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BEGIN:VEVENT
SUMMARY:Bei Wang (University of Utah - USA)
DTSTART;VALUE=DATE-TIME:20210820T150000Z
DTEND;VALUE=DATE-TIME:20210820T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/1
DESCRIPTION:Title: Sheaf-Theoretic Stratification Learning From Geometric and Topological Pe
rspectives\nby Bei Wang (University of Utah - USA) as part of GEOTOP-A
seminar\n\n\nAbstract\nWe investigate a sheaf-theoretic interpretation of
stratification learning from geometric and topological perspectives. Our
main result is the construction of stratification learning algorithms fram
ed in terms of a sheaf on a partially ordered set with the Alexandroff top
ology. We prove that the resulting decomposition is the unique minimal str
atification for which the strata are homogeneous and the given sheaf is co
nstructible. In particular\, when we choose to work with the local homolog
y sheaf\, our algorithm gives an alternative to the local homology transfe
r algorithm given in Bendich et al. (2012)\, and the cohomology stratifica
tion algorithm given in Nanda (2020). Additionally\, we give examples of s
tratifications based on the geometric techniques of Breiding et al. (2018)
\, illustrating how the sheaf-theoretic approach can be used to study stra
tifications from both topological and geometric perspectives. This approac
h also points toward future applications of sheaf theory in the study of t
opological data analysis by illustrating the utility of the language of sh
eaf theory generalizing existing algorithms. This is joint work with Adam
Brown.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusu Wang (UC San Diego - USA)
DTSTART;VALUE=DATE-TIME:20210903T150000Z
DTEND;VALUE=DATE-TIME:20210903T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/2
DESCRIPTION:Title: Persistent Laplacian: properties and algorithms\nby Yusu Wang (UC San
Diego - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nThe combinatorial
graph Laplacian\, as an operator on functions defined on the vertex set o
f a graph\, is a fundamental object in the analysis of and optimization on
graphs. There is also an algebraic topology view of the graph Laplacian w
hich arises through considering boundary operators and specific inner prod
ucts defined on simplicial (co)chain groups. This permits extending the gr
aph Laplacian to a more general operator\, the q-th combinatorial Laplacia
n to a given simplicial complex. An extension of this combinatorial Laplac
ian to the setting of pairs (or more generally\, a sequence of) simplicial
complexes was recently introduced by (R.) Wang\, Nguyen and Wei. In this
talk\, I will present serveral results (including a persistent version of
the Cheeger inequality) from our recent study of the theoretical propertie
s for the persistence Laplacian\, as well as efficient algorithms to compu
te it. This is joint work with Facundo Memoli and Zhengchao Wan.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enzo Orlandini (Physics U. Padova - Italy)
DTSTART;VALUE=DATE-TIME:20210917T150000Z
DTEND;VALUE=DATE-TIME:20210917T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/3
DESCRIPTION:Title: Getting interlocked circular chains through the needle’s eye\nby En
zo Orlandini (Physics U. Padova - Italy) as part of GEOTOP-A seminar\n\n\n
Abstract\nThe process of driven translocation of polymer chains through a
narrow pore can be severely hindered by the presence of self and mutual en
tanglement. In circular chains this entanglement is trapped in the form of
knots and links that may act as potential obstruction at the pore affecti
ng the translocation dynamics. Here we present theoretical results mainly
based on extensive Langevin simulations on the driven translocation dynami
cs of topologically linked rings. We highlight the role of link complexity
\, pore size and driving force field on the translocation process and sug
gest how to extend nanopore sensing techniques to probe the topological pr
operties of these systems and\, for instance\, to distinguish knotted from
linked states and two component to multicomponent links.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynn Zechiedrich (Baylor College of Medicine - USA)
DTSTART;VALUE=DATE-TIME:20211001T150000Z
DTEND;VALUE=DATE-TIME:20211001T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/4
DESCRIPTION:Title: Cooperativity of looping- and supercoiling-mediated base-pair disruption
among distant sites modulates the 3-D structure of DNA to control its acti
vity\nby Lynn Zechiedrich (Baylor College of Medicine - USA) as part o
f GEOTOP-A seminar\n\n\nAbstract\nJonathan M. Fogg and Lynn Zechiedrich\n\
nBaylor College of Medicine\n\nDNA in cells is supercoiled and constrained
into loops. Despite the ubiquity and importance of supercoiling in regula
ting nearly every aspect of DNA activity\, relatively little is known abou
t how. To determine how supercoiling influenced DNA shape\, we determined
the 3-D structures of individual 336 bp DNA minicircles over a wide range
of supercoiling from s = -0.019 to +0.085 (Irobalieva et al. 2015). Superc
oiled DNA forms far more bent and contorted shapes than predicted. We soug
ht to understand how DNA formed these shapes using coarse-grained molecula
r dynamics simulations (Wang et al. 2017)\, which predicted that site-spec
ific disruptions to base pairing may explain otherwise energetically unfav
orable sharp DNA bends. Likewise\, bending strain at the apices of highly
writhed DNA circles leads to broken base pairs. Probing for and mapping wh
ere base-pair disruptions occur\, we discovered that negative supercoiling
transmits mechanical stress along the DNA backbone to disrupt base pairin
g at specific distant sites (Fogg et al. 2021). This unprecedented base-pa
ir disruption cooperativity among distant sites localizes certain sequence
s to superhelical apices to facilitate DNA writhing and relieve torsional
strain\, likely preventing more extensive denaturation that can cause geno
mic instability. We also discovered how cells may exploit DNA looping to p
osition DNA nicks to facilitate repair. Our data explain how DNA can form
short loops through base-pair disruption and reveal a complex interplay be
tween looping- and supercoiling-mediated site-specific disruptions to base
pairing and the 3-D conformation of DNA\, which influence how genomes are
stored\, replicated\, transcribed\, repaired\, and likely other aspects o
f DNA activity. We hope to harness these looping- and supercoiling-mediate
d site-specific denaturation and mechanical correlations to design novel D
NA shapes for nanotechnology.\n\nIrobalieva\, R.N.*\, Fogg\, J.M.*\, Catan
ese\, D.J.\, Sutthibutpong\, T.\, Chen\, M.\, Barker\, A.K.\, Ludtke\, S.J
.\, Harris\, S.A.\, Schmid\, M.F.\, Chiu\, W.\, and Zechiedrich\, L. (2015
) Structural diversity of supercoiled DNA. Nature Comm. Oct 12\;6:8440 PMC
4608029 (*equal contribution)\n\nWang\, Q.\, Irobalieva\, R. N.\, Chiu\, W
.\, Schmid\, M. F.\, Fogg\, J. M.\, Zechiedrich\, L.\, and Pettitt\, B.M.
