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BEGIN:VEVENT
SUMMARY:Zhen-Chun Chen (National Taiwan Ocean University)
DTSTART;VALUE=DATE-TIME:20230913T060000Z
DTEND;VALUE=DATE-TIME:20230913T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/1
DESCRIPTION:Title:
數學力學與計算-邊界元走過四十年\nby Zhen-Chun Chen (Nat
ional Taiwan Ocean University) as part of Trends in Mathematical Research\
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://researchseminars.org/talk/MAC8028/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shu-Cheng Chang (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20230920T060000Z
DTEND;VALUE=DATE-TIME:20230920T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/2
DESCRIPTION:Title:
From Thurston Geometrization Conjecture to Mori Minimal Model Program\
nby Shu-Cheng Chang (National Taiwan University) as part of Trends in Math
ematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nA ce
ntral problem of differential geometry is the geometrization problem on ma
nifolds. In particular\, it is to determine which manifolds admit certain
geometric structures. One of methods is to understand and classify the sin
gularity models of the corresponding nonlinear geometric evolution equatio
n\, and to connect it to the existence problem of geometric structures on
manifolds. \n In 1982\, R. Hamilton introduced the Ricci flow and then
by studying the singularity models of Ricci flow\, G. Perelman completely
solved Thurston geometrization conjecture and Poincare conjecture for a cl
osed 3-manifold in 2002 and 2003.\n On the other hand\, Mori minimal mo
del program in birational geometry can be viewed as the complex analogue o
f Thurston's geometrization conjecture. In 1985\, H.-D. Cao introduced the
Kähler-Ricci flow and then recaptured the Calabi-Yau Conjecture. Moreove
r\, there is a conjecture picture by Song-Tian that the Kähler-Ricci flo
w should carry out the analytic minimal model program with scaling on proj
ective varieties. Recently\, Song-Weinkove established the above conjectur
e on a projective algebraic surface. Furthermore\, via the Sasaki-Ricci fl
ow\, Chang-Lin-Wu proved the Sasaki analogue of minimal model program on c
losed quasi-regular Sasakian 5-manifolds.\n In this lecture\, I will add
ress the above issues in some detail.\n
LOCATION:https://researchseminars.org/talk/MAC8028/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Duncan (Academia Sinica)
DTSTART;VALUE=DATE-TIME:20231004T060000Z
DTEND;VALUE=DATE-TIME:20231004T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/3
DESCRIPTION:Title:
A Guide to Moonshine\nby John Duncan (Academia Sinica) as part of Tren
ds in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbst
ract\nAndrew Ogg gave a geometric description of the primes that divide th
e order of the monster finite simple group in 1973\, and thus initiated th
e theory of monstrous moonshine. Since then\, the pursuit of moonshine has
illuminated powerful relationships between algebraic\, geometric and numb
er theoretic structures. We will present an introductory overview of this
theory.\n
LOCATION:https://researchseminars.org/talk/MAC8028/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Payne (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20231018T060000Z
DTEND;VALUE=DATE-TIME:20231018T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/4
DESCRIPTION:Title:
Multi-scale\, multi-compartment modelling of the human brain\nby Steph
en Payne (National Taiwan University) as part of Trends in Mathematical Re
search\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nThe increasing
rates of cerebrovascular diseases\, such as stroke and dementia\, mean tha
t understanding cerebral blood flow and its control in both healthy and di
seased states has become an important clinical problem. However this is ma
de challenging by the spatial and temporal limitations of human brain imag
ing 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 di
scuss the work that we have done to construct models of cerebral blood flo
w that cover the many length scales involved\, running from a few micromet
res to a few millimetres. I will show how we have developed such models fr
om the bottom up\, through highly detailed modelling of the microcirculati
on and the application of homogenisation and optimisation methods\, in ord
er to generate a full-brain model of blood flow and oxygen transport. I wi
ll then talk about how this can be applied (and validated) in pathological
conditions\, in particular the treatment of acute ischaemic stroke. I wil
