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BEGIN:VEVENT
SUMMARY:Christine Breiner (Brown University)
DTSTART:20231130T140000Z
DTEND:20231130T150000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/1
DESCRIPTION:Title: Harmonic Maps to Metric Spaces with Upper Curvature Bounds\nby Ch
ristine Breiner (Brown University) as part of IUT Mathematics Research Sem
inars (IMRS)\n\n\nAbstract\nA natural notion of energy for a map is given
by measuring how much the map stretches at each point and integrating that
quantity over the domain. Harmonic maps are critical points for the energ
y and existence and compactness results for harmonic maps have played a ma
jor role in the advancement of geometric analysis. Gromov-Schoen and Korev
aar-Schoen developed a theory of harmonic maps into metric spaces with non
-positive curvature in order to address rigidity problems in geometric gro
up theory. In this talk we consider harmonic maps into metric spaces with
upper curvature bounds. We will define these objects\, state some key resu
lts\, and demonstrate their application to rigidity and uniformization pro
blems.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byungdo Park (Chungbuk National University)
DTSTART:20231211T123000Z
DTEND:20231211T133000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/2
DESCRIPTION:Title: Differential Cohomology and Gerbes: An Introduction to Higher Differe
ntial Geometry\nby Byungdo Park (Chungbuk National University) as part
of IUT Mathematics Research Seminars (IMRS)\n\nLecture held in https://me
et.google.com/rhw-ernk-ndg.\n\nAbstract\nDifferential cohomology is a topi
c that has been attracting considerable interest.\nMany interesting applic
ations in mathematics and physics have been known\; description of\nWZW te
rms\, string structures\, study of conformal immersions\, classifications
of Ramond-\nRamond fields to list a few\, and it is also an interesting ap
plication of the theory of infinity\ncategories. I will try to give an aud
ience-friendly overview of differential cohomology and a\nclassification o
f higher line bundles (a. k. a. U(1)-banded gerbes) with connection. I wil
l\nstart from scratch and assume only some basic differential geometry and
algebraic topology\nso that it would be accessible to most graduate stude
nts.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byungdo Park (Chungbuk National University)
DTSTART:20231218T123000Z
DTEND:20231218T133000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/3
DESCRIPTION:Title: Differential Cohomology and Gerbes: An Introduction to Higher Differe
ntial Geometry II\nby Byungdo Park (Chungbuk National University) as p
art of IUT Mathematics Research Seminars (IMRS)\n\nLecture held in https:/
/meet.google.com/rhw-ernk-ndg.\n\nAbstract\nDifferential cohomology is a t
opic that has been attracting considerable interest. Many interesting appl
ications in mathematics and physics have been known\; description of WZW t
erms\, string structures\, study of conformal immersions\, classifications
of Ramond- Ramond fields to list a few\, and it is also an interesting ap
plication of the theory of infinity categories. I will try to give an audi
ence-friendly overview of differential cohomology and a classification of
higher line bundles (a. k. a. U(1)-banded gerbes) with connection. I will
start from scratch and assume only some basic differential geometry and al
gebraic topology so that it would be accessible to most graduate students.