(2017) DNA sequence determines conformational distribution of minicircles
under torsional stress. Nucleic Acids Res. 45\, 7633–7642 PMC5737869\n\n
Fogg\, J.M.\, Judge\, A.K.\, Stricker\, E.\, Chan\, H.L.\, and Zechiedrich
\, L. Supercoiling and looping promote DNA base accessibility and coordina
tion among distant sites. Nature Comm. in press.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Janet M. Thornton (EMBL-EBI - UK)
DTSTART;VALUE=DATE-TIME:20211015T150000Z
DTEND;VALUE=DATE-TIME:20211015T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/5
DESCRIPTION:Title: The Wonderful World of Protein Structures\nby Janet M. Thornton (EMBL
-EBI - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nThis talk will aim t
o present an overview of the three dimensional structures of proteins. The
se large and intricate molecules perform the vast majority of the biologic
al functions of life and the structures of over 170\,000 proteins have bee
n determined and are stored in the Protein Databank. A detailed understand
ing of their structures has gradually emerged over the last 50 years. Chir
ality within protein structures is observed at all 'levels' of structure\,
starting with the basic stereochemistry of the polypeptide chain\, throug
h local chain folding\, to the 'tertiary' structure of the whole chain and
even to chirality of large complexes.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fazle Hussain and Jie Yao (Texas Tech University - USA)
DTSTART;VALUE=DATE-TIME:20211029T150000Z
DTEND;VALUE=DATE-TIME:20211029T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/6
DESCRIPTION:Title: Dynamics of viscous vortex knots and links\nby Fazle Hussain and Jie
Yao (Texas Tech University - USA) as part of GEOTOP-A seminar\n\n\nAbstrac
t\nReconnection is the process by which two approaching vortices cut and c
onnect to each other. As a topologically changing event\, it has been a su
bject of considerable fundamental interest for decades – not only in (cl
assical) viscous flows but also in quantum fluids\, as well as in numerous
other fields\, such as plasmas\, polymers\, DNAs\, and so on. For viscous
fluid flows\, reconnection is believed to play a significant role in vari
ous important phenomena\, such as turbulence cascade\, fine-scale mixing\,
and aerodynamic noise generation. We first delineate the underlying mecha
nism involved in vortex reconnection and its apparent role in turbulence c
ascade. Then we address the helicity dynamics involved in viscous reconnec
tion occurring in evolutions of a trefoil knotted vortex and a Hopf-link.
For both cases\, we find that the global helicity *H* gradually decre
ases before reconnection but sharply increases during reconnection – thi
s effect increases with increasing vortex Reynolds number (*Re≡circula
tion/viscousity*). This suggests that *H* for viscous flows is not
conserved as *Re→∞*. Both positive and negative helical structur
es are simultaneously generated before and during reconnection\, and their
different decay rates due to asymmetric reconnection appears to cause suc
h an increase of *H* during reconnection. By examining the topologica
l aspects of the helicity dynamics\, we find that different from *H*\
, the sum of linking and writhing numbers (i.e.\, *Lk+Wr*) continuous
ly drop during reconnection. Our results suggest that the twist\, which in
creases with *Re*\, plays a more important role in helicity dynamics
than recognized before\, particularly at high *Re*.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paweł Dłotko (Dioscuri Center - Poland)
DTSTART;VALUE=DATE-TIME:20211112T160000Z
DTEND;VALUE=DATE-TIME:20211112T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/7
DESCRIPTION:Title: Data\, their relations and shape - topology in action\nby Paweł Dło
tko (Dioscuri Center - Poland) as part of GEOTOP-A seminar\n\n\nAbstract\n
Topological data analysis is a rapidly developing area of mathematics with
applications in data science. In addition to revealing the shape of data
we develop tools for visualizing high dimensional scalar and vector valued
functions. As an example\, we explore relations between various knot inva
riants\, and extrapolate how presented tools may help to compare various\,
high-dimensional descriptors of fixed datasets. In particular\, we show h
ow these ideas can be used to compare different mapper-type graphs of the
same dataset. This is a joint work with Davide Gurnari\, Anna Jurek\, Simo
n Rudkin and Radmila Sazdanovic.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Rieser (CIMAT - Mexico)
DTSTART;VALUE=DATE-TIME:20211119T160000Z
DTEND;VALUE=DATE-TIME:20211119T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/8
DESCRIPTION:Title: Applied topology from the classical point of view\nby Antonio Rieser
(CIMAT - Mexico) as part of GEOTOP-A seminar\n\n\nAbstract\nWe generalize
several basic notions in algebraic topology to categories which contain bo
th topological spaces classically treated by classical homotopy theory as
well as more discrete and combinatorial spaces of interest in applications
\, such as graphs and point clouds. The advantage of doing so is that ther
e are now non-trivial 'continuous' maps from paracompact Hausdorff spaces
to finite spaces (given the appropriate structure)\, and one may then comp
are the resulting topological invariants on each side functorially. We fin
d that there are a number of possible such categories\, each with its own
particular homotopy theory and associated homologies\, and\, additionally\
, that there is a generalization of the coarse category which allows finit
e sets to be non-trivial (i.e. not 'coarsely' equivalent to a point). We w
ill give an overview of these theories and several applications\, show how
they are related to familiar objects in applied topology\, such as the Vi
etoris-Rips homology\, and discuss the advantages and disadvantages of eac
h. We finish by describing a recent construction of sheaf theory in the ca
tegory of Cech closure spaces\, a strict generalization of the category of
topological spaces.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Leygonie (University of Oxford - UK)
DTSTART;VALUE=DATE-TIME:20211203T160000Z
DTEND;VALUE=DATE-TIME:20211203T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/9
DESCRIPTION:Title: Inverse Problems for Persistent Homology\nby Jacob Leygonie (Universi
ty of Oxford - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nPersistent H
omology (PH) is a widely used topological descriptor for data. In order to
get a systematic understanding of the data science scenarios where PH is
successful\, it is crucial to know about its discriminative power\, i.e. t
he ability to identify and disambiguate patterns in the data\, or in other
words it is crucial to know about the information loss and the invariance
s of PH. Formally these interrogations translate into the following invers
e problem: Given an element in the image of PH\, a so-called barcode D\, w
hat is the fiber (pre-image) of PH over D? There are several ways of defin
ing PH: for point clouds in a metric space\, for filter functions on a sim
plicial complex and for continuous functions on an arbitrary space\, to na
me a few. Hence there are as many inverse problems to address. In this tal
k I will review the simplicial situation as well as that of Morse function
s on a smooth manifold\, with the aim of showing some geometrically surpri
sing fibers and transmitting my interest for these intricate inverse probl
ems.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kahle (Ohio State University - USA)
DTSTART;VALUE=DATE-TIME:20211210T160000Z
DTEND;VALUE=DATE-TIME:20211210T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/10
DESCRIPTION:Title: Configurations spaces of particles: homological solid\, liquid\, and gas
\nby Matthew Kahle (Ohio State University - USA) as part of GEOTOP-A s
eminar\n\n\nAbstract\nConfiguration spaces of points in the plane are well
studied and the topology of such spaces is well understood. But what if y
ou replace points by particles with some positive thickness\, and put them
in a container with boundaries? It seems like not much is known. To mathe
maticians\, this is a natural generalization of the configuration space of
points\, perhaps interesting for its own sake. But is also important from
the point of view of physics––physicists might call such a space the
"phase space" or "energy landscape" for a hard-spheres system. Since hard-
spheres systems are observed experimentally to undergo phase transitions (
analogous to water changing into ice)\, it would be quite interesting to u
nderstand topological underpinnings of such transitions.\n\nWe have just s
tarted to understand the homology of these configuration spaces\, and base
