the conc
ept of beta-dimensional BMO space \\( BMO^\\beta \\) and the associated Jo
hn-Nirenberg inequality. We will discuss the mapping properties of Riesz p
otentials within \\(BMO^\\beta\\) spaces\, focusing specifically on the Mo
rrey spaces and weak Lebesgue spaces \\(L^{n/ \\alpha\,\\infty} (\\mathbb{
R}^n)\\). Additionally\, we present that \\( I_\\alpha f \\in BMO^{n-\\al
pha + \\epsilon} \\) is actually a necessary and sufficient condition for
\\( I_\\alpha f \\in BMO \\) when \\( f \\) is a non-negative function.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Bogdan Raita (Georgetown University)
DTSTART;VALUE=DATE-TIME:20240618T073000Z
DTEND;VALUE=DATE-TIME:20240618T083000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/46
DESCRIPTION:Title: Self improving size estimates in compensated compactne
ss\nby Dr. Bogdan Raita (Georgetown University) as part of Nonlinear A
nalysis Seminar Series\n\nLecture held in Room 509\, Cosmology Building\,
National Taiwan University.\n\nAbstract\nWe review some recent results in
compensated compactness\, concerning primarily concentration effects of pd
e constrained sequences. We show that Müller's $L\\log L$ bound \n $$\n
\\Phi(Du)\\geq 0\,\\\,Du\\in L^q(\\mathbb{R}^n)\\implies \\Phi(Du)\\in
L\\log L_{loc}\n$$\n for $\\Phi =\\det$ and $q=n$ holds for quasiconcav
e $\\Phi$ which are homogeneous of degree $q>1$. This contrasts similar Ha
rdy bounds which hold only for null Lagrangians.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. José Carlos Bellido (Universidad de Castilla-La Mancha)
DTSTART;VALUE=DATE-TIME:20240507T070000Z
DTEND;VALUE=DATE-TIME:20240507T080000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/47
DESCRIPTION:Title: Nonlocal gradients and applications to Continuum Mecha
nics\nby Dr. José Carlos Bellido (Universidad de Castilla-La Mancha)
as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210
in NTNU Gongguan Campus Mathematics Building.\n\nAbstract\nThis presentati
on collects joint work with C. Mora-Corral\, J. Cueto\, H. Schönberger\,
P. Radu and M. Foss. \n\nInterest in nonlocal gradients has increased in t
he last decades due to development of nonlocal modeling in a variety of fi
elds\, including mechanics and materials science. We start by defining non
local gradients in a general context\, where their calculation depends on
a general kernel. Our goal is to explore the structural properties of spac
es associated with these gradients. From a functional analysis perspective
\, we seek kernels that make these spaces useful for studying variational
problems and\, consequently\, applicable to physical models. Beyond the th
eoretical groundwork\, we delve into the mathematical intricacies of these
new functional spaces. These spaces are essential for understanding nonlo
cal phenomena and capturing behavior that local models might miss. Nonloca
l gradients find practical applications in solid mechanics\, particularly
in finite elasticity. Additionally\, we establish connections between non
local models derived from nonlinearly elastic models and the well-known Er
ingen’s nonlocal model of linear elasticity. Remarkably\, these solid me
chanics models can be seen as a special case of state-based peridynamics\,
a continuum theory designed to address material failure where classical e
lasticity theories fall short.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Riju Basak (National Taiwan Normal University)
DTSTART;VALUE=DATE-TIME:20240514T073000Z
DTEND;VALUE=DATE-TIME:20240514T083000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/48
DESCRIPTION:Title: Wave equation on Hardy spaces\nby Dr. Riju Basak (
National Taiwan Normal University) as part of Nonlinear Analysis Seminar S
eries\n\nLecture held in Room 509\, Cosmology Building\, National Taiwan U
niversity.\n\nAbstract\nThe sharp fixed-time estimates for the solution of
the Cauchy problem associated with the standard Euclidean Laplacian on Le
besgue and Hardy spaces were first studied independently by A. Miyachi and
J.C. Peral in 1980. However\, the sharp fixed-time estimate is still not
available for many operators\, especially on Hardy spaces for $0< p <1 $.