\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byungdo Park (Chungbuk National University)
DTSTART:20231225T123000Z
DTEND:20231225T133000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/4
DESCRIPTION:Title: Differential Cohomology and Gerbes: An Introduction to Higher Differe
ntial Geometry III\nby Byungdo Park (Chungbuk National University) as
part of IUT Mathematics Research Seminars (IMRS)\n\nLecture held in https:
//meet.google.com/rhw-ernk-ndg.\n\nAbstract\nDifferential cohomology is a
topic that has been attracting considerable interest. Many interesting app
lications in mathematics and physics have been known\; description of WZW
terms\, string structures\, study of conformal immersions\, classification
s of Ramond- Ramond fields to list a few\, and it is also an interesting a
pplication of the theory of infinity categories. I will try to give an aud
ience-friendly overview of differential cohomology and a classification of
higher line bundles (a. k. a. U(1)-banded gerbes) with connection. I will
start from scratch and assume only some basic differential geometry and a
lgebraic topology so that it would be accessible to most graduate students
.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Kitabeppu (Kumamoto University)
DTSTART:20240424T123000Z
DTEND:20240424T133000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/5
DESCRIPTION:Title: Coarse Ricci Curvature of Hypergraphs\nby Yu Kitabeppu (Kumamoto
University) as part of IUT Mathematics Research Seminars (IMRS)\n\n\nAbstr
act\nThere are several notions of (lower bound of) Ricci curvature on disc
rete spaces. I\nwill give a new notion of Ricci curvature on hypergraphs r
elated to the Lin- Lu-Yau’s coarse\nRicci curvature on graphs (LLY curva
ture for short). The definition of LLY curvature defined\nby using the Mar
kov chain on vertex set on graph. Since the Laplacian of hypergraph is non
linear\, it is difficult to define Ricci curvature on hypergraphs in the s
ame way as LLY one. In\nmy talk\, I explain how to overcome such difficult
ies and tell the geometric consequences of\nassuming lower bound of Ricci
curvature. These are based on two joint works with M.IkedaY.Takai-T.Uehara
\, and with E.Matsumoto.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American Univ. of Sharjah)
DTSTART:20240527T063000Z
DTEND:20240527T080000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/6
DESCRIPTION:Title: Topology and Geometry of Configuration Spaces I\nby Sadok Kallel
(American Univ. of Sharjah) as part of IUT Mathematics Research Seminars (
IMRS)\n\nLecture held in https://meet.google.com/wbd-bwhg-xzd.\n\nAbstract
\nConfiguration spaces of distinct points have seen an explosion in intere
st\nand in the number of publications. Applications have long gone beyond\
nalgebraic topology to encompass all modern aspects of geometry\, analysis
\, and\nmathematical physics\, further making incursions into the applied
science fields.\nThis series of lectures will introduce and explain some o
f the many constructions\nand results in the theory\, with an eye on appli
cations.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American Univ. of Sharjah)
DTSTART:20240527T113000Z
DTEND:20240527T130000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/7
DESCRIPTION:Title: Topology and Geometry of Configuration Spaces II\nby Sadok Kallel
(American Univ. of Sharjah) as part of IUT Mathematics Research Seminars
(IMRS)\n\nLecture held in https://meet.google.com/rhw-ernk-ndg.\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American Univ. of Sharjah)
DTSTART:20240528T073000Z
DTEND:20240528T090000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/8
DESCRIPTION:Title: Topology and Geometry of Configuration Spaces III\nby Sadok Kalle
l (American Univ. of Sharjah) as part of IUT Mathematics Research Seminars
(IMRS)\n\nLecture held in https://meet.google.com/wbd-bwhg-xzd.\n\nAbstra
ct\nConfiguration spaces of distinct points have seen an explosion in inte
rest\nand in the number of publications. Applications have long gone beyon
d\nalgebraic topology to encompass all modern aspects of geometry\, analys
is\, and\nmathematical physics\, further making incursions into the applie
d science fields.\nThis series of lectures will introduce and explain some
of the many constructions\nand results in the theory\, with an eye on app
lications.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American Univ. of Sharjah)
DTSTART:20240528T113000Z
DTEND:20240528T130000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/9
DESCRIPTION:Title: Topology and Geometry of Configuration Spaces IV\nby Sadok Kallel
(American Univ. of Sharjah) as part of IUT Mathematics Research Seminars
(IMRS)\n\nLecture held in https://meet.google.com/wbd-bwhg-xzd.\n\nAbstrac
t\nConfiguration spaces of distinct points have seen an explosion in inter
est\nand in the number of publications. Applications have long gone beyond
\nalgebraic topology to encompass all modern aspects of geometry\, analysi
s\, and\nmathematical physics\, further making incursions into the applied
science fields.\nThis series of lectures will introduce and explain some
of the many constructions\nand results in the theory\, with an eye on appl
ications.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xinrui Zhao (MIT)