l conclude by discussing how we next plan to use multiple time scales in t
he context of chronic diseases such as dementia and to quantify the effect
s of interventions such as sleep and exercise on disease progression.\n
LOCATION:https://researchseminars.org/talk/MAC8028/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuh-Jye Lee (Academia Sinica)
DTSTART;VALUE=DATE-TIME:20231025T060000Z
DTEND;VALUE=DATE-TIME:20231025T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
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\nLectu
re held in NTNU Gongguan S101.\n\nAbstract\nIn the rapidly evolving realm
of machine learning\, algorithm effectiveness often faces limitations due
to data quality and availability. Traditional approaches grapple with data
sharing due to legal and privacy concerns. The federated learning framewo
rk addresses this challenge. Federated learning is a decentralized approac
h where model training occurs on client sides\, preserving privacy by keep
ing data localized. Instead of sending raw data to a central server\, only
model updates are exchanged\, enhancing data security. We apply this fram
ework to Sparse Principal Component Analysis (SPCA) in this work. SPCA aim
s to attain sparse component loading while maximizing data variance for im
proved interpretability. We introduce a least squares approximation to ori
ginal PCA\, adding an $\\ell_1$ norm regularization term to enhance princi
pal component sparsity\, aiding variable identification and interpretabili
ty. The problem is formulated as a consensus optimization challenge and so
lved using the Alternating Direction Method of Multipliers (ADMM). Our ext
ensive experiments involve both IID and non-IID random features across var
ious data owners. Results on synthetic and public datasets affirm the effi
cacy of our federated SPCA approach.\n
LOCATION:https://researchseminars.org/talk/MAC8028/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyung-Youn Kim (National Chung Hsing University)
DTSTART;VALUE=DATE-TIME:20231101T060000Z
DTEND;VALUE=DATE-TIME:20231101T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/6
DESCRIPTION:Title:
Potential theory of anisotropic Markov processes\nby Kyung-Youn Kim (N
ational Chung Hsing University) as part of Trends in Mathematical Research
\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nHeat kernel is the fu
ndamental solution of the heat equation\, and it is also the transition de
nsity of the diffusion process corresponding to the Laplacian. These relat
ion is also ture for non-local operators\, and corresponding process is a
discontinuous Markov process. \nIn this talk\, we consider anisotropic Ma
rkov processes.\nLet $L_i$\, $i=1\,\\ldots\,d$\, be identical and independ
ent $1$-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 parallel to t
he coordinate axes.\nWe discuss the sharp two-sided heat kernel bounds for
$M$ on $C^{1\,1}$ open set $D\\subset {\\rm I\\!R}^d$ as well as the pote
ntial theory of anisotropic Markov process. This is the joint work with Li
dan Wang.\n \n\n\n[1.] Dirichlet Heat kernel estimates for a large class o
f anisotropic Markov process(with Lidan Wang).\n
LOCATION:https://researchseminars.org/talk/MAC8028/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA (TBA)
DTSTART;VALUE=DATE-TIME:20230927T060000Z
DTEND;VALUE=DATE-TIME:20230927T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
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://researchseminars.org/talk/MAC8028/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shagnik Das (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20231011T060000Z
DTEND;VALUE=DATE-TIME:20231011T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/8
DESCRIPTION:Title:
Covering grids with multiplicity\nby Shagnik Das (National Taiwan Univ
ersity) as part of Trends in Mathematical Research\n\nLecture held in NTNU
Gongguan S101.\n\nAbstract\nIt is a fairly simple exercise to determine t
he minimum number of hyperplanes needed to cover all the points of a finit
e grid $S_1$ x $S_2$ x ... x $S_d \\in \\mathbb{F}^d$. However\, the situa
tion becomes much more complex if you add the condition that one of the po
ints of the grid must be avoided\, leading to a classic problem in combina
torial 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 varia
nt of the problem where the nonzero points of a hypercube should be covere
d multiple times while avoiding the origin\, brought renewed interest to t
his problem. In addition to Alon-Füredi-style algebraic arguments\, they
