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BEGIN:VEVENT
SUMMARY:Christine Breiner (Brown University)
DTSTART:20231130T140000Z
DTEND:20231130T150000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/1
DESCRIPTION:Title: Ha
rmonic Maps to Metric Spaces with Upper Curvature Bounds\nby Christine
Breiner (Brown University) as part of IUT Mathematics Research Seminars (
IMRS)\n\n\nAbstract\nA natural notion of energy for a map is given by meas
uring how much the map stretches at each point and integrating that quanti
ty over the domain. Harmonic maps are critical points for the energy and e
xistence and compactness results for harmonic maps have played a major rol
e in the advancement of geometric analysis. Gromov-Schoen and Korevaar-Sch
oen developed a theory of harmonic maps into metric spaces with non-positi
ve curvature in order to address rigidity problems in geometric group theo
ry. In this talk we consider harmonic maps into metric spaces with upper c
urvature bounds. We will define these objects\, state some key results\, a
nd demonstrate their application to rigidity and uniformization problems.\
n
LOCATION:https://researchseminars.org/talk/IMSRS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byungdo Park (Chungbuk National University)
DTSTART:20231211T123000Z
DTEND:20231211T133000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/2
DESCRIPTION:Title: Di
fferential Cohomology and Gerbes: An Introduction to Higher Differential G
eometry\nby Byungdo Park (Chungbuk National University) as part of IUT
Mathematics Research Seminars (IMRS)\n\nLecture held in https://meet.goog
le.com/rhw-ernk-ndg.\n\nAbstract\nDifferential cohomology is a topic that
has been attracting considerable interest.\nMany interesting applications
in mathematics and physics have been known\; description of\nWZW terms\, s
tring structures\, study of conformal immersions\, classifications of Ramo
nd-\nRamond fields to list a few\, and it is also an interesting applicati
on of the theory of infinity\ncategories. I will try to give an audience-f
riendly overview of differential cohomology and a\nclassification of highe
r line bundles (a. k. a. U(1)-banded gerbes) with connection. I will\nstar
t from scratch and assume only some basic differential geometry and algebr
aic topology\nso that it would be accessible to most graduate students.\n
LOCATION:https://researchseminars.org/talk/IMSRS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byungdo Park (Chungbuk National University)
DTSTART:20231218T123000Z
DTEND:20231218T133000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/3
DESCRIPTION:Title: Di
fferential Cohomology and Gerbes: An Introduction to Higher Differential G
eometry II\nby Byungdo Park (Chungbuk National University) as part of
IUT Mathematics Research Seminars (IMRS)\n\nLecture held in https://meet.g
oogle.com/rhw-ernk-ndg.\n\nAbstract\nDifferential cohomology is a topic th
at has been attracting considerable interest. Many interesting application
s in mathematics and physics have been known\; description of WZW terms\,
string structures\, study of conformal immersions\, classifications of Ram
ond- Ramond fields to list a few\, and it is also an interesting applicati
on of the theory of infinity categories. I will try to give an audience-fr
iendly overview of differential cohomology and a classification of higher
line bundles (a. k. a. U(1)-banded gerbes) with connection. I will start f
rom scratch and assume only some basic differential geometry and algebraic
topology so that it would be accessible to most graduate students.\n
LOCATION:https://researchseminars.org/talk/IMSRS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byungdo Park (Chungbuk National University)
DTSTART:20231225T123000Z
DTEND:20231225T133000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/4
DESCRIPTION:Title: Di
fferential Cohomology and Gerbes: An Introduction to Higher Differential G
eometry 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 t
hat has been attracting considerable interest. Many interesting applicatio
ns in mathematics and physics have been known\; description of WZW terms\,
string structures\, study of conformal immersions\, classifications of Ra
mond- Ramond fields to list a few\, and it is also an interesting applicat
ion of the theory of infinity categories. I will try to give an audience-f
riendly 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 algebrai
c topology so that it would be accessible to most graduate students.\n
LOCATION:https://researchseminars.org/talk/IMSRS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Kitabeppu (Kumamoto University)
DTSTART:20240424T123000Z
