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BEGIN:VEVENT
SUMMARY:Zhen-Chun Chen (National Taiwan Ocean University)
DTSTART:20230913T060000Z
DTEND:20230913T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/1
DESCRIPTION:Title: 數學力學與計算-邊界元走過四十年\nby Zhen-Chun Ch
en (National Taiwan Ocean University) as part of Trends in Mathematical Re
search\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\n有幸自1983
年在台大土木接觸結構學中的影響線，後經修習物理數
學方知那是格林函數的一種。1984年第一屆應力所林紹雄
教授開授的應用數學課程讓本人對於勢能理論有了更深
入的了解，於碩(1984-1986)博士(1990-1994)論文議題也是圍繞
著邊界元與積分方程。講者有幸在1986-1990年間到中山科
學研究院二所三組服務，有機會將所發展的對偶邊界元
素法應用在火箭、飛彈與飛機的氣動力與結構應力分析
方面，讓超奇異積分方程與Hadamard有限部(finite part)不再
那麼不可親近。\n\n2003年李明恭主任所主辦的台灣計算數
學研討會在林文偉教授與劉晉良教授的推薦下，本人得
以Plenary lecture進行大會報告，將我們在工程應用時所需
要學習與用到的數學進行介紹並得以解決實際工程問題
分享給數學界的朋友，交流過程中個人收穫良多並受到
啟發。本演講擬從數學力學與計算的角度檢視四十年來
邊界元所呈現的Paradise\, Parasite與Paradox的三種面相和個人
感受與體會，並以蘇東坡的一首詩〈觀潮〉\n\n廬山煙雨
浙江潮，未到千般恨不消。\n到得還來別無事，廬山煙雨
浙江潮。\n\n作為結語，從看山是山，進而看山不是山到
終究看山又是山的心境分享，野人獻曝與數學力學界的
朋友們交流與切磋。\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shu-Cheng Chang (National Taiwan University)
DTSTART:20230920T060000Z
DTEND:20230920T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/2
DESCRIPTION:Title: From Thurston Geometrization Conjecture to Mori Minimal Model Progr
am\nby Shu-Cheng Chang (National Taiwan University) as part of Trends
in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstrac
t\nA central problem of differential geometry is the geometrization proble
m on manifolds. In particular\, it is to determine which manifolds admit c
ertain geometric structures. One of methods is to understand and classify
the singularity models of the corresponding nonlinear geometric evolution
equation\, and to connect it to the existence problem of geometric structu
res on manifolds. \n In 1982\, R. Hamilton introduced the Ricci flow an
d then by studying the singularity models of Ricci flow\, G. Perelman comp
letely solved Thurston geometrization conjecture and Poincare conjecture f
or a closed 3-manifold in 2002 and 2003.\n On the other hand\, Mori min
imal model program in birational geometry can be viewed as the complex ana
logue of Thurston's geometrization conjecture. In 1985\, H.-D. Cao introdu
ced the Kähler-Ricci flow and then recaptured the Calabi-Yau Conjecture.