used linear programming to asymptotically resolve the problem in certain r
anges.\n\nDespite all the attention this problem has received\, there rema
in many open problems\, even in the case of two-dimensional grids over $\\
mathbb{R}$. In this talk\, after surveying the background and introducing
the techniques used\, we shall present some recent results that resolve th
e problem for almost all two-dimensional grids.\n\nThe new results are joi
nt work with Anurag Bishnoi\, Simona Boyadzhiyska and Yvonne den Bakker\,
and separately with Valjakas Djaljapayan\, Yen-Chi Roger Lin and Wei-Hsuan
Yu.\n
LOCATION:https://researchseminars.org/talk/MAC8028/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART;VALUE=DATE-TIME:20231108T060000Z
DTEND;VALUE=DATE-TIME:20231108T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/9
DESCRIPTION:Title:
The derived Bézout theorem\nby Adeel Khan (Academia Sinica) as part o
f Trends in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n
\nAbstract\nGiven two smooth algebraic curves of degrees $d$ and $e$ in th
e complex projective plane\, Bezout’s theorem is a classical result asse
rting that the intersection consists of either infinitely many or exactly
$d\\cdot e$ points\, counted with multiplicities. Generalizing this formu
la to intersections in higher-dimensional projective space was a task that
fuelled much of 20th century algebraic geometry\, eventually culminating
in J.-P. Serre’s solution in 1958.\n\nWe will review some of this histor
y before presenting a 21st century point of view on Bézout’s theorem.
Specifically\, we will see that the modern language of derived algebraic g
eometry allows us to give a simple definition of intersection multipliciti
es\, which unlike Serre’s formula applies even to non-proper intersectio
ns\, and yields a vast generalization of Bézout theorem for arbitrary int
ersections of projective hypersurfaces.\n
LOCATION:https://researchseminars.org/talk/MAC8028/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Fuchs (National Chengchi University)
DTSTART;VALUE=DATE-TIME:20231129T060000Z
DTEND;VALUE=DATE-TIME:20231129T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/10
DESCRIPTION:Title: Gene-tree statistics: moments and limit laws for ancestral configurations
\nby Michael Fuchs (National Chengchi University) as part of Trends in
Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\
nFor a given species tree\, ancestral configurations are the gene lineages
which can be present at a node of the species tree over the set of all ge
ne trees. Root ancestral configurations are the ancestral configurations w
hich are present at the root. They play an important role in a (standard)
algorithm for computing probabilities of gene trees that have evolved with
in the given species tree. In particular\, their number is a measure for t
he complexity of this algorithm. In this talk\, we give background\, revie
w recent results about the number of ancestral configurations and root anc
estral configurations for matching species and gene trees under the unifor
m and Yule Harding model\, and explain our recent refinements of these re
sults which concern moments and limit laws. The talk is based on joint wor
k with F. Disanto (University of Pisa)\, A. R. Paningbatan (University of
the Philippines Diliman)\, C.-Y. Huang (National Chiao Tung University)\,
and N. A. Rosenberg (Stanford University).\n
LOCATION:https://researchseminars.org/talk/MAC8028/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melaine Saillenfest (IMCCE\, Observatoire de Paris\, France)
DTSTART;VALUE=DATE-TIME:20231206T060000Z
DTEND;VALUE=DATE-TIME:20231206T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/11
DESCRIPTION:Title: Coevolution of moons and the spin axis of their host planet\nby Melai
ne Saillenfest (IMCCE\, Observatoire de Paris\, France) as part of Trends
in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstrac
t\nAstrometric observations of the moons of Jupiter and Saturn have reveal
ed that their orbits expand over time faster than previously thought. This
significant orbital "migration" implies that efficient mechanisms of tida
l energy dissipation are at play in the interiors of gaseous planets. Thes
e findings profoundly affect our understanding of the formation and evolut
ion of moons\, but also of the spin-axis dynamics of their host planet. Th
e coupling between the planet's spin-axis dynamics (the "Cassini states")
and the moons' orbital dynamics (the "Laplace plane") can gradually tilt t
he planet and make the system converge to a highly unstable configuration.