d on our results so far we suggest working definitions of "homological sol
id\, liquid\, and gas". This is joint work with a number of collaborators\
, including Hannah Alpert\, Ulrich Bauer\, Robert MacPherson\, and Kelly S
pendlove.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Ratiu (EPFL & Shanghai Jiao Tong University - Switzerland an
d China)
DTSTART;VALUE=DATE-TIME:20220121T160000Z
DTEND;VALUE=DATE-TIME:20220121T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/11
DESCRIPTION:Title: The Geometry of Fluid Dynamics\nby Tudor Ratiu (EPFL & Shanghai Jiao
Tong University - Switzerland and China) as part of GEOTOP-A seminar\n\n\
nAbstract\nFluid motion has a remarkable geometric structure generated by
Poisson structures on the Hamiltonian and variational structures on the La
grangian side. I will briefly review the standard results for ideal incomp
ressible homogeneous flows and then show how this is extended to fluids wi
th advected quantities. A much more elaborate extension happens for the Er
ingen model of liquid crystals because these fluids have internal structur
e. Then I will introduce a momentum map with values in differential charac
ters that captures topological information\, something the classical momen
tum map cannot do. This has consequences in hydrodynamics\, specifically f
or Clebsch variables\, since it permits to deal with solutions whose helic
ity is integer valued.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús Rodríguez-Viorato (CIMAT - México)
DTSTART;VALUE=DATE-TIME:20220204T160000Z
DTEND;VALUE=DATE-TIME:20220204T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/12
DESCRIPTION:Title: Topological Analysis from Latent Semantic Analysis\nby Jesús Rodrí
guez-Viorato (CIMAT - México) as part of GEOTOP-A seminar\n\n\nAbstract\n
Latent Semantic Analysis is one of the most widely used and accepted techn
iques in natural language processing. A better understanding of the topolo
gy of Latent Spaces could lead to better applications. We applied differen
t topological techniques such as Ballmapper and persistent homology to the
Latent Semantic representation of hundreds of thousands of abstracts and
titles from the ArXiv database. We will present a comprehensible synthesis
of our computations\, comparing results between different time frames and
ArXiv categories.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Tulio Angulo (UNAM - México)
DTSTART;VALUE=DATE-TIME:20220218T160000Z
DTEND;VALUE=DATE-TIME:20220218T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/13
DESCRIPTION:Title: Coexistence holes in ecological systems\nby Marco Tulio Angulo (UNAM
- México) as part of GEOTOP-A seminar\n\n\nAbstract\nA central challenge
of Ecology is to explain the enormous biodiversity of species that we fin
d on Earth\, from the diversity of plant and animal species that stably co
exist in tropical forests to the variety of microbial species that coexist
in our gut. Ecologists have focused on characterizing the "limits" of spe
cies coexistence ---that is\, the maximum number of different species that
can coexist under given constraints. Yet\, little is known about the stru
cture of species coexistence below such limits. Namely\, is it possible to
assemble an ecological system by adding one species at a time until reach
ing the coexistence limits? Or is it possible to find obstructions where s
pecies coexistence abruptly breaks before reaching the limits? To address
these questions\, we built a novel formalism based on hypergraphs and Alge
braic Topology to show that\, below its limits\, species coexistence in ec
ological systems has ubiquitous obstructions that we call "coexistence hol
es". A coexistence hole occurs during an assembly process when a species c
ollection does not coexist\, although we can assemble it from sub-collecti
ons that coexist. Using theoretical and experimental ecological systems\,
we provide direct evidence showing that coexistence holes obey regularitie
s. Namely\, their diversity is constrained by the internal structure of sp
ecies interactions\, while their frequency can be explained by external fa
ctors acting on these systems. Overall\, our work provides one of the firs
t applications of Algebraic Topology to Ecology\, unveiling how biodiversi
ty is a discontinuous process driven by internal design constraints.\n\nTh
is is joint work with Aaron Kelley (IM-UNAM)\, Luis Montejano (IM-UNAM)\,
Chuliang Song (McGill/Toronto University) and Serguei Saavedra (MIT).\n\nR
eferences:\n[1] Angulo\, Marco Tulio\, et al. "Coexistence holes character
ize the assembly and disassembly of multispecies systems." Nature Ecology
& Evolution (2021): 1-11.\n[2] Letten\, A. D. (2021). "Coexistence holes f
ill a gap in community assembly theory." Nature Ecology & Evolution\, 1-2.
\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Knudson (University of Florida - USA)
DTSTART;VALUE=DATE-TIME:20220311T160000Z
DTEND;VALUE=DATE-TIME:20220311T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/14
DESCRIPTION:Title: Discrete Stratified Morse Theory\nby Kevin Knudson (University of Fl
orida - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nIn this talk I wil
l describe a discrete version of stratified Morse theory and give several
examples of the utility of theory. This is joint work with Bei Wang.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Randall Kamien (University of Pennsylvania - USA)
DTSTART;VALUE=DATE-TIME:20220318T160000Z
DTEND;VALUE=DATE-TIME:20220318T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/15
DESCRIPTION:Title: A New Classification of Topological Defects\nby Randall Kamien (Univ
ersity of Pennsylvania - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nS
mectic liquid crystals are layered systems that abound in nature. I will i
ntroduce these materials and show how the long-lived\, topologically prote
cted excitations defy simple classification. I will describe our attempts.
\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carina Curto (The Pennsylvania State University - USA)
DTSTART;VALUE=DATE-TIME:20220401T160000Z
DTEND;VALUE=DATE-TIME:20220401T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/16
DESCRIPTION:Title: Dynamically relevant motifs in inhibition-dominated networks\nby Car
ina Curto (The Pennsylvania State University - USA) as part of GEOTOP-A se
minar\n\n\nAbstract\nMany networks in the brain possess an abundance of in
hibition\, which serves to shape and stabilize neural dynamics. The neuron
s in such networks exhibit intricate patterns of connectivity whose struct
ure controls the allowed patterns of neural activity. In this work\, we ex
amine inhibitory threshold-linear networks (TLNs) whose dynamics are const
rained by an underlying directed graph. We develop a set of parameter-inde
pendent graph rules that enable us to predict features of the dynamics\, s
uch as emergent sequences and dynamic attractors\, from properties of the
graph. These rules provide a direct link between the structure and functio
n of inhibition-dominated networks\, yielding new insights into how connec
tivity shapes dynamics in real neural circuits. Recently\, we have used th
ese ideas to classify dynamic attractors in a two-parameter family of TLNs
spanning all 9608 directed graphs of size n=5. Remarkably\, we find a str
iking modularity in the dynamic attractors\, with identical or near-identi
cal attractors arising in networks that are otherwise dynamically inequiva
lent. This suggests that\, just as one can store multiple static patterns
as stable fixed points in a Hopfield model\, a variety of dynamic attracto
rs can also be embedded in TLNs in a modular fashion.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (London Institute for Mathematical Science & Merton Co
llege\, Oxford University)
DTSTART;VALUE=DATE-TIME:20220422T150000Z
DTEND;VALUE=DATE-TIME:20220422T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/17
DESCRIPTION:Title: Universes as Bigdata: Physics\, Geometry and Machine-Learning\nby Y
ang-Hui He (London Institute for Mathematical Science & Merton College\, O
xford University) as part of GEOTOP-A seminar\n\n\nAbstract\nThe search fo
r the Theory of Everything has led to superstring theory\, which then led
physics\, first to algebraic/differential geometry/topology\, and then to
computational geometry\, and now to data science.\nWith a concrete playgro
und of the geometric landscape\, accumulated by the collaboration of physi
cists\, mathematicians and computer scientists over the last 4 decades\, w
e show how the latest techniques in machine-learning can help explore prob
lems of interest to theoretical physics and to pure mathematics.\nAt the c
ore of our programme is the question: how can AI help us with mathematics?