Moreover\, there is a conjecture picture by Song-Tian that the Kähler-Ri
cci flow should carry out the analytic minimal model program with scaling
on projective varieties. Recently\, Song-Weinkove established the above co
njecture on a projective algebraic surface. Furthermore\, via the Sasaki-R
icci flow\, Chang-Lin-Wu proved the Sasaki analogue of minimal model progr
am on closed quasi-regular Sasakian 5-manifolds.\n In this lecture\, I w
ill address the above issues in some detail.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Duncan (Academia Sinica)
DTSTART:20231004T060000Z
DTEND:20231004T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/3
DESCRIPTION:Title: A Guide to Moonshine\nby John Duncan (Academia Sinica) as part
of Trends in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\
n\nAbstract\nAndrew Ogg gave a geometric description of the primes that di
vide the order of the monster finite simple group in 1973\, and thus initi
ated the theory of monstrous moonshine. Since then\, the pursuit of moonsh
ine has illuminated powerful relationships between algebraic\, geometric a
nd number theoretic structures. We will present an introductory overview o
f this theory.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Payne (National Taiwan University)
DTSTART:20231018T060000Z
DTEND:20231018T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/4
DESCRIPTION:Title: Multi-scale\, multi-compartment modelling of the human brain\nb
y Stephen Payne (National Taiwan University) as part of Trends in Mathemat
ical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nThe incr
easing rates of cerebrovascular diseases\, such as stroke and dementia\, m
ean that understanding cerebral blood flow and its control in both healthy
and diseased states has become an important clinical problem. However thi
s is made challenging by the spatial and temporal limitations of human bra
in imaging and the number of blood vessels involved in a what is a highly
complex dynamic regulating system over many length scales. In this talk I
will discuss the work that we have done to construct models of cerebral bl
ood flow that cover the many length scales involved\, running from a few m
icrometres to a few millimetres. I will show how we have developed such mo
dels from the bottom up\, through highly detailed modelling of the microci
rculation and the application of homogenisation and optimisation methods\,
in order to generate a full-brain model of blood flow and oxygen transpor
t. I will then talk about how this can be applied (and validated) in patho
logical conditions\, in particular the treatment of acute ischaemic stroke
. I will conclude by discussing how we next plan to use multiple time scal
es in the context of chronic diseases such as dementia and to quantify the
effects of interventions such as sleep and exercise on disease progressio
n.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuh-Jye Lee (Academia Sinica)
DTSTART:20231025T060000Z
DTEND:20231025T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/5
DESCRIPTION:Title: Federated Learning for Sparse Principal Component Analysis\nby
Yuh-Jye Lee (Academia Sinica) as part of Trends in Mathematical Research\n
\nLecture held in NTNU Gongguan S101.\n\nAbstract\nIn the rapidly evolving
realm of machine learning\, algorithm effectiveness often faces limitatio
ns due to data quality and availability. Traditional approaches grapple wi
th data sharing due to legal and privacy concerns. The federated learning
framework addresses this challenge. Federated learning is a decentralized
approach where model training occurs on client sides\, preserving privacy
by keeping data localized. Instead of sending raw data to a central server
\, only model updates are exchanged\, enhancing data security. We apply th
is framework to Sparse Principal Component Analysis (SPCA) in this work. S
PCA aims to attain sparse component loading while maximizing data variance
for improved interpretability. We introduce a least squares approximation
to original PCA\, adding an $\\ell_1$ norm regularization term to enhance
principal component sparsity\, aiding variable identification and interpr
etability. The problem is formulated as a consensus optimization challenge
and solved using the Alternating Direction Method of Multipliers (ADMM).
Our extensive experiments involve both IID and non-IID random features acr
oss various data owners. Results on synthetic and public datasets affirm t
he efficacy of our federated SPCA approach.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyung-Youn Kim (National Chung Hsing University)