This mechanism has direct applications in the Solar system: Jupiter today
is about to start the tilting phase\, Saturn is probably halfway in\, and
Uranus may have completed the final unstable stage.\n
LOCATION:https://researchseminars.org/talk/MAC8028/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Tai Fang (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20231122T060000Z
DTEND;VALUE=DATE-TIME:20231122T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/12
DESCRIPTION:Title: 防疫的數學–基礎再生數 R0\nby Chi-Tai Fang (National Taiwa
n University) as part of Trends in Mathematical Research\n\nLecture held i
n NTNU Gongguan S101.\n\nAbstract\n• 數學與防疫\n• Basic Reproduc
tive 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://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;VALUE=DATE-TIME:20240221T060000Z
DTEND;VALUE=DATE-TIME:20240221T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/13
DESCRIPTION:Title: A nonlocal reaction diffusion model of West Nile virus with vertical tran
smission\nby Dr. Feng-Bin Wang (Division of Natural Science\, Center f
or General Education\, Chang Gung University\, Taiwan) as part of Trends i
n Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract
\nWest Nile virus (WNv) is a mosquito-borne infection\, causing health cha
llenges to bird\nand human populations. In this talk\, I plan to propose a
general nonlocal reaction-diffusion model to explore\nthe combined effect
of alternative hosts\, vector-host movement and spatial-temporal environm
ental\nstructure on WNv transmission dynamics. The model is partially dege
nerate and\nits solution maps lack compactness due to the absence of diffu
sion terms in larval equations.\nFor this tightly coupled disease model\,
we introduce the mosquito reproduction number \nand WNv reproduction numbe
r\, respectively\, and further show that these two aforementioned\nreprodu
ction numbers completely determine the threshold behaviour of the disease\
nspread. Numerical simulations support our analytic results and suggest th
at environmental\nheterogeneity plays an important role in shaping WNv dyn
amics. Moreover\, bird migration may increase the disease risk.\n\nThis ta
lk is based on a joint work with Drs. Ruiwen Wu and Xiao-Qiang Zhao.\n
LOCATION:https://researchseminars.org/talk/MAC8028/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nguyễn Lê Trâm (National Taiwan Normal University)
DTSTART;VALUE=DATE-TIME:20231115T060000Z
DTEND;VALUE=DATE-TIME:20231115T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/14
DESCRIPTION:Title: Interval Valued Optimization Problems on Hadamard Manifolds\nby Nguy
ễn Lê Trâm (National Taiwan Normal University) as part of Trends in Ma
thematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nIn
this talk\, we will introduce the interval optimization problems (IOPs)\n
on Hadamard manifolds. To achieve the theoretical results\, we build up so
me new concepts about gH-directional derivative\, gH-Gateaux and gH-Freche
t differentiability of interval valued functions and their properties on H
adamard manifolds. More specifically\, we characterize the optimality cond
itions for the IOPs on the Hadamard manifolds. For unconstrained problems\
, the existence of efficient points and the steepest descent algorithm are
investigated. To the contrast\, the KKT conditions and exact penalty appr
oach are explored in the ones involving inequality constraints. The obtain
ed results pave a way to further study on Riemannian interval optimization
\nproblems (RIOPs).\n
LOCATION:https://researchseminars.org/talk/MAC8028/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Cruz-Uribe (University of Alabama)
DTSTART;VALUE=DATE-TIME:20231213T060000Z