\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Grosberg (NYU - USA)
DTSTART;VALUE=DATE-TIME:20220506T150000Z
DTEND;VALUE=DATE-TIME:20220506T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/18
DESCRIPTION:Title: Is Trivial Knot Really So Trivial?\nby Alexander Grosberg (NYU - USA
) as part of GEOTOP-A seminar\n\n\nAbstract\nWhile topological ideas are w
idely popular in physics\, topology of classical linear threads of polymer
s presents steep mathematical and conceptual challenges\, with application
s in both biopolymers and materials. I will concentrate on the simplest c
ase of polymer unknots and review what is known about fluctuations and sta
tistical mechanics of such objects based mostly on simulations\, experimen
ts\, and hand-waving theoretical arguments. Continuing with increasingly
sophisticated models and phenomena\, I will review several more recent the
oretical and experimental achievements\, and conclude with the discussion
of a controversial concept of “topological glass”.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Landi (Università di Modena e Reggio Emilia - Italy)
DTSTART;VALUE=DATE-TIME:20220520T150000Z
DTEND;VALUE=DATE-TIME:20220520T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/19
DESCRIPTION:Title: Multi-parameter persistence from the viewpoint of discrete Morse theory.
\nby Claudia Landi (Università di Modena e Reggio Emilia - Italy) as
part of GEOTOP-A seminar\n\n\nAbstract\nAlthough there is no doubt that mu
lti-parameter persistent homology is a useful tool for the topological ana
lysis of multivariate data\, a complete understanding of these modules is
still lacking. Issues such as computation\, visualization\, and interpreta
tion of the output remain difficult to solve. In this talk\, I will show h
ow discrete Morse theory may enhance our understanding of multi-parameter
persistence by connecting the combinatorial properties of the critical cel
ls of multi-filtered data to the algebraic properties of their persistence
modules.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Gang Wen (MIT - USA)
DTSTART;VALUE=DATE-TIME:20220603T150000Z
DTEND;VALUE=DATE-TIME:20220603T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/20
DESCRIPTION:Title: From topological order to origin of elementary particles (from algebra t
o geometry)\nby Xiao-Gang Wen (MIT - USA) as part of GEOTOP-A seminar\
n\n\nAbstract\nI will discuss the world of many-body long range entangleme
nt. It turns out that both topological quantum matter and elementary parti
cles arise from many-body long range entanglement.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisbeth Fajstrup (Aalborg University - Denmark)
DTSTART;VALUE=DATE-TIME:20220819T150000Z
DTEND;VALUE=DATE-TIME:20220819T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/21
DESCRIPTION:Title: Collapsing in directed topology\nby Lisbeth Fajstrup (Aalborg Univer
sity - Denmark) as part of GEOTOP-A seminar\n\n\nAbstract\nIn a simplicial
complex\, a pair of simplices are a collapsing pair\, if one is a unique
maximal coface of the other which is then a free face. Such a pair can be
collapsed by removal of the two simplices and all simplices between them
– think about an edge in a solid tetrahedron\; collapsing means removing
the edge\, the interior of the tetrahedron and the interior of the two fa
ces containing that edge. This leads to a homotopy equivalence. There is a
similar notion for cubical complexes. A sequence of collapses leads to a
simpler (fewer simplices/cubes) space.\nFor a directed space\, which is a
topological space with a selected set of paths\, the directed paths\, dire
cted homotopy equivalence is a very strong requirement\, and not what shou
ld be the basis of collapsing.\nWe study the following setting: A Euclidea
n Cubical Complex\, an ECC\, is a subset of R^n which is a union of elemen
tary cubes. An elementary cube is a product of n intervals [ai\,ai+e]\, wh
ere e is either 0 or 1. A directed path in an ECC is continuous and non-de
creasing in all coordinates.\nWe define a notion of collapse with the aim
of preserving various properties of spaces of directed paths.\nThis is joi
nt work with the WiT\, Women in Topology\, group R. Belton\, R. Brooks\, S
.Ebli\, L.F.\, B.T.Fasy\, N.Sanderson\, E. Vidaurre.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Scolamiero (KTH Royal Institute of Technology - Sweden)
DTSTART;VALUE=DATE-TIME:20220902T150000Z
DTEND;VALUE=DATE-TIME:20220902T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/22
DESCRIPTION:Title: Stable and interpretable topological feature maps\nby Martina Scolam
iero (KTH Royal Institute of Technology - Sweden) as part of GEOTOP-A semi
nar\n\n\nAbstract\nPersistent homology\, a popular method in TDA\, can be
used to define feature maps encoding geometrical properties of data. In th
is talk I will present a method\, developed by the TDA group at KTH\, whic
h allows to construct feature maps with learnable parameters\, stable with
respect to distances on persistence modules. The feature maps are in fact
defined starting from distances between persistence modules rather than o
n the barcode decomposition\, making the method suitable for generalisatio
ns. Particular focus will be on understanding parametrised families of suc
h feature maps\, such as those stable with respect to p-Wasserstein distan
ce. The use of Wasserstein stable features will be illustrated on real wor
ld and artificial datasets.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Baltag (Universiteit van Amsterdam - Netherlands)
DTSTART;VALUE=DATE-TIME:20220923T150000Z
DTEND;VALUE=DATE-TIME:20220923T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/23
DESCRIPTION:Title: The Topology of Knowing (Or How to Avoid Unexpected Exams)\nby Alex
andru Baltag (Universiteit van Amsterdam - Netherlands) as part of GEOTOP-
A seminar\n\n\nAbstract\nIn this talk I will present applications of Gener
al Topology to Epistemic Logic (=the logical aspects of knowledge\, knowab
iity and belief) and Formal Learning Theory. I show that topological metho
ds can throw light on issues such as the value of simplicity as a learning
strategy (cf. Ockham's Razor) and the analysis of epistemic paradoxes (e.