DTEND:20240424T133000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/5
DESCRIPTION:Title: Co
arse Ricci Curvature of Hypergraphs\nby Yu Kitabeppu (Kumamoto Univers
ity) as part of IUT Mathematics Research Seminars (IMRS)\n\n\nAbstract\nTh
ere are several notions of (lower bound of) Ricci curvature on discrete sp
aces. I\nwill give a new notion of Ricci curvature on hypergraphs related
to the Lin- Lu-Yau’s coarse\nRicci curvature on graphs (LLY curvature fo
r short). The definition of LLY curvature defined\nby using the Markov cha
in on vertex set on graph. Since the Laplacian of hypergraph is nonlinear\
, it is difficult to define Ricci curvature on hypergraphs in the same way
as LLY one. In\nmy talk\, I explain how to overcome such difficulties and
tell the geometric consequences of\nassuming lower bound of Ricci curvatu
re. These are based on two joint works with M.IkedaY.Takai-T.Uehara\, and
with E.Matsumoto.\n
LOCATION:https://researchseminars.org/talk/IMSRS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American Univ. of Sharjah)
DTSTART:20240527T063000Z
DTEND:20240527T080000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/6
DESCRIPTION:Title: To
pology and Geometry of Configuration Spaces I\nby Sadok Kallel (Americ
an Univ. of Sharjah) as part of IUT Mathematics Research Seminars (IMRS)\n
\nLecture held in https://meet.google.com/wbd-bwhg-xzd.\n\nAbstract\nConfi
guration spaces of distinct points have seen an explosion in interest\nand
in the number of publications. Applications have long gone beyond\nalgebr
aic 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 of the m
any constructions\nand results in the theory\, with an eye on applications
.\n
LOCATION:https://researchseminars.org/talk/IMSRS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American Univ. of Sharjah)
DTSTART:20240527T113000Z
DTEND:20240527T130000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/7
DESCRIPTION:Title: To
pology and Geometry of Configuration Spaces II\nby Sadok Kallel (Ameri
can 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://researchseminars.org/talk/IMSRS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American Univ. of Sharjah)
DTSTART:20240528T073000Z
DTEND:20240528T090000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/8
DESCRIPTION:Title: To
pology and Geometry of Configuration Spaces III\nby Sadok Kallel (Amer
ican Univ. of Sharjah) as part of IUT Mathematics Research Seminars (IMRS)
\n\nLecture held in https://meet.google.com/wbd-bwhg-xzd.\n\nAbstract\nCon
figuration spaces of distinct points have seen an explosion in interest\na
nd in the number of publications. Applications have long gone beyond\nalge
braic topology to encompass all modern aspects of geometry\, analysis\, an
d\nmathematical physics\, further making incursions into the applied scien
ce fields.\nThis series of lectures will introduce and explain some of the
many constructions\nand results in the theory\, with an eye on applicatio
ns.\n
LOCATION:https://researchseminars.org/talk/IMSRS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sadok Kallel (American Univ. of Sharjah)
DTSTART:20240528T113000Z
DTEND:20240528T130000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/9
DESCRIPTION:Title: To
pology and Geometry of Configuration Spaces IV\nby Sadok Kallel (Ameri
can Univ. of Sharjah) as part of IUT Mathematics Research Seminars (IMRS)\
n\nLecture held in https://meet.google.com/wbd-bwhg-xzd.\n\nAbstract\nConf
iguration spaces of distinct points have seen an explosion in interest\nan
d in the number of publications. Applications have long gone beyond\nalgeb
raic topology to encompass all modern aspects of geometry\, analysis\, and
\nmathematical physics\, further making incursions into the applied scienc
e fields.\nThis series of lectures will introduce and explain some of the
many constructions\nand results in the theory\, with an eye on application
s.\n
LOCATION:https://researchseminars.org/talk/IMSRS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xinrui Zhao (MIT)
DTSTART:20241003T133000Z
DTEND:20241003T143000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/10
DESCRIPTION:Title: U
nique continuation problem on RCD spaces\nby Xinrui Zhao (MIT) as part
of IUT Mathematics Research Seminars (IMRS)\n\nLecture held in https://me
et.google.com/osu-pcqp-bqs.\n\nAbstract\nIn this talk we will sketch the p
roof of the unique continuation property of harmonic functions and caloric
functions on any RCD(K\,2) spaces and a counterexample for the strong uni
que continuation property of harmonic function on an RCD(K\,4) space. This
characterizes one of the significant differences between RCD spaces and s