DTSTART:20231101T060000Z
DTEND:20231101T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/6
DESCRIPTION:Title: Potential theory of anisotropic Markov processes\nby Kyung-Youn
Kim (National Chung Hsing University) as part of Trends in Mathematical R
esearch\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nHeat kernel is
the fundamental solution of the heat equation\, and it is also the transi
tion density of the diffusion process corresponding to the Laplacian. Thes
e relation is also ture for non-local operators\, and corresponding proces
s is a discontinuous Markov process. \nIn this talk\, we consider anisotr
opic Markov processes.\nLet $L_i$\, $i=1\,\\ldots\,d$\, be identical and i
ndependent $1$-dimensional L\\'evy processes.\nDefine a Markov process $M:
=(M_1\, \\ldots\, M_d)$ whose jumping kernel is comparable to that of $L:=
(L_1\, \\ldots\, L_d)$.\nThen $M$ is a pure jump process that jumps parall
el to the coordinate axes.\nWe discuss the sharp two-sided heat kernel bou
nds for $M$ on $C^{1\,1}$ open set $D\\subset {\\rm I\\!R}^d$ as well as t
he potential theory of anisotropic Markov process. This is the joint work
with Lidan Wang.\n \n\n\n[1.] Dirichlet Heat kernel estimates for a large
class of anisotropic Markov process(with Lidan Wang).\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA (TBA)
DTSTART:20230927T060000Z
DTEND:20230927T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/7
DESCRIPTION:by TBA (TBA) as part of Trends in Mathematical Research\n\nLec
ture held in NTNU Gongguan S101.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shagnik Das (National Taiwan University)
DTSTART:20231011T060000Z
DTEND:20231011T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/8
DESCRIPTION:Title: Covering grids with multiplicity\nby Shagnik Das (National Taiw
an University) as part of Trends in Mathematical Research\n\nLecture held
in NTNU Gongguan S101.\n\nAbstract\nIt is a fairly simple exercise to dete
rmine the minimum number of hyperplanes needed to cover all the points of
a finite grid $S_1$ x $S_2$ x ... x $S_d \\in \\mathbb{F}^d$. However\, th
e situation becomes much more complex if you add the condition that one of
the points of the grid must be avoided\, leading to a classic problem in
combinatorial geometry. This was resolved by Alon and Füredi in a classic
result that popularised the use of algebraic methods in combinatorics.\n\
nRecent work of Clifton and Huang\, in which they considered the question
a variant of the problem where the nonzero points of a hypercube should be
covered multiple times while avoiding the origin\, brought renewed intere
st to this problem. In addition to Alon-Füredi-style algebraic arguments\
, they used linear programming to asymptotically resolve the problem in ce
rtain ranges.\n\nDespite all the attention this problem has received\, the
re remain many open problems\, even in the case of two-dimensional grids o
ver $\\mathbb{R}$. In this talk\, after surveying the background and intro
ducing the techniques used\, we shall present some recent results that res
olve the problem for almost all two-dimensional grids.\n\nThe new results
are joint work with Anurag Bishnoi\, Simona Boyadzhiyska and Yvonne den Ba
kker\, and separately with Valjakas Djaljapayan\, Yen-Chi Roger Lin and We
i-Hsuan Yu.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART:20231108T060000Z
DTEND:20231108T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/9
DESCRIPTION:Title: The derived Bézout theorem\nby Adeel Khan (Academia Sinica) as
part of Trends in Mathematical Research\n\nLecture held in NTNU Gongguan
S101.\n\nAbstract\nGiven two smooth algebraic curves of degrees $d$ and $e
$ in the complex projective plane\, Bezout’s theorem is a classical resu
lt asserting that the intersection consists of either infinitely many or e
xactly $d\\cdot e$ points\, counted with multiplicities. Generalizing thi
s formula to intersections in higher-dimensional projective space was a ta
sk that fuelled much of 20th century algebraic geometry\, eventually culmi
nating in J.-P. Serre’s solution in 1958.\n\nWe will review some of this
history before presenting a 21st century point of view on Bézout’s the
orem. Specifically\, we will see that the modern language of derived alge
braic geometry allows us to give a simple definition of intersection multi
plicities\, which unlike Serre’s formula applies even to non-proper inte
rsections\, and yields a vast generalization of Bézout theorem for arbitr
ary intersections of projective hypersurfaces.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Fuchs (National Chengchi University)