g. the connection between the so-called Surprise Exam Paradox and the Cant
or-Bendixson process of calculating the perfect core). Time-permitting\, I
may present some complete and decidable logical axiomatizations of these
notions and maybe even give a hint concerning the completeness proofs.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jérémy Ledent (University of Strathclyde - UK)
DTSTART;VALUE=DATE-TIME:20220930T150000Z
DTEND;VALUE=DATE-TIME:20220930T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/24
DESCRIPTION:Title: Knowledge and topology: a simplicial approach\nby Jérémy Ledent (U
niversity of Strathclyde - UK) as part of GEOTOP-A seminar\n\n\nAbstract\n
Multi-agent Epistemic Logic is a modal logic of knowledge. It allows to re
ason about a finite set of agents who may know facts about the world\, and
about each other. In this talk\, I will present a new semantics for epist
emic logic\, based on simplicial complexes. In this approach\, the knowled
ge of the agents is modeled by a higher-dimensional space called a simplic
ial model\; and the truth of an epistemic logic formula can be evaluated b
y inspecting the various possible paths in this space. I will illustrate t
hese ideas using examples from the theory of distributed computing\, where
the agents correspond to individual processes who can exchange informatio
n in order to solve a task. Both topological invariants and logical invari
ants can be leveraged to prove that some distributed computing tasks are i
mpossible to solve.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chad Giusti (University of Delaware - USA)
DTSTART;VALUE=DATE-TIME:20221021T150000Z
DTEND;VALUE=DATE-TIME:20221021T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/26
DESCRIPTION:Title: Tracking cycles in neural codes\nby Chad Giusti (University of Delaw
are - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nCircular coordinate
systems -- here\, cycles -- are ubiquitous in data encoded by the brain. C
lassical ideas from topology tell us that the structure of the encoded dat
a must be reflected in the activity of the encoding neural populations\, a
nd methods from topological data analysis have been highly successful at d
etecting signatures of such encodings. The next natural question we might
ask is how we assign meaning or semantics to observed cycles Here\, we des
cribe a new method for using a measure of cross-similarity to register\, o
r falsify the registration of\, cycles across populations. We demonstrate
its use in simulated and experimental data\, and discuss ongoing work usin
g these tools to investigate how feed-forward networks propagate cycles. T
his is joint work with Iris Yoon\, Niko Schonsheck\, and several others.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Lackenby (University of Oxford - UK)
DTSTART;VALUE=DATE-TIME:20221104T160000Z
DTEND;VALUE=DATE-TIME:20221104T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/27
DESCRIPTION:Title: Knot theory and machine learning\nby Marc Lackenby (University of Ox
ford - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nKnot theory is divid
ed into several subfields. One of these is hyperbolic knot theory\, which
is focused on the hyperbolic structure that exists on many knot complement
s. Another branch of knot theory is concerned with invariants that have co
nnections to 4-manifolds\, for example the knot signature and Heegaard Flo
er homology. In my talk\, I will describe a new relationship between these
two fields that was discovered with the aid of machine learning. Specific
ally\, we show that the knot signature can be estimated surprisingly accur
ately in terms of hyperbolic invariants. We introduce a new real-valued in
variant called the natural slope of a hyperbolic knot in the 3-sphere\, wh
ich is defined in terms of its cusp geometry. Our main result is that twic
e the knot signature and the natural slope differ by at most a constant ti
mes the hyperbolic volume divided by the cube of the injectivity radius. T
his theorem has applications to Dehn surgery and to 4-ball genus. We will
also present a refined version of the inequality where the upper bound is
a linear function of the volume\, and the slope is corrected by terms corr
esponding to short geodesics that have odd linking number with the knot. M
y talk will outline the proofs of these results\, as well as describing th
e role that machine learning played in their discovery.\n\nThis is joint w
ork with Alex Davies\, Andras Juhasz\, and Nenad Tomasev.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Barenghi (Newcastle University - UK)
DTSTART;VALUE=DATE-TIME:20221118T160000Z
DTEND;VALUE=DATE-TIME:20221118T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/28
DESCRIPTION:Title: Is turbulence knotted?\nby Carlo Barenghi (Newcastle University - UK
) as part of GEOTOP-A seminar\n\n\nAbstract\nVortex lines and streamlines
in turbulent flows\, visualized in the experiments or in the numerics\, ap
pear chaotic\, twisted\, perhaps linked or knotted. The physical meaning o
f this complexity and its relation to the dynamics is still obscure. In th
is lecture I shall address this problem - the geometrical and topological
complexity of turbulence - in the arguably simpler context of "quantum flu
ids".\n\nQuantum fluids (superfluid helium\, atomic Bose-Einstein condensa
tes\, etc)are studied in the laboratory at temperatures close to absolute
zero. At these low temperatures the fundamental quantum properties of matt
er are not masked by thermal disorder. In particular\, any rotational mot
ion is constrained by quantum mechanics to individual vortex lines of fixe
d strength (phase defects of a complex order parameter)\, unlike what happ
ens in ordinary fluids where vorticity is a continuous field. Quantum turb
ulence\, created by stirring a quantum fluid\, is thus conceptually simple
r than ordinary turbulence\, consisting of a tangle of individual vortex l
ines rather than a disordered continuous vorticity field.\n\nAfter describ
ing some surprising similarities between quantum turbulence and ordinary t
urbulence\, I shall show how the geometry and the topology of quantum turb
ulence can be quantified in a relatively simple way\, hence demonstrate th
at quantum turbulence is indeed knotted. Is ordinary turbulence knotted to
o?\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Di Giovanni (Twitter - UK)
DTSTART;VALUE=DATE-TIME:20221209T160000Z
DTEND;VALUE=DATE-TIME:20221209T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/30
DESCRIPTION:Title: Over-squashing and over-smoothing through the lenses of curvature and mu
lti-particle dynamics\nby Francesco Di Giovanni (Twitter - UK) as part
of GEOTOP-A seminar\n\n\nAbstract\nI am going to talk about two problems
that Message Passing Neural Networks (MPNNs) have been shown to be struggl
ing from. The first one – known as over-squashing – is unavoidable in
the MPNN class and concerns the input graph topology. This relates to how
information propagates in a graph. We show that discrete curvature quantit
ies (old and new) could help us understand where messages are being lost a
nd we can provably characterize the over-squashing phenomenon in terms of
curvature. The second problem consists in analysing GNNs as multi-particle
dynamics using the lens of gradient flows of an energy. We investigate wh
at happens when instead of learning the MPNN equations we learn an energy
and then let the equations follow the gradient flow of such energy. This a
llows us to understand further the role of the channel-mixing matrix that
is ubiquitous in standard graph convolutional models as a bilinear potenti
al inducing both attraction and repulsion along edges via its positive and
negative eigenvalues respectively.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Baez (UC Riverside - USA)
DTSTART;VALUE=DATE-TIME:20220909T150000Z
DTEND;VALUE=DATE-TIME:20220909T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/31
DESCRIPTION:Title: Compositional Modeling with Decorated Cospans\nby John Baez (UC Rive
rside - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nOne goal of applie
d category theory is to understand open systems: that is\, systems with a
boundary of some sort\, through which matter\, energy or information can f
low in or out. We can describe a large class of open systems using the m
athematics of decorated cospans\, which we explain here. In various examp
les these ideas have been implemented in software. An interesting example
comes from stock-flow diagrams\, which are widely used in epidemiology to
model the dynamics of populations. Although tools already exist for build
ing these diagrams and simulating the systems they describe\, we have crea
ted a new package called StockFlow which uses decorated cospans to overcom
e limitations of the existing tools. This is joint work with Xiaoyan Li\,
Sophie Libkind\, Nathaniel Osgood and Evan Patterson.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Bubenik (University of Florida - USA)
DTSTART;VALUE=DATE-TIME:20221014T150000Z
DTEND;VALUE=DATE-TIME:20221014T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/32
DESCRIPTION:Title: Topological Data Analysis for Biological Images and Video\nby Peter
Bubenik (University of Florida - USA) as part of GEOTOP-A seminar\n\n\nAbs
tract\nI will present the results of two projects applying topological dat
a analysis (TDA) and machine learning (ML) to biological data. In the firs