\n\nIn this talk\, we shall discuss fixed-time estimates for the solution
of the wave equation associated with the twisted Laplacian. This talk is b
ased on a joint work with K. Jotsaroop.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Eitan Tadmor (University of Maryland\, College Park)
DTSTART;VALUE=DATE-TIME:20241119T010000Z
DTEND;VALUE=DATE-TIME:20241119T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/49
DESCRIPTION:by Prof. Eitan Tadmor (University of Maryland\, College Park)
as part of Nonlinear Analysis Seminar Series\n\nLecture held in Room M210
in NTNU Gongguan Campus Mathematics Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Diego Cordoba (ICMAT)
DTSTART;VALUE=DATE-TIME:20241008T073000Z
DTEND;VALUE=DATE-TIME:20241008T083000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/50
DESCRIPTION:Title: Finite time blow-up for the hypodissipative Navier Sto
kes equations\nby Prof. Diego Cordoba (ICMAT) as part of Nonlinear Ana
lysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus
Mathematics Building.\n\nAbstract\nIn this talk we establish the formation
of singularities of classical solutions with finite energy of the forced
fractional Navier Stokes equations where the dissipative term is given by
$|\\nabla|^{\\alpha}$ for any $\\alpha\\in [0\, \\alpha_0)$ ($\\alpha_0 =
0.09\\cdots$).\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Yoshihiro Sawano (Chuo University)
DTSTART;VALUE=DATE-TIME:20240910T010000Z
DTEND;VALUE=DATE-TIME:20240910T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/51
DESCRIPTION:Title: A norm close to the $L^1$-norm\nby Prof. Yoshihiro
Sawano (Chuo University) as part of Nonlinear Analysis Seminar Series\n\n
Lecture held in Room M210 in NTNU Gongguan Campus Mathematics Building.\n\
nAbstract\nAround 10 years ago\, Armin Schikorra\, Daniel Spector\, Jean V
an Schaftingen pointed out that there exists a variant of the boundedness
of the Riesz potential $I_\\alpha$ which maps $L^1$ to weak $L^{\\frac{n}{
n-\\alpha}}$. The goal of this talk is to extend it to Morrey spaces. Some
variants as well as the proof will be discussed. This is a joint work wit
h Denny Ivanal Hakim and Mei Dita Kumala at Bandung Institute Technology.\
n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Blake Temple (UC Davis)
DTSTART;VALUE=DATE-TIME:20241015T010000Z
DTEND;VALUE=DATE-TIME:20241015T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/52
DESCRIPTION:Title: On the Essential Regularity of Singular Connections in
Geometry\nby Prof. Blake Temple (UC Davis) as part of Nonlinear Analy
sis Seminar Series\n\nLecture held in Room M212 in NTNU Gongguan Campus Ma
thematics Building.\n\nAbstract\nAuthor together with collaborator Moritz
Reintjes recently introduced the Regularity Transformation Equations (RT-e
quations)\, an elliptic\, non-invariant system of equations which determin
e the Jacobians of coordinate transformations which (locally) lift the reg
ularity of a connection to one derivative above the regularity of its Riem
ann curvature tensor. Our existence theory for the RT-equations generali
ze celebrated results of Kazden-DeTurck\, valid for Riemannian metrics\, t
o arbitrary non-Riemannian connections\, including the metrics and connect
ions of General Relativity. Authors have found applications of the RT-eq
uations\, including extending Uhlenbeck compactness from Riemannian to non
-Riemannian connections on vector bundles\, extending existence and unique
ness of ODEs one derivative below the threshold for Picard's method\, and
an application to the Strong Cosmic Censorship Conjecture (Reintjes). In
this talk I discuss our forthcoming paper in which we use the theory of t
he RT-equations to give a necessary and sufficient condition for determini
ng when a singularity appearing in a connection or metric in geometry can
be regularized by coordinate transformation\; we establish the consistency
of the $\\textit{essential}$\, highest possible regularity to which a sin
gular connection can be regularized by coordinate transformation\; and we
describe an explicit procedure (based in the RT-equations) for constructin
g the coordinate transformations which lift a singular connection to its e
ssential regularity. Results apply both locally and globally\, and we sho
w that there always exists a maximal $C^\\infty$ atlas on a manifold which
globally preserves the essential regularity of any connection. Our neces
sary and sufficient condition relies on our existence theory for the RT-eq
uations which we currently require connection regularity in $L^p$\, $p>n$\
, sufficient to address shock wave singularities in GR\, but not yet black
hole singularities. Extending our existence theory to the case $p\\verb+
<+n$ is an important topic of authors' current research.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Simon Bortz (University of Alabama)
DTSTART;VALUE=DATE-TIME:20241022T010000Z
DTEND;VALUE=DATE-TIME:20241022T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/53
DESCRIPTION:Title: Regularity of Co-normal Derivatives and Weights\nb
y Prof. Simon Bortz (University of Alabama) as part of Nonlinear Analysis
Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathem
atics Building.\n\nAbstract\nThis talk is concerned with the properties of
the co-normal derivative of (adjoint) solutions to elliptic and parabolic
PDEs in divergence form\, that is\, $Lu = -div A \\nabla u = 0$ or $L = -
\\partial_t u - div A \\nabla u = 0$ in some domain $\\Omega$. Specificall
y\, the properties of co-normal derivative on a subset of the boundary wh
ere the solution $u$ vanishes. A prototypical situation is when $\\Omega$
is the upper half space ($\\{(x\,\\lambda) : x \\in \\mathbb{R}^n\, \\lamb
da > 0\\}$ or $\\{(t\,x\,\\lambda) : t\\in \\mathbb{R}\, x \\in \\mathbb{R
}^n\, \\lambda > 0\\}$) and $u$ is the Green function of $L$ with pole at
infinity and\, in that case\, the co-normal derivative is the elliptic/par
abolic measure. \n\nIn this talk\, I will introduce the co-normal derivati
ve and discuss some sufficient conditions on the coefficients $A$ for the
co-normal derivative to be quantitatively absolutely continuous with respe
ct to surface measure or even have a density that is $\\dot{C}^\\alpha_{lo
c}$ (locally H\\"older continuous) on the boundary. The method will unify
these regimes\, by refining the work of David\, Li and Mayboroda and combi
ning it with some of my recent work with Toro and Zhao\, and Egert and Saa
ri. For simplicity\, in the talk $\\Omega$ will be assumed to be the upper
half space\, but more exotic domains can be considered.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Reinaldo Resende (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20241001T010000Z
DTEND;VALUE=DATE-TIME:20241001T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/55
DESCRIPTION:Title: Regularity results for area minimizing currents\nb
y Dr. Reinaldo Resende (Carnegie Mellon University) as part of Nonlinear A
nalysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongguan Campu
s Mathematics Building.\n\nAbstract\nWe will explore exciting new results
on the interior and boundary regularity of currents $T$ solving the orient
ed Plateau’s problem\, with a special focus on higher codimensions. We w
ill extend well-known estimates concerning the Hausdorff dimension of the
interior singular set of $T$ to a broader context\, and also share results
from an upcoming work that optimally resolves several long-standing open
questions on boundary regularity. Additionally\, we’ll discuss recent ad
vancements in the rectifiability of the singular set and\, if time permits
\, review the general proof strategy for these regularity results using mu
ltivalued functions and the frequency function.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Willie Wong (Michigan State University)
DTSTART;VALUE=DATE-TIME:20241126T010000Z
DTEND;VALUE=DATE-TIME:20241126T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/56
DESCRIPTION:by Prof. Willie Wong (Michigan State University) as part of No
nlinear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gongg
uan Campus Mathematics Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Thomas Hou (Caltech)
DTSTART;VALUE=DATE-TIME:20241105T010000Z
DTEND;VALUE=DATE-TIME:20241105T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/57
DESCRIPTION:by Prof. Thomas Hou (Caltech) as part of Nonlinear Analysis Se
minar Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathemat
ics Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Luis Silvestre (University of Chicago)
DTSTART;VALUE=DATE-TIME:20241029T010000Z
DTEND;VALUE=DATE-TIME:20241029T020000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/58
DESCRIPTION:Title: The Landau equation does not blow up\nby Prof. Lui
s Silvestre (University of Chicago) as part of Nonlinear Analysis Seminar
Series\n\nLecture held in Room M210 in NTNU Gongguan Campus Mathematics Bu
ilding.\n\nAbstract\nThe Landau equation is one of the main equations in k
inetic theory. It models the evolution of the density of particles when th
ey are assumed to repel each other by Coulomb potentials. It is a limit ca
se of the Boltzmann equation with very soft potentials. In the space-homog
eneous case\, we show that the Fisher information is monotone decreasing i
n time. As a consequence\, we deduce that for any initial data the solutio
ns stay smooth and never blow up\, closing a well-known open problem in th
e area.\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Thomas Schmidt (University of Hamburg)
DTSTART;VALUE=DATE-TIME:20241112T073000Z
DTEND;VALUE=DATE-TIME:20241112T083000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/59
DESCRIPTION:by Prof. Thomas Schmidt (University of Hamburg) as part of Non
linear Analysis Seminar Series\n\nLecture held in Room M210 in NTNU Gonggu
an Campus Mathematics Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prof. Franz Gmeineder (University of Konstanz)
DTSTART;VALUE=DATE-TIME:20241203T073000Z
DTEND;VALUE=DATE-TIME:20241203T083000Z
DTSTAMP;VALUE=DATE-TIME:20241016T071748Z
UID:Nonlinear_Analysis_Seminar/60
DESCRIPTION:by Prof. Franz Gmeineder (University of Konstanz) as part of N
onlinear Analysis Seminar Series\n\nLecture held in Room M212 in NTNU Gong
guan Campus Mathematics Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Nonlinear_Analysis_Seminar/60/
END:VEVENT
END:VCALENDAR