DTEND;VALUE=DATE-TIME:20231213T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/15
DESCRIPTION:Title: Norm inequalities for linear and multilinear singular integrals on weight
ed and variable exponent Hardy spaces\nby David Cruz-Uribe (University
of Alabama) as part of Trends in Mathematical Research\n\nLecture held in
NTNU Gongguan S101.\n\nAbstract\nI will discuss a (relatively) new approa
ch\nto norm inequalities in the weighted and variable exponent Hardy\nspac
es. The weighted Hardy spaces $H^p(w)$\, $p>0$\, where $w$ is a\nMuckenho
upt weight\, were first considered by Stromberg and Torchinsky\nin the 198
0s. The variable Lebesgue space $L^{p(\\cdot)}$ is\,\nintuitively\, a cla
ssical Lebesgue space with the constant exponent $p$\nreplaced by an expon
ent function $p(\\cdot)$. They have been studied\nextensively for the las
t 30 years. The corresponding variable Hardy\nspaces $H^{p(\\cdot)}$ were
introduced by me and Li-An Wang and\nindependently by Nakai and Sawano.\n
\nWe give inter-related conditions\non a Calderon-Zygmund singular integra
l operator $T$\, a weight $w$\,\nand an exponent $p(\\cdot)$ for $T$ to sa
tisfy estimates of the\nform$$ T : H^p(w) \\rightarrow L^p(w)\, \\qquad T:
H^{p(\\cdot)}\n\\rightarrow L^{p(\\cdot)}.$$ Some of our results were kno
wn for\nconvolution type singular integrals\, but we give new and simpler\
nproofs and give extensions to non-convolution type operators. Our\nproof
s depend very heavily on three tools: atomic decompositions of\nthe Hardy
spaces\, vector-valued inequalities\, and the Rubio de Francia\ntheory of
extrapolation.\n\nWe will also discuss generalizations of these\nresults t
o the bilinear setting\, where we prove norm inequalities of\nthe form\n$$
T: H^{p_1}(w_1) \\times H^{p_2}(w_2) \\rightarrow L^p(w)\, $$\nwhere $T$
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 c
onsider norm inequalities of the form\n$$ T: H^{p_1(\\cdot)}\\times H^{p_
2(\\cdot)}\\rightarrow L^{p(\\cdot)}. $$\n\nThis is joint work with Kabe M
oen and Hanh Nguyen of the University of\nAlabama.\n
LOCATION:https://researchseminars.org/talk/MAC8028/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Jan Harold Alcantara (RIKEN\, Japan)
DTSTART;VALUE=DATE-TIME:20240227T060000Z
DTEND;VALUE=DATE-TIME:20240227T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/16
DESCRIPTION:Title: Theoretical smoothing frameworks for nonsmooth bilevel optimization probl
ems\nby Dr. Jan Harold Alcantara (RIKEN\, Japan) as part of Trends in
Mathematical Research\n\nLecture held in NTNU Gongguan S506.\n\nAbstract\n
The optimal value function approach provides a useful reformulation of the
bilevel optimization problem\, but its utility is often hindered by the n
onsmoothness of the value function even in cases when the associated lower
-level function is smooth. In this talk\, we present two smoothing strateg
ies for the value function associated with lower-level functions that are
not necessarily smooth but are Lipschitz continuous. The first method empl
oys a quadratic regularization approach for partially convex lower-level f
unctions\, while the second utilizes entropic regularization for general l
ower-level objective functions. Meanwhile\, the property known as gradient
consistency is crucial in ensuring that a designed smoothing algorithm is
globally subsequentially convergent to stationary points of the equivalen
t reformulation of the bilevel problem. With this in mind\, we show that t
he proposed smooth approximations satisfy the gradient consistent property
under certain conditions on the lower-level function.\n
LOCATION:https://researchseminars.org/talk/MAC8028/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Anastasia Molchanova (University of Vienna)