t\, we have developed a new tool\, TDAExplore\, that combines TDA and ML t
o both classify biological images and to provide a visualization that is b
iologically informative. In the second\, we use TDA and ML to classify qua
si-periodic biological videos and we apply TDA to such a video to produce
synthetic periodic videos.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Érika Roldán (Max Planck Institute for Mathematics in the Scienc
es (MiS) Leipzig - Germany)
DTSTART;VALUE=DATE-TIME:20230127T160000Z
DTEND;VALUE=DATE-TIME:20230127T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/34
DESCRIPTION:Title: Topology of random 2-dimensional cubical complexes\nby Érika Roldá
n (Max Planck Institute for Mathematics in the Sciences (MiS) Leipzig - Ge
rmany) as part of GEOTOP-A seminar\n\n\nAbstract\nWe study a natural model
of random 2-dimensional cubical complexes which are subcomplexes of an n-
dimensional cube\, and where every possible square (2-face) is included in
dependently with probability p. Our main result exhibits a sharp threshold
$p=1/2$ for homology vanishing as the dimension n goes to infinity. This
is a 2-dimensional analogue of the Burtin and Erdős-Spencer theorems char
acterizing the connectivity threshold for random graphs on the 1-skeleton
of the n-dimensional cube. Our main result can also be seen as a cubical c
ounterpart to the Linial-Meshulam theorem for random 2-dimensional simplic
ial complexes. However\, the models exhibit strikingly different behaviors
. We show that if $p > 1 - √1/2 ≈ 0.2929$\, then with high probability
the fundamental group is a free group with one generator for every maxima
l 1-dimensional face. As a corollary\, homology vanishing and simple conne
ctivity have the same threshold. This is joint work with Matthew Kahle and
Elliot Paquette.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ingrid Membrillo Solís (University of Southampton - UK)
DTSTART;VALUE=DATE-TIME:20230217T160000Z
DTEND;VALUE=DATE-TIME:20230217T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/36
DESCRIPTION:Title: Spaces of discrete vector fields and their applications to complex syste
ms dynamics\nby Ingrid Membrillo Solís (University of Southampton - U
K) as part of GEOTOP-A seminar\n\n\nAbstract\nA complex system is formed b
y entities that\, through their interactions and dependencies\, give rise
to a unified whole with properties and behavior distinct from those of its
constituent parts. Examples of complex systems are the human brain\, livi
ng cells\, the Earth's global climate\, organisms\, smart materials\, ecos
ystems and the economy. Modelling complex systems dynamics is challenging
due to the high dimensionality and variety of the non-linear phenomena tha
t these systems exhibit\, such as network and pattern formation\, evolutio
n\, adaptation and self-organization. \n\nIn this talk\, we will present a
data-driven approach to studying complex systems using spaces of discrete
vector fields. These spaces can be endowed with a family of metrics that
allow us to keep track of the dynamics of complex systems. We will show t
hat this geometric framework can be used for dimensionality reduction\, de
tection of stable and unstable global attractors\, and quantification of p
hysical properties. In particular\, we will show applications to the analy
sis of data obtained from simulations and experiments of soft matter mater
ials\, and simulations of pattern formation on curved domains. This is par
t of joint works with M. Van Rossem\, T. Orlova\, N. Podoliak\, T. Madelei
ne\, H. Sohn\, I. Smalyukh\, G. D'Alessandro\, M. Kaczmarek and J. Brodzki
.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armajac Raventós Pujol (Universidad Autónoma de Madrid - Spain)
DTSTART;VALUE=DATE-TIME:20230303T160000Z
DTEND;VALUE=DATE-TIME:20230303T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/37
DESCRIPTION:Title: Simplicial complexes and the index lemma: A pathway to reach agreements
fairly\nby Armajac Raventós Pujol (Universidad Autónoma de Madrid -
Spain) as part of GEOTOP-A seminar\n\n\nAbstract\nAggregating individual p
references is a fundamental problem in democracy:\nHow can we take collect
ive decisions fairly based on individual preferences? Arrow's impossibilit
y theorem (1951) proves that it is not possible to do it when we assume so
me apparently mild conditions. Fortunately\, in some cases\, aggregation i
s possible when the domain of individual preferences is restricted. That i
s\, when voters can only report some preferences\, good aggregation rules
exist. However\, no theorem characterizes the domains in which aggregation
is possible\, and the\nproblem remains open.\n\nDespite the Arrovian mode
l being purely combinatorial\, Baryshnikov (1993) used simplicial complexe
s and homology to prove Arrow's theorem and exposed a conjecture which cha
racterized restricted domains through homology groups. The main drawback o
f using homology is that it is not affordable for most of the social scien
tists. Therefore\, instead of homology\, we have used combinatorial topolo
gy tools such as the Index Lemma (the combinatorial counterpart to Poincar
e's Lemma) to tackle the problem. First\, we have proved the Arrow's impos
sibility theorem\, showing that combinatorial topology is helpful for our
purposes.\n\nSecond\, we have characterized the domains allowing aggregati
on rules for the base case of two voters and three candidates. Our charact
erization proves that homology groups are not enough to characterize such
domains. Our result gives us hope to obtain a general characterization of
the good domains for aggregating preferences. Moreover\, it could be imple
mented computationally\, making it handled by practitioners in politics an
d economics.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darrick Lee (EPFL - Switzerland)
DTSTART;VALUE=DATE-TIME:20230317T160000Z
DTEND;VALUE=DATE-TIME:20230317T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/38
DESCRIPTION:Title: Mapping Space Signatures\nby Darrick Lee (EPFL - Switzerland) as par
t of GEOTOP-A seminar\n\n\nAbstract\nThe path signature is a characterizat
ion of paths which has led to the development of rough paths in stochastic
analysis\, and a powerful set of novel tools for time series data in mach
ine learning. In this talk\, we begin with some background on signature me
thods in machine learning. We introduce the mapping space signature\, a ge
neralization of the path signature for maps from higher dimensional cubica
l domains (such as images or videos)\, which is motivated by the topologic
al/geometric perspective of iterated integrals of differential forms by K.
T. Chen. The mapping space signature shares many of the analytic and alge
braic properties of the path signature\, in particular it is universal and
characteristic. This is joint work with Chad Giusti\, Vidit Nanda\, and H
arald Oberhauser.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Koya Shimokawa (Ochanomizu University - Japan)
DTSTART;VALUE=DATE-TIME:20230331T160000Z
DTEND;VALUE=DATE-TIME:20230331T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/39
DESCRIPTION:Title: Applications of band surgery on knots and links\nby Koya Shimokawa (
Ochanomizu University - Japan) as part of GEOTOP-A seminar\n\n\nAbstract\n
We consider local moves of knots and links\, called band surgeries. A band
surgery usually changes the topology of knots and links. Signatures\, Jon
es polynomials\, and other link invariants can be used to show the absence
of band surgery between a given pair of links. A band surgery has been us
ed for establishing mathematical models of DNA recombination and anti-para
llel reconnection of vortex knots and links. In this talk\, we discuss app
lications of results of band surgeries to the unlinking of DNA links by si
te-specific recombination and to the untying of vortex knots by anti-paral
lel reconnection.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bastian Rieck (Institute of AI for Health and the Helmholtz Pionee
r Campus of Helmholtz Munich - Germany)
DTSTART;VALUE=DATE-TIME:20230414T160000Z
DTEND;VALUE=DATE-TIME:20230414T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/40
DESCRIPTION:Title: Curvature for Graph Learning\nby Bastian Rieck (Institute of AI for
Health and the Helmholtz Pioneer Campus of Helmholtz Munich - Germany) as
part of GEOTOP-A seminar\n\n\nAbstract\nCurvature bridges geometry and top
ology\, using local\ninformation to derive global statements. While well-k
nown in a\ndifferential topology context\, it was recently extended to the
\ndomain of graphs. In fact\, graphs give rise to various notions\nof curv
ature\, which differ in expressive power and purpose. We\nwill give a brie
f overview of curvature in graphs\, define some relevant concepts\, and sh
ow their utility for data science and machine learning applications. In pa
rticular\, we shall discuss\ntwo applications: first\, the use of curvatur
e to *distinguish*\nbetween different models for synthesising new graphs f
rom some\nunknown distribution\; second\, a novel *framework* for defining
curvature for hypergraphs\, whose structural properties require a more ge
neric setting. We will also describe new applications\nthat are specifical
ly geared towards a treatment by curvature\,\nthus underlining the utility
of this concept for data science.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Liu (Institute of Theoretical Physics\, Faculty of Science\, B