DTSTART:20231129T060000Z
DTEND:20231129T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/10
DESCRIPTION:Title: Gene-tree statistics: moments and limit laws for ancestral configu
rations\nby Michael Fuchs (National Chengchi University) as part of Tr
ends in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAb
stract\nFor a given species tree\, ancestral configurations are the gene l
ineages which can be present at a node of the species tree over the set of
all gene trees. Root ancestral configurations are the ancestral configura
tions which are present at the root. They play an important role in a (sta
ndard) algorithm for computing probabilities of gene trees that have evolv
ed within the given species tree. In particular\, their number is a measur
e for the complexity of this algorithm. In this talk\, we give background\
, review recent results about the number of ancestral configurations and r
oot ancestral configurations for matching species and gene trees under the
uniform and Yule Harding model\, and explain our recent refinements of t
hese results which concern moments and limit laws. The talk is based on jo
int work with F. Disanto (University of Pisa)\, A. R. Paningbatan (Univers
ity of the Philippines Diliman)\, C.-Y. Huang (National Chiao Tung Univers
ity)\, and N. A. Rosenberg (Stanford University).\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melaine Saillenfest (IMCCE\, Observatoire de Paris\, France)
DTSTART:20231206T060000Z
DTEND:20231206T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/11
DESCRIPTION:Title: Coevolution of moons and the spin axis of their host planet\nb
y Melaine Saillenfest (IMCCE\, Observatoire de Paris\, France) as part of
Trends in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\n
Abstract\nAstrometric observations of the moons of Jupiter and Saturn have
revealed that their orbits expand over time faster than previously though
t. This significant orbital "migration" implies that efficient mechanisms
of tidal energy dissipation are at play in the interiors of gaseous planet
s. These findings profoundly affect our understanding of the formation and
evolution of moons\, but also of the spin-axis dynamics of their host pla
net. The coupling between the planet's spin-axis dynamics (the "Cassini st
ates") and the moons' orbital dynamics (the "Laplace plane") can gradually
tilt the planet and make the system converge to a highly unstable configu
ration. This mechanism has direct applications in the Solar system: Jupite
r today is about to start the tilting phase\, Saturn is probably halfway i
n\, and Uranus may have completed the final unstable stage.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Tai Fang (National Taiwan University)
DTSTART:20231122T060000Z
DTEND:20231122T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/12
DESCRIPTION:Title: 防疫的數學–基礎再生數 R0\nby Chi-Tai Fang (Nationa
l Taiwan University) as part of Trends in Mathematical Research\n\nLecture
held in NTNU Gongguan S101.\n\nAbstract\n• 數學與防疫\n• Basic R
eproductive Number R0\n• 運用數學在疫苗全面接種前控制疫
情\n• 傳染病學學分學程數理建模組說明\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Feng-Bin Wang (Division of Natural Science\, Center for Genera
l Education\, Chang Gung University\, Taiwan)
DTSTART:20240221T060000Z
DTEND:20240221T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/13
DESCRIPTION:Title: A nonlocal reaction diffusion model of West Nile virus with vertic
al transmission\nby Dr. Feng-Bin Wang (Division of Natural Science\, C
enter for General Education\, Chang Gung University\, Taiwan) as part of T
rends in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nA
bstract\nWest Nile virus (WNv) is a mosquito-borne infection\, causing hea
lth challenges to bird\nand human populations. In this talk\, I plan to pr
opose a general nonlocal reaction-diffusion model to explore\nthe combined
effect of alternative hosts\, vector-host movement and spatial-temporal e
nvironmental\nstructure on WNv transmission dynamics. The model is partial
ly degenerate and\nits solution maps lack compactness due to the absence o
f diffusion terms in larval equations.\nFor this tightly coupled disease m
odel\, we introduce the mosquito reproduction number \nand WNv reproductio
n number\, respectively\, and further show that these two aforementioned\n
reproduction numbers completely determine the threshold behaviour of the d
isease\nspread. Numerical simulations support our analytic results and sug
gest that environmental\nheterogeneity plays an important role in shaping
WNv dynamics. Moreover\, bird migration may increase the disease risk.\n\n