DTSTART;VALUE=DATE-TIME:20240320T060000Z
DTEND;VALUE=DATE-TIME:20240320T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/18
DESCRIPTION:Title: Lavrentiev Phenomenon in Nonlinear Elasticity\nby Dr. Anastasia Molch
anova (University of Vienna) as part of Trends in Mathematical Research\n\
nLecture held in NTNU Gongguan S101.\n\nAbstract\nIn the calculus of varia
tions\, Lavrentiev's phenomenon refers to the situation when the minimum v
alue of a certain functional varies significantly depending on the space o
f functions considered.\nIn this talk\, we present a new example of Lavren
tiev's phenomenon in the context of nonlinear elasticity. This example is
based on an interplay of the elastic energy’s resistance to infinite com
pression and the Ciarlet–Necas condition\, a constraint preventing globa
l interpenetration of matter on sets of full measure.\n
LOCATION:https://researchseminars.org/talk/MAC8028/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Chun-Yen Shen (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20240327T060000Z
DTEND;VALUE=DATE-TIME:20240327T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/19
DESCRIPTION:Title: Discretized Sum-Product and Geometric Measure Theory\nby Dr. Chun-Yen
Shen (National Taiwan University) as part of Trends in Mathematical Resea
rch\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nIn this talk\, I w
ill first briefly review the history of sum-product estimates in the setti
ng of finite fields and mention the applications of sum-product type probl
ems. Then I will start introducing the celebrated result of Bourgain about
the discretized sum-product estimates and the applications to geometric m
easure theory problems. Finally I will talk about our recent results about
expanding polynomials in terms of Hausdorff dimension and discuss their s
um-product phenomena.\n
LOCATION:https://researchseminars.org/talk/MAC8028/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Yi-Hsuan Lin (National Yang Ming Chiao Tung University)
DTSTART;VALUE=DATE-TIME:20240313T060000Z
DTEND;VALUE=DATE-TIME:20240313T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/20
DESCRIPTION:Title: Nonlocality helps\nby Dr. Yi-Hsuan Lin (National Yang Ming Chiao Tung
University) as part of Trends in Mathematical Research\n\nLecture held in
NTNU Gongguan S101.\n\nAbstract\nIn this talk\, we will review several no
nlocal inverse problems\, and explain how nonlocality helps us to solve re
lated inverse problems.\n
LOCATION:https://researchseminars.org/talk/MAC8028/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Mei-Heng Yueh (National Taiwan Normal University)
DTSTART;VALUE=DATE-TIME:20240306T060000Z
DTEND;VALUE=DATE-TIME:20240306T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/21
DESCRIPTION:Title: Theoretical Foundation of the Stretch Energy Minimization for Area-Preser
ving 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 function
al particularly defined for the measurement of the area distortion for sim
plicial mapping\, which has been applied to efficiently compute area-prese
rving parameterizations of simplicial surfaces. The stretch energy has a n
ice geometric interpretation that is helpful for the generalization of the
functional to higher dimensional manifold mappings. On the application as
pect\, parameterizations of simplicial surfaces have been widely applied i
n computer graphics that aim to efficiently compute a diffeomorphism betwe
en a simplicial surface and a canonical domain. This provides the surface
with a unified coordinate system that simplifies various image and geometr
y processing tasks such as alignment and blending of images and surfaces.