eijing University of Technology - China)
DTSTART;VALUE=DATE-TIME:20230428T150000Z
DTEND;VALUE=DATE-TIME:20230428T160000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/41
DESCRIPTION:Title: Role of topology in study of cascade evolutions of physical knot/link co
mplex systems\nby Xin Liu (Institute of Theoretical Physics\, Faculty
of Science\, Beijing University of Technology - China) as part of GEOTOP-A
seminar\n\n\nAbstract\nRecent laboratory and numerical experiments in cla
ssical and quantum fluids and in recombinant DNA plasmids show that physic
al knots/links are highly unstable\, decaying from a high-topological comp
lexity state to a low-complexity state through a series of reconnection ev
ents. A possible theoretical picture for this phenomenon is that hierarchy
of topological complexity is\nclosely related to spectrum of energy or ot
her dynamical properties. For this study the following\nprogress would be
reviewed: (i) ropelengths/crossing numbers of prime knots and links versus
the\ngroundstate energy spectrum\; (ii) adapted HOMFLYPT polynomial value
s used to quantify\ncomplexity of torus knots and links\; (iii) complexity
degree of a knot defined in a Legendre\npolynomial basis in a suitably de
fined knot polynomial space. Some relevant undergoing\nnumerical simulatio
n work is introduced as well. Our emphasis will be placed on the role that
\ntopologically non-conservative transitions play in the evolution of a kn
ot complex system\, in the\nhope of finding a scalar topological invariant
to manage energy or other spectrums.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mónica Clapp (Instituto de Matemáticas UNAM - Mexico)
DTSTART;VALUE=DATE-TIME:20230519T160000Z
DTEND;VALUE=DATE-TIME:20230519T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/43
DESCRIPTION:Title: Optimal partitions for the Yamabe equation\nby Mónica Clapp (Instit
uto de Matemáticas UNAM - Mexico) as part of GEOTOP-A seminar\n\n\nAbstra
ct\nThe Yamabe equation on a Riemannian manifold $(M\, g)$ is of\nrelevanc
e in differential geometry. A positive solution to it gives rise to a metr
ic\non M which has constant scalar curvature and is conformally equivalent
to the\ngiven metric $g$.\nAn optimal $\\ell$-partition for the Yamabe eq
uation is a cover of M by $\\ell$-pairwise\ndisjoint open subsets such tha
t the Yamabe equation with Dirichlet boundary\ncondition has a least energ
y solution on each one of these sets\, and the sum of\nthe energies of the
se solutions is minimal. Such a partition induces a generalized\nmetric th
at vanishes on a set of measure zero and is conformally equivalent to\n$g$
in the complement.\nI will present some results obtained in collaboration
with Angela Pistoia\n(La Sapienza Universit`a di Roma) and Hugo Tavares (
Universidade de Lisboa)\nthat ensure the existence and establish qualitati
ve properties of this type of\npartitions. To do this\, we use some ideas
from physics.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Galaz-García (Durham University - UK)
DTSTART;VALUE=DATE-TIME:20230602T160000Z
DTEND;VALUE=DATE-TIME:20230602T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/44
DESCRIPTION:Title: Metric geometry of spaces of persistence diagrams\nby Fernando Galaz
-García (Durham University - UK) as part of GEOTOP-A seminar\n\n\nAbstrac
t\nPersistence diagrams are central objects in topological data analysis.
They are pictorial representations of persistence homology modules and des
cribe topological features of a data set at different scales. In this talk
\, I will discuss the geometry of spaces of persistence diagrams and conne
ctions with the theory of Alexandrov spaces\, which are metric generalizat
ions of complete Riemannian manifolds with sectional curvature bounded bel
ow. In particular\, I will discuss how one can assign to a metric pair $(X
\,A)$ a one-parameter family of pointed metric spaces of (generalized) per
sistence diagrams $D_p(X\,A)$ with points in $(X\,A)$ via a family of func
tors $D_p$ with $p\\in [1\,\\infty]$. These spaces are equipped with the p
-Wasserstein distance when $p\\geq 1$ and the bottleneck distance when $p=
\\infty$. The functors $D_p$ preserve natural metric properties of the spa
ce $X$\, including non-negative curvature in the triangle comparison sense
when $p=2$. When $p=\\infty$\, the functor $D_\\infty$ is sequentially co
ntinuous with respect to a suitable notion of Gromov–Hausdorff convergen
ce of metric pairs. When $(X\,A) = (\\mathbb{R}^2\,\\Delta)$\, where $\\De
lta$ is the diagonal of $\\mathbb{R}^2$\, one recovers previously known pr
operties of the usual spaces of persistence diagrams. This is joint work w
ith Mauricio Che\, Luis Guijarro\, Ingrid Membrillo Solis\, and Motiejus V
aliunas.\n\nhttps://arxiv.org/abs/2109.14697\n\nhttps://arxiv.org/abs/2205
.09718\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fred Chazal (INRIA Saclay - France)
DTSTART;VALUE=DATE-TIME:20230113T160000Z
DTEND;VALUE=DATE-TIME:20230113T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/45
DESCRIPTION:Title: Measure Vectorization for Automatic Topologically-Oriented Learning with
guarantees.\nby Fred Chazal (INRIA Saclay - France) as part of GEOTOP
-A seminar\n\n\nAbstract\nRobust topological information commonly comes in
the form of a set of persistence diagrams that can be seen as discrete me
asures and are uneasy to use in generic machine learning frameworks. \n\n
In this talk we will introduce a fast\, learnt\, unsupervised vectorizatio
n method\, named ATOL\, for measures in Euclidean spaces and use it for re
flecting underlying changes in topological behaviour in machine learning c
ontexts. The algorithm is simple and efficiently discriminates important s
pace regions where meaningful differences to the mean measure arise. We wi
ll show that it is proven to be able to separate clusters of persistence d
iagrams. We will illustrate the strength and robustness of our approach on
a few synthetic and real data sets.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Oudot (INRIA Saclay - France.)
DTSTART;VALUE=DATE-TIME:20230210T160000Z
DTEND;VALUE=DATE-TIME:20230210T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/46
DESCRIPTION:Title: Signed rank decompositions for multi-parameter persistence: from Moebius
inversion to relative homological algebra\nby Steve Oudot (INRIA Sacl
ay - France.) as part of GEOTOP-A seminar\n\n\nAbstract\nA question that c
omes up repeatedly in recent developments on\nmulti-parameter persistence
is to define mathematically sound and\ncomputationally tractable notions o
f approximation for multi-parameter\npersistence modules. As $\\mathbb{R}^
n$ is of wild representation type\, one\nseeks to approximate arbitrary (s
ay\, finitely presentable) modules by\nmodules coming from some subcategor
y that is easier to work with in\npractice. An obvious candidate subcatego
ry is the one of\ninterval-decomposable modules\, whose summands are indic
ator modules of\nintervals (i.e. convex\, connected subsets of $\\mathbb{R
}^n$\, equipped\nwith the product order). Indeed\, interval-decomposable m
odules are\nconvenient to work with\, since they are easy to encode and ma
nipulate on\na computer\, and to interpret visually. Several notions of mo
dule\napproximation using this subcategory have been proposed\, among whic
h the\nmost common one seeks to preserve the rank invariant when switching
from\nthe original module to its interval-decomposable approximation. The
\nmotivation is that\, the rank invariant being one of the weakest\ninvari
ants available to us\, preserving it is considered to be a minimum.\nAs it
turns out\, this is not always possible\, however one can always\ndecompo
se the rank invariant of the module as a $\\mathbb{Z}$-linear\ncombination
of rank invariants of interval modules. Thus\, a weaker form\nof preserva
tion of the rank invariant is possible\, in which the interval\nsummands a
re signed (hence the name "signed rank decomposition"). This\nfact can be
viewed as a consequence of the Moebius inversion formula\,\nbut more funda
mentally\, it can be obtained by working in the\nGrothendieck group relat
ive to an appropriate exact structure\, where the\nrank invariant of the m
odule becomes equal to the alternating sum of the\nrank invariants of the
various terms in the module's minimal relative\nprojective resolution. Thi
s alternative proof strategy offers some\nsignificant benefits: (1) it lin
ks the coefficients in the decomposition\nto the structure of the module\,
as in the 1-parameter setting\; (2) it\nprovides a roadmap to study their
bottleneck stability\; (3) it connects\nmulti-parameter persistence to re
lative homological algebra\, thereby\npaving the way towards the definitio
n of more refined invariants for\nmulti-parameter persistence modules usin
g larger classes of projectives.\nThe purpose of my talk will be to tell t
his story.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reidun Twarock (The University of York - UK)
DTSTART;VALUE=DATE-TIME:20221216T160000Z
DTEND;VALUE=DATE-TIME:20221216T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/47
DESCRIPTION:Title: Geometry in the Fight against Viral Infection\nby Reidun Twarock (Th
e University of York - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nThe
Covid-19 pandemic has highlighted the need for novel antiviral strategies.