mooth manifolds. We will also talk about some related open problems. The t
alk is based on joint works with Qin Deng.\n
LOCATION:https://researchseminars.org/talk/IMSRS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Allen (Lehman College\, CUNY)
DTSTART:20241107T133000Z
DTEND:20241107T143000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/11
DESCRIPTION:Title: O
n the Scalar Compactness Conjecture in the Conformal Case\nby Brian Al
len (Lehman College\, CUNY) as part of IUT Mathematics Research Seminars (
IMRS)\n\nLecture held in https://meet.google.com/czn-govf-esv.\n\nAbstract
\nUnderstanding in what sense scalar curvature is flexible versus rigid ha
s been an important area of investigation in geometric analysis. We have m
any rigidity phenomena involving scalar curvature understood and we are re
cently turning to the question of stability. One question in this directio
n asks\, If we take a sequence of Riemannian manifolds with non-negative s
calar curvature\, then what additional hypotheses need to be added to ensu
re that a subsequence exists which converges to a metric space with some n
otion of weakly non-negative scalar curvature? In this talk we will invest
igate this question in the case where the sequence of Riemannian manifolds
is conformal to the round sphere.\n
LOCATION:https://researchseminars.org/talk/IMSRS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Munn (Google)
DTSTART:20241114T133000Z
DTEND:20241114T143000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/12
DESCRIPTION:Title: L
everaging implicit bias to improve efficiencies in training and fine-tunin
g ML models\nby Michael Munn (Google) as part of IUT Mathematics Resea
rch Seminars (IMRS)\n\n\nAbstract\nIn classical statistical learning theor
y\, the bias variance tradeoff describes the relationship between the comp
lexity of a model and the accuracy of its predictions on new data. In shor
t\, simpler models are preferable to more complex ones and\, in practice\,
we often employ many techniques to control the model complexity. However\
, the best way to correctly measure the complexity of modern machine learn
ing models remains an open question. In this talk\, we will discuss the no
tion of geometric complexity and present some of our previous research whi
ch aims to address this fundamental problem. We'll also discuss current an
d future work which leverages this insight to devise strategies for more e
fficient model pre-training and fine-tuning.\n
LOCATION:https://researchseminars.org/talk/IMSRS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Ketterer (Maynooth University)
DTSTART:20241121T133000Z
DTEND:20241121T143000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/13
DESCRIPTION:Title: G
luing spaces that satisfy the Bakry-Emery condition\nby Christian Kett
erer (Maynooth University) as part of IUT Mathematics Research Seminars (I
MRS)\n\nLecture held in https://meet.google.com/poi-jmvy-mgb.\n\nAbstract\
nI will present conditions such that the glued space of two weighted Riem
annian manifolds with boundary and a Bakry-Emery lower Ricci curvature bou
nd satisfies a curvature-dimension condition. For the case of classical R
icci lower bounds this follows from a theorem of Perelman. Moreover these
conditions in return are implied by a curvature-dimension condition for th
e glued space\, and this is new even for the unweighted case.\n
LOCATION:https://researchseminars.org/talk/IMSRS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demetre Kazaras (Michigan State University)
DTSTART:20241205T133000Z
DTEND:20241205T143000Z
DTSTAMP:20260422T212705Z
UID:IMSRS/14
DESCRIPTION:Title: S
calar curvature and codimension 2 collapse\nby Demetre Kazaras (Michig
an 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 b
ound on their scalar curvature. These manifolds are toy models for spatial
geometry in general relativity. Our motivational question will be "How fl
at is an isolated gravitational system with very little total mass?" Objec
ts like gravity wells and black holes can distort geometry without accumul
ating much mass\, making this a subtle question. In addition to discussing
progress\, I will present a "drawstring" construction\, which modifies a
manifold near a given curve\, reducing its length with negligible damage t
o a scalar curvature lower bound. Unexpected examples are produced with r
elevance to a few problems. This construction extends ideas of Basilio-Dod
ziuk-Sormani and Lee-Naber-Neumayer\, and is based on joint work with Kai
Xu\n
LOCATION:https://researchseminars.org/talk/IMSRS/14/
END:VEVENT
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