DTSTART:20241003T133000Z
DTEND:20241003T143000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/10
DESCRIPTION:Title: Unique continuation problem on RCD spaces\nby Xinrui Zhao (MIT)
as part of IUT Mathematics Research Seminars (IMRS)\n\nLecture held in htt
ps://meet.google.com/osu-pcqp-bqs.\n\nAbstract\nIn this talk we will sketc
h the proof of the unique continuation property of harmonic functions and
caloric functions on any RCD(K\,2) spaces and a counterexample for the str
ong unique continuation property of harmonic function on an RCD(K\,4) spac
e. This characterizes one of the significant differences between RCD space
s and smooth manifolds. We will also talk about some related open problems
. The talk is based on joint works with Qin Deng.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Allen (Lehman College\, CUNY)
DTSTART:20241107T133000Z
DTEND:20241107T143000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/11
DESCRIPTION:Title: On the Scalar Compactness Conjecture in the Conformal Case\nby B
rian Allen (Lehman College\, CUNY) as part of IUT Mathematics Research Sem
inars (IMRS)\n\nLecture held in https://meet.google.com/czn-govf-esv.\n\nA
bstract\nUnderstanding in what sense scalar curvature is flexible versus r
igid has been an important area of investigation in geometric analysis. We
have many rigidity phenomena involving scalar curvature understood and we
are recently turning to the question of stability. One question in this d
irection asks\, If we take a sequence of Riemannian manifolds with non-neg
ative scalar curvature\, then what additional hypotheses need to be added
to ensure that a subsequence exists which converges to a metric space with
some notion of weakly non-negative scalar curvature? In this talk we will
investigate this question in the case where the sequence of Riemannian ma
nifolds is conformal to the round sphere.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Munn (Google)
DTSTART:20241114T133000Z
DTEND:20241114T143000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/12
DESCRIPTION:Title: Leveraging implicit bias to improve efficiencies in training and fin
e-tuning ML models\nby Michael Munn (Google) as part of IUT Mathematic
s Research Seminars (IMRS)\n\n\nAbstract\nIn classical statistical learnin
g theory\, the bias variance tradeoff describes the relationship between t
he complexity of a model and the accuracy of its predictions on new data.
In short\, simpler models are preferable to more complex ones and\, in pra
ctice\, we often employ many techniques to control the model complexity. H
owever\, the best way to correctly measure the complexity of modern machin
e learning models remains an open question. In this talk\, we will discuss
the notion of geometric complexity and present some of our previous resea
rch which aims to address this fundamental problem. We'll also discuss cur
rent and future work which leverages this insight to devise strategies for
more efficient model pre-training and fine-tuning.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Ketterer (Maynooth University)
DTSTART:20241121T133000Z
DTEND:20241121T143000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/13
DESCRIPTION:Title: Gluing spaces that satisfy the Bakry-Emery condition\nby Christi
an Ketterer (Maynooth University) as part of IUT Mathematics Research Semi
nars (IMRS)\n\nLecture held in https://meet.google.com/poi-jmvy-mgb.\n\nAb
stract\nI will present conditions such that the glued space of two weight
ed Riemannian manifolds with boundary and a Bakry-Emery lower Ricci curvat
ure bound satisfies a curvature-dimension condition. For the case of clas
sical Ricci lower bounds this follows from a theorem of Perelman. Moreover
these conditions in return are implied by a curvature-dimension condition
for the glued space\, and this is new even for the unweighted case.\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demetre Kazaras (Michigan State University)
DTSTART:20241205T133000Z
DTEND:20241205T143000Z
DTSTAMP:20260404T094547Z
UID:IMSRS/14
DESCRIPTION:Title: Scalar curvature and codimension 2 collapse\nby Demetre Kazaras
(Michigan State University) as part of IUT Mathematics Research Seminars (
IMRS)\n\nLecture held in https://meet.google.com/vbg-acos-cow.\n\nAbstract
\nThis talk is about the structure of Riemannian 3-manifolds satisfying a
lower bound on their scalar curvature. These manifolds are toy models for
spatial geometry in general relativity. Our motivational question will be
"How flat is an isolated gravitational system with very little total mass?
" Objects like gravity wells and black holes can distort geometry without
accumulating much mass\, making this a subtle question. In addition to dis
cussing progress\, I will present a "drawstring" construction\, which modi
fies a manifold near a given curve\, reducing its length with negligible d
amage to a scalar curvature lower bound. Unexpected examples are produced
with relevance to a few problems. This construction extends ideas of Basi
lio-Dodziuk-Sormani and Lee-Naber-Neumayer\, and is based on joint work wi
th Kai Xu\n
LOCATION:https://stable.researchseminars.org/talk/IMSRS/14/
END:VEVENT
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