In this talk\, I will introduce the theoretical foundation of stretch ener
gy minimization for the computation of area-preserving parameterizations o
f simplicial surfaces. Applications in image and surface blending and area
-preserving deformations will be demonstrated to highlight the practical u
tility of the parameterizations.\n
LOCATION:https://researchseminars.org/talk/MAC8028/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Oscar Dominguez Bonilla (Cunef Universidad)
DTSTART;VALUE=DATE-TIME:20240403T060000Z
DTEND;VALUE=DATE-TIME:20240403T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/22
DESCRIPTION:Title: Energy conservation of Euler solutions via sparseness\nby Dr. Oscar D
ominguez Bonilla (Cunef Universidad) as part of Trends in Mathematical Res
earch\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\nA friendly intro
duction to new tools we use to study energy conservation of solutions to E
uler equations of fluid dynamics. In particular\, we develop sparse decomp
ositions and extrapolation techniques. The talk is based on joint work wit
h M. Milman.\n
LOCATION:https://researchseminars.org/talk/MAC8028/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Hao-Wei Huang (National Tsing Hua University)
DTSTART;VALUE=DATE-TIME:20240515T060000Z
DTEND;VALUE=DATE-TIME:20240515T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/23
DESCRIPTION:Title: Hadamard product of random matrices and their limiting spectral distribut
ions\nby Dr. Hao-Wei Huang (National Tsing Hua University) as part of
Trends in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\n
Abstract\nIn this talk I shall present the limiting spectral distributions
of the Hadamard products of random matrices GUEs. In certain scenarios\,
the limiting spectral distributions of such random matrix models exist and
can be described in terms of square free convolutions. One related questi
on to square free additive convolution is to investigate when the multipli
cative convolution of the semi-circular law and a probability law on the p
ositive real line has a semi-circular law as a component in the free addit
ive convolution. We shall answer this question by offering necessary and s
ufficient conditions. This is joint work with Ming Hsiao.\n
LOCATION:https://researchseminars.org/talk/MAC8028/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Hui-Yu Hsu (National Tsing Hua University)
DTSTART;VALUE=DATE-TIME:20240501T060000Z
DTEND;VALUE=DATE-TIME:20240501T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/24
DESCRIPTION:Title: Characteristics of students' cognitive behaviors during mathematics probl
em solving: An ERP perspective\nby Dr. Hui-Yu Hsu (National Tsing Hua
University) as part of Trends in Mathematical Research\n\nLecture held in
NTNU Gongguan S101.\n\nAbstract\nThe presentation aims to demonstrate the
ERP techniques and how they allow us to understand students' cognitive cha
racteristics that cannot be identified in traditional research methods. Th
e presentation focuses on reporting the characteristics of high school stu
dents when they solve different mathematics problems (function and geometr
y). Additionally\, we will also illustrate the similarities and difference
s in brain activities performed by giftedness and general high school stud
ents.\n
LOCATION:https://researchseminars.org/talk/MAC8028/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. John Lin (National Taiwan Normal University)
DTSTART;VALUE=DATE-TIME:20240410T060000Z
DTEND;VALUE=DATE-TIME:20240410T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/25
DESCRIPTION:Title: Automated prediction of problem solving performance using eye movement: C
an AI help?\nby Dr. John Lin (National Taiwan Normal University) as pa
rt of Trends in Mathematical Research\n\nLecture held in NTNU Gongguan S10
1.\n\nAbstract\nWith the ability to predict learning behaviors in complex
scenarios\, artificial intelligence (AI) shows its potential in assessing
the problem-solving performance. Given that AI\, data-driven algorithms\,
could be helpful to address random signals (e.g.\, random fixations)\, usi
ng AI to predict learning performance based on eye movements seems promisi
ng. The aims to explorer the potential of an AI\, designed based on the lo
ng-short-term memory neural structure\, to predict whether mathematics pro
blems could be solved in a digital problem-solving scenario using eye move
ments. Sixty-one students participated in this study. We examined whether
types of eye movement features (AOI-based vs. fixation-based features) and
information (Separated vs. integrated steps) during solving problems coul
d impact the performance of AI models. In additional\, the effects of two
hyper-parameters\, activations in hidden layers and number of neuros\, wer
e examined. The results suggested that fixation-based features outperform
AOI-based features. Furthermore\, information in separated steps could pro