This talk is based on a joint work with Drs. Ruiwen Wu and Xiao-Qiang Zhao
.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nguyễn Lê Trâm (National Taiwan Normal University)
DTSTART:20231115T060000Z
DTEND:20231115T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/14
DESCRIPTION:Title: Interval Valued Optimization Problems on Hadamard Manifolds\nb
y Nguyễn Lê Trâm (National Taiwan Normal University) as part of Trends
in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstra
ct\nIn this talk\, we will introduce the interval optimization problems (I
OPs)\non Hadamard manifolds. To achieve the theoretical results\, we build
up some new concepts about gH-directional derivative\, gH-Gateaux and gH-
Frechet differentiability of interval valued functions and their propertie
s on Hadamard manifolds. More specifically\, we characterize the optimalit
y conditions for the IOPs on the Hadamard manifolds. For unconstrained pro
blems\, the existence of efficient points and the steepest descent algorit
hm are investigated. To the contrast\, the KKT conditions and exact penalt
y approach are explored in the ones involving inequality constraints. The
obtained results pave a way to further study on Riemannian interval optimi
zation\nproblems (RIOPs).\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Cruz-Uribe (University of Alabama)
DTSTART:20231213T060000Z
DTEND:20231213T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/15
DESCRIPTION:Title: Norm inequalities for linear and multilinear singular integrals on
weighted and variable exponent Hardy spaces\nby David Cruz-Uribe (Uni
versity of Alabama) as part of Trends in Mathematical Research\n\nLecture
held in NTNU Gongguan S101.\n\nAbstract\nI will discuss a (relatively) new
approach\nto norm inequalities in the weighted and variable exponent Hard
y\nspaces. The weighted Hardy spaces $H^p(w)$\, $p>0$\, where $w$ is a\nM
uckenhoupt weight\, were first considered by Stromberg and Torchinsky\nin
the 1980s. The variable Lebesgue space $L^{p(\\cdot)}$ is\,\nintuitively\
, a classical Lebesgue space with the constant exponent $p$\nreplaced by a
n exponent function $p(\\cdot)$. They have been studied\nextensively for
the last 30 years. The corresponding variable Hardy\nspaces $H^{p(\\cdot)
}$ were introduced by me and Li-An Wang and\nindependently by Nakai and Sa
wano.\n\nWe give inter-related conditions\non a Calderon-Zygmund singular
integral operator $T$\, a weight $w$\,\nand an exponent $p(\\cdot)$ for $T
$ to satisfy estimates of the\nform$$ T : H^p(w) \\rightarrow L^p(w)\, \\q
quad T: H^{p(\\cdot)}\n\\rightarrow L^{p(\\cdot)}.$$ Some of our results w
ere known for\nconvolution type singular integrals\, but we give new and s
impler\nproofs and give extensions to non-convolution type operators. Our
\nproofs depend very heavily on three tools: atomic decompositions of\nthe
Hardy spaces\, vector-valued inequalities\, and the Rubio de Francia\nthe
ory of extrapolation.\n\nWe will also discuss generalizations of these\nre
sults to the bilinear setting\, where we prove norm inequalities of\nthe f
orm\n$$ T: H^{p_1}(w_1) \\times H^{p_2}(w_2) \\rightarrow L^p(w)\, $$\nwh
ere $T$ is a bilinear Calder\\'on-Zygmund singular integral operator\,\n$p
\,\\\,p_1\,\\\,p_2>0$ and \n$$ \\frac{1}{p_1}+\\frac{1}{p_2} = \\frac{1}{p
}\, $$\nand the weights $w\,\\\,w_1\,\\\,w_2$ are Muckenhoupt weights.\nWe
also consider norm inequalities of the form\n$$ T: H^{p_1(\\cdot)}\\time
s H^{p_2(\\cdot)}\\rightarrow L^{p(\\cdot)}. $$\n\nThis is joint work with
Kabe Moen and Hanh Nguyen of the University of\nAlabama.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Jan Harold Alcantara (RIKEN\, Japan)
DTSTART:20240227T060000Z
DTEND:20240227T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/16
DESCRIPTION:Title: Theoretical smoothing frameworks for nonsmooth bilevel optimizatio
n problems\nby Dr. Jan Harold Alcantara (RIKEN\, Japan) as part of Tre
nds in Mathematical Research\n\nLecture held in NTNU Gongguan S506.\n\nAbs
tract\nThe optimal value function approach provides a useful reformulation
of the bilevel optimization problem\, but its utility is often hindered b
y the nonsmoothness of the value function even in cases when the associate
d lower-level function is smooth. In this talk\, we present two smoothing
strategies for the value function associated with lower-level functions th
at are not necessarily smooth but are Lipschitz continuous. The first meth
od employs a quadratic regularization approach for partially convex lower-
level functions\, while the second utilizes entropic regularization for ge