In this talk\, I will demonstrate that insights into the geometric princi
ples underpinning virus architecture provide a key to uncovering the mecha
nisms by which viruses replicate and infect their hosts. Geometric and top
ological descriptors of virus architecture\, combined with stochastic simu
lations\, reveal how viruses navigate the knife’s edge between stability
and instability\, guaranteeing protection for their genetic cargo while a
lso enabling its timely release. Models of virus architecture also provide
a novel perspective on open problems in virus assembly. This includes the
origin and control\nof polymorphic particle assembly\, which arises\, amo
ngst others\, when virus-derived protein containers are functionalised to
present antigens for applications in vaccinology. They moreover play an in
strumental role in the discovery of genome-encoded virus assembly instruct
ions. These results shed new light on selective pressures on viral evoluti
on and pave the way for innovation in antiviral therapy and virus nanotech
nology.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia R. Gel (UT Dallas - USA)
DTSTART;VALUE=DATE-TIME:20230818T160000Z
DTEND;VALUE=DATE-TIME:20230818T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/48
DESCRIPTION:by Yulia R. Gel (UT Dallas - USA) as part of GEOTOP-A seminar\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Levi (University of Aberdeen - UK)
DTSTART;VALUE=DATE-TIME:20230901T160000Z
DTEND;VALUE=DATE-TIME:20230901T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/49
DESCRIPTION:by Ran Levi (University of Aberdeen - UK) as part of GEOTOP-A
seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petar Pavešić (University of Ljubljana - Slovenia)
DTSTART;VALUE=DATE-TIME:20230908T160000Z
DTEND;VALUE=DATE-TIME:20230908T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/50
DESCRIPTION:by Petar Pavešić (University of Ljubljana - Slovenia) as par
t of GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabel Darcy (University of Iowa - USA)
DTSTART;VALUE=DATE-TIME:20230922T160000Z
DTEND;VALUE=DATE-TIME:20230922T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/51
DESCRIPTION:by Isabel Darcy (University of Iowa - USA) as part of GEOTOP-A
seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eggers (Bristol\, UK)
DTSTART;VALUE=DATE-TIME:20231006T160000Z
DTEND;VALUE=DATE-TIME:20231006T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/52
DESCRIPTION:by Jens Eggers (Bristol\, UK) as part of GEOTOP-A seminar\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ximena Fernández (Durham University\, UK)
DTSTART;VALUE=DATE-TIME:20231013T160000Z
DTEND;VALUE=DATE-TIME:20231013T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/53
DESCRIPTION:by Ximena Fernández (Durham University\, UK) as part of GEOTO
P-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Feichtner-Kozlov (University of Bremen - Germany)
DTSTART;VALUE=DATE-TIME:20231020T160000Z
DTEND;VALUE=DATE-TIME:20231020T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/54
DESCRIPTION:by Dmitry Feichtner-Kozlov (University of Bremen - Germany) as
part of GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (Virginia Commonwealth University - USA)
DTSTART;VALUE=DATE-TIME:20231103T160000Z
DTEND;VALUE=DATE-TIME:20231103T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/55
DESCRIPTION:by Allison Moore (Virginia Commonwealth University - USA) as p
art of GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clayton Shonkwiler (Colorado State - USA)
DTSTART;VALUE=DATE-TIME:20231117T160000Z
DTEND;VALUE=DATE-TIME:20231117T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/56
DESCRIPTION:by Clayton Shonkwiler (Colorado State - USA) as part of GEOTOP
-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wojciech Chacholski (KTH - Sweden)
DTSTART;VALUE=DATE-TIME:20231201T160000Z
DTEND;VALUE=DATE-TIME:20231201T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/57
DESCRIPTION:by Wojciech Chacholski (KTH - Sweden) as part of GEOTOP-A semi
nar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain Goriely (Oxford - UK)
DTSTART;VALUE=DATE-TIME:20231208T160000Z
DTEND;VALUE=DATE-TIME:20231208T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/58
DESCRIPTION:by Alain Goriely (Oxford - UK) as part of GEOTOP-A seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunnar Hornig (Dundee University - UK)
DTSTART;VALUE=DATE-TIME:20230616T160000Z
DTEND;VALUE=DATE-TIME:20230616T170000Z
DTSTAMP;VALUE=DATE-TIME:20230605T071908Z
UID:GEOTOP-A/60
DESCRIPTION:Title: Magnetohydrodynamic relaxation\, helicity and minimum energy states in m
agnetised plasmas\nby Gunnar Hornig (Dundee University - UK) as part o
f GEOTOP-A seminar\n\n\nAbstract\nDuring the turbulent relaxation of a pla
sma with a high magnetic Reynolds number\, the magnetic energy is typicall
y dissipated faster than the magnetic helicity. Hence one can attempt to d
escribe the result of such a relaxation as a state that minimises the ener
gy while preserving the magnetic helicity. Mathematically the relation bet
ween magnetic helicity and energy is defined by an inequality\, $|H(B)| \\
le (2/C) E(B)$\, a result that was first shown in a classical paper by V.I
. Arnold (1974) for simply connected domains. The formula shows how a non-
trivial magnetic field topology (a non-zero helicity) forms a lower bound
for the magnetic energy. The formula contains a constant C\, which is the
smallest possible eigenvalue of the curl operator in a magnetically closed
domain. The corresponding eigenfield is a state of maximum helicity for a
given energy. We will discuss under which circumstances these maximum hel
icity (minimum energy) states can be reached\, show how Arnold’s formula
can be applied to non-simply connected domains\, and how one can modify A
rnold’s formula to find lower bounds for the energy even if $H(B)=0$.\n\
nReferences:\n\nArnold\, V.I.\, The asymptotic Hopf invariant and its appl
ication\, Sel. Math. Sov.\, 5\, 327 (1986)\n\nCandelaresi\, S.\, Pontin\,
D. I.\, Hornig\, G.\, & Podger\, B. Topological Constraints in the reconne
ction of vortex braids\, Physics of Fluids\, (33)\, 056101 (2021)\n\nYeate
s\, A.R.\, Hornig\, G. and Wilmot-Smith\, A.L. Topological Constraints on
Magnetic Relaxation\, Phys. Rev. Lett.\, 105\, 085002 (2010)\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/60/
END:VEVENT
END:VCALENDAR