vide higher accuracy than that in the integrated steps. Regarding the impa
ct of hyper-parameters on AI performance\, the activation function ‘tanh
’ and thirty neurons in each layer could be used to train AI models with
higher accuracy. The inconsistent between human and AI-based assessment w
ere discussed and visualized.\n
LOCATION:https://researchseminars.org/talk/MAC8028/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Juang Jong (National Yang Ming Chiao Tung University)
DTSTART;VALUE=DATE-TIME:20240424T060000Z
DTEND;VALUE=DATE-TIME:20240424T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/26
DESCRIPTION:Title: A Novel Discrete Time and Discrete State Cucker-Smale Model\nby Dr. J
uang Jong (National Yang Ming Chiao Tung University) as part of Trends in
Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n\nAbstract\n
Abstract. The study of flocking motion has found widespread applications i
n fields such as biology\, ecology\, robotics\, control theory\, sensor ne
tworks\, sociology\, and economics. The most celebrated model in this mult
idisciplinary area is given by Cucker and Smale (which is referred to as t
he C-S model hereafter). In this talk\, we will begin by briefly reviewing
the C-S model and its extensions. Motivated by the fact that every comput
er is a finite automation\, we next address a C-S model that is discrete i
n both time and state.\n
LOCATION:https://researchseminars.org/talk/MAC8028/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Sean McCurdy (National Taiwan Normal University)
DTSTART;VALUE=DATE-TIME:20240417T060000Z
DTEND;VALUE=DATE-TIME:20240417T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/27
DESCRIPTION:Title: Cantor Sets: a brief survey\nby Dr. Sean McCurdy (National Taiwan Nor
mal University) as part of Trends in Mathematical Research\n\nLecture held
in NTNU Gongguan S101.\n\nAbstract\nCantor sets were intoduced by the num
ber theorist HJS Smith in 1875 and have been an important source of exampl
es\, counterexamples\, and inspiration ever since. They are one of the pro
totypical fractals. And\, they are an active focus of research to this day
. This talk aims to introduce Cantor sets to Masters students. After the b
asic construction and some historical remarks\, we will survey a few diffe
rent ways that modern mathematicians are still learning new things about C
antor sets. Emphasis will be on pictures and big ideas.\n
LOCATION:https://researchseminars.org/talk/MAC8028/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Cody Stockdale (Clemson University)
DTSTART;VALUE=DATE-TIME:20240529T060000Z
DTEND;VALUE=DATE-TIME:20240529T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/28
DESCRIPTION:by Dr. Cody Stockdale (Clemson University) as part of Trends i
n Mathematical Research\n\nLecture held in NTNU Gongguan S101.\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/MAC8028/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Chiun-Chuan Chen (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20240522T060000Z
DTEND;VALUE=DATE-TIME:20240522T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/29
DESCRIPTION:by Dr. Chiun-Chuan Chen (National Taiwan University) as part o
f Trends in Mathematical Research\n\nLecture held in NTNU Gongguan S101.\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/MAC8028/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dr. Nobuo Sato (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20240508T060000Z
DTEND;VALUE=DATE-TIME:20240508T070000Z
DTSTAMP;VALUE=DATE-TIME:20240423T104148Z
UID:MAC8028/30
DESCRIPTION:Title: Iterated beta integrals\nby Dr. Nobuo Sato (National Taiwan Universit
y) as part of Trends in Mathematical Research\n\nLecture held in NTNU Gong
guan S101.\n\nAbstract\nI will explain my recent work on iterated beta int
egrals with Minoru Hirose at Nagoya University. Iterated beta integrals ar
e a type of iterated integrals on branched universal abelian coverings of
the projective line\, which commonly generalize hyperlogarithms and beta i
ntegrals. In addition to the properties that generalize those of hyperloga
rithms and beta integrals\, iterated beta integrals enjoy a new property t
hat we call translation invariance. The translation invariance yields equa
lities between iterated integrals on translation-equivalent coverings of t
he projective line\, and especially for genus-zero pair of translation-equ
ivalent coverings\, it yields non-trivial equalities between special value
s of hyperlogarithms. Such equalities include the famous 2-3-2 formula 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 formul
as of a similar kind. By classifying all genus-zero pairs\, some new inter
esting cases popped up\, one of which resolves a conjecture by Charlton co
ncerning the area of a family of Lawson surfaces.\n
LOCATION:https://researchseminars.org/talk/MAC8028/30/
END:VEVENT
END:VCALENDAR