neral lower-level objective functions. Meanwhile\, the property known as g
radient consistency is crucial in ensuring that a designed smoothing algor
ithm is globally subsequentially convergent to stationary points of the eq
uivalent reformulation of the bilevel problem. With this in mind\, we show
that the proposed smooth approximations satisfy the gradient consistent p
roperty under certain conditions on the lower-level function.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Anastasia Molchanova (University of Vienna)
DTSTART:20240320T060000Z
DTEND:20240320T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/18
DESCRIPTION:Title: Lavrentiev Phenomenon in Nonlinear Elasticity\nby Dr. Anastasi
a Molchanova (University of Vienna) as part of Trends in Mathematical Rese
arch\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nIn the calculus o
f variations\, Lavrentiev's phenomenon refers to the situation when the mi
nimum value of a certain functional varies significantly depending on the
space of functions considered.\nIn this talk\, we present a new example of
Lavrentiev's phenomenon in the context of nonlinear elasticity. This exam
ple is based on an interplay of the elastic energy’s resistance to infin
ite compression and the Ciarlet–Necas condition\, a constraint preventin
g global interpenetration of matter on sets of full measure.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Chun-Yen Shen (National Taiwan University)
DTSTART:20240327T060000Z
DTEND:20240327T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/19
DESCRIPTION:Title: Discretized Sum-Product and Geometric Measure Theory\nby Dr. C
hun-Yen Shen (National Taiwan University) as part of Trends in Mathematica
l Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nIn this tal
k\, I will first briefly review the history of sum-product estimates in th
e setting of finite fields and mention the applications of sum-product typ
e problems. Then I will start introducing the celebrated result of Bourgai
n about the discretized sum-product estimates and the applications to geom
etric measure theory problems. Finally I will talk about our recent result
s about expanding polynomials in terms of Hausdorff dimension and discuss
their sum-product phenomena.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Yi-Hsuan Lin (National Yang Ming Chiao Tung University)
DTSTART:20240313T060000Z
DTEND:20240313T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/20
DESCRIPTION:Title: Nonlocality helps\nby Dr. Yi-Hsuan Lin (National Yang Ming Chi
ao Tung University) as part of Trends in Mathematical Research\n\nLecture
held in NTNU Gongguan S101.\n\nAbstract\nIn this talk\, we will review sev
eral nonlocal inverse problems\, and explain how nonlocality helps us to s
olve related inverse problems.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Mei-Heng Yueh (National Taiwan Normal University)
DTSTART:20240306T060000Z
DTEND:20240306T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/21
DESCRIPTION:Title: Theoretical Foundation of the Stretch Energy Minimization for Area
-Preserving Simplicial Mappings\nby Dr. Mei-Heng Yueh (National Taiwan
Normal University) as part of Trends in Mathematical Research\n\nLecture
held in NTNU Gongguan S101.\n\nAbstract\nThe stretch energy is an energy f
unctional particularly defined for the measurement of the area distortion
for simplicial mapping\, which has been applied to efficiently compute are
a-preserving parameterizations of simplicial surfaces. The stretch energy
has a nice geometric interpretation that is helpful for the generalization
of the functional to higher dimensional manifold mappings. On the applica
tion aspect\, parameterizations of simplicial surfaces have been widely ap
plied in computer graphics that aim to efficiently compute a diffeomorphis
m between a simplicial surface and a canonical domain. This provides the s
urface with a unified coordinate system that simplifies various image and
geometry processing tasks such as alignment and blending of images and sur
faces. In this talk\, I will introduce the theoretical foundation of stret
ch energy minimization for the computation of area-preserving parameteriza
tions of simplicial surfaces. Applications in image and surface blending a
nd area-preserving deformations will be demonstrated to highlight the prac
tical utility of the parameterizations.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Oscar Dominguez Bonilla (Cunef Universidad)
DTSTART:20240403T060000Z
DTEND:20240403T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/22
DESCRIPTION:Title: Energy conservation of Euler solutions via sparseness\nby Dr.
Oscar Dominguez Bonilla (Cunef Universidad) as part of Trends in Mathemati
cal Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nA friendl
y introduction to new tools we use to study energy conservation of solutio
ns to Euler equations of fluid dynamics. In particular\, we develop sparse
decompositions and extrapolation techniques. The talk is based on joint w
ork with M. Milman.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Hao-Wei Huang (National Tsing Hua University)
DTSTART:20240515T060000Z
DTEND:20240515T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/23
DESCRIPTION:Title: Hadamard product of random matrices and their limiting spectral di
stributions\nby Dr. Hao-Wei Huang (National Tsing Hua University) as p
art of Trends in Mathematical Research\n\nLecture held in NTNU Gongguan S1
01.\n\nAbstract\nIn this talk I shall present the limiting spectral distri
butions of the Hadamard products of random matrices GUEs. In certain scena
rios\, the limiting spectral distributions of such random matrix models ex
ist and can be described in terms of square free convolutions. One related
question to square free additive convolution is to investigate when the m
ultiplicative convolution of the semi-circular law and a probability law o
n the positive real line has a semi-circular law as a component in the fre
e additive convolution. We shall answer this question by offering necessar
y and sufficient conditions. This is joint work with Ming Hsiao.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Hui-Yu Hsu (National Tsing Hua University)
DTSTART:20240501T060000Z
DTEND:20240501T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/24
DESCRIPTION:Title: Characteristics of students' cognitive behaviors during mathematic
s problem solving: An ERP perspective\nby Dr. Hui-Yu Hsu (National Tsi
ng Hua University) as part of Trends in Mathematical Research\n\nLecture h
eld in NTNU Gongguan S101.\n\nAbstract\nThe presentation aims to demonstra
te the ERP techniques and how they allow us to understand students' cognit
ive characteristics that cannot be identified in traditional research meth
ods. The presentation focuses on reporting the characteristics of high sch
ool students when they solve different mathematics problems (function and
geometry). Additionally\, we will also illustrate the similarities and dif
ferences in brain activities performed by giftedness and general high scho
ol students.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. John Lin (National Taiwan Normal University)
DTSTART:20240410T060000Z
DTEND:20240410T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/25
DESCRIPTION:Title: Automated prediction of problem solving performance using eye move
ment: Can AI help?\nby Dr. John Lin (National Taiwan Normal University
) as part of Trends in Mathematical Research\n\nLecture held in NTNU Gongg
uan S101.\n\nAbstract\nWith the ability to predict learning behaviors in c
omplex scenarios\, artificial intelligence (AI) shows its potential in ass
essing the problem-solving performance. Given that AI\, data-driven algori
thms\, could be helpful to address random signals (e.g.\, random fixations
)\, using AI to predict learning performance based on eye movements seems
promising. The aims to explorer the potential of an AI\, designed based on
the long-short-term memory neural structure\, to predict whether mathemat
ics problems could be solved in a digital problem-solving scenario using e
ye movements. Sixty-one students participated in this study. We examined w
hether types of eye movement features (AOI-based vs. fixation-based featur
es) and information (Separated vs. integrated steps) during solving proble
ms could impact the performance of AI models. In additional\, the effects
of two hyper-parameters\, activations in hidden layers and number of neuro
s\, were examined. The results suggested that fixation-based features outp
erform AOI-based features. Furthermore\, information in separated steps co
uld provide higher accuracy than that in the integrated steps. Regarding t
he impact of hyper-parameters on AI performance\, the activation function
‘tanh’ and thirty neurons in each layer could be used to train AI mode
ls with higher accuracy. The inconsistent between human and AI-based asses
sment were discussed and visualized.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Juang Jong (National Yang Ming Chiao Tung University)
DTSTART:20240424T060000Z
DTEND:20240424T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/26
DESCRIPTION:Title: A Novel Discrete Time and Discrete State Cucker-Smale Model\nb
y Dr. Juang Jong (National Yang Ming Chiao Tung University) as part of Tre
nds in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbs
tract\nAbstract. The study of flocking motion has found widespread applica
tions in fields such as biology\, ecology\, robotics\, control theory\, se
nsor networks\, sociology\, and economics. The most celebrated model in th
is multidisciplinary area is given by Cucker and Smale (which is referred
to as the C-S model hereafter). In this talk\, we will begin by briefly re
viewing the C-S model and its extensions. Motivated by the fact that every
computer is a finite automation\, we next address a C-S model that is dis
crete in both time and state.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Sean McCurdy (National Taiwan Normal University)
DTSTART:20240417T060000Z
DTEND:20240417T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/27
DESCRIPTION:Title: Cantor Sets: a brief survey\nby Dr. Sean McCurdy (National Tai
wan Normal University) as part of Trends in Mathematical Research\n\nLectu
re held in NTNU Gongguan S101.\n\nAbstract\nCantor sets were intoduced by
the number theorist HJS Smith in 1875 and have been an important source of
examples\, counterexamples\, and inspiration ever since. They are one of
the prototypical fractals. And\, they are an active focus of research to t
his day. This talk aims to introduce Cantor sets to Masters students. Afte
r the basic construction and some historical remarks\, we will survey a fe
w different ways that modern mathematicians are still learning new things
about Cantor sets. Emphasis will be on pictures and big ideas.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Cody Stockdale (Clemson University)
DTSTART:20240529T060000Z
DTEND:20240529T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/28
DESCRIPTION:Title: On the Calderón-Zygmund theory of singular integrals\nby Dr.
Cody Stockdale (Clemson University) as part of Trends in Mathematical Rese
arch\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nThe seminal work
of Calderón and Zygmund on singular integral operators has greatly influe
nced modern harmonic analysis. We begin our discussion with some classical
aspects of CZ theory\, including examples and applications\, and then foc
us on the crucial weak-type $(1\,1)$ estimate for CZ operators. We investi
gate techniques for obtaining weak-type inequalities that use the CZ decom
position and ideas inspired by Nazarov\, Treil\, and Volberg. We discuss v
arious applications of these methods.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Chiun-Chuan Chen (National Taiwan University)
DTSTART:20240522T060000Z
DTEND:20240522T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/29
DESCRIPTION:Title: Propagating direction in the two species Lotka-Volterra competitio
n-diffusion system\nby Dr. Chiun-Chuan Chen (National Taiwan Universit
y) as part of Trends in Mathematical Research\n\nLecture held in NTNU Gong
guan S101.\n\nAbstract\nThe sign of the traveling wave speed in the two sp
ecies Lotka-Volterra competition-diffusion system under strong competition
provides important information about the competitive advantage of the spe
cies. To study the sign problem of the speed\, we propose a mini-max chara
cterization of the coefficients in the reaction terms when the wave speed
is zero. Applying our characterization\, some explicit conditions under wh
ich the speed sign can be determined are obtained.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Nobuo Sato (National Taiwan University)
DTSTART:20240508T060000Z
DTEND:20240508T070000Z
DTSTAMP:20260404T111111Z
UID:MAC8028/30
DESCRIPTION:Title: Iterated beta integrals\nby Dr. Nobuo Sato (National Taiwan Un
iversity) as part of Trends in Mathematical Research\n\nLecture held in NT
NU Gongguan S101.\n\nAbstract\nI will explain my recent work on iterated b
eta integrals with Minoru Hirose at Nagoya University. Iterated beta integ
rals are a type of iterated integrals on branched universal abelian coveri
ngs of the projective line\, which commonly generalize hyperlogarithms and
beta integrals. In addition to the properties that generalize those of hy
perlogarithms and beta integrals\, iterated beta integrals enjoy a new pro
perty that we call translation invariance. The translation invariance yiel
ds equalities between iterated integrals on translation-equivalent coverin
gs of the projective line\, and especially for genus-zero pair of translat
ion-equivalent coverings\, it yields non-trivial equalities between specia
l values of hyperlogarithms. Such equalities include the famous 2-3-2 form
ula for multiple zeta values proved by Zagier\, its analog for multiple t-
values\, the 2-1 formula for multiple zeta star values\, and various other
formulas of a similar kind. By classifying all genus-zero pairs\, some ne
w interesting cases popped up\, one of which resolves a conjecture by Char
lton concerning the area of a family of Lawson surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/MAC8028/30/
END:VEVENT
END:VCALENDAR