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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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
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:20240715T180145Z
UID:GEOTOP-A/48
DESCRIPTION:Title: Coupling Time-Aware Multipersistence Knowledge Representation with Graph
Convolutional Networks for Time Series Forecasting\nby Yulia R. Gel (
UT Dallas - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nGraph Neural N
etworks (GNNs) are proven to be a powerful machinery for learning complex
dependencies in multivariate spatio-temporal processes. However\, most exi
sting GNNs have inherently static architectures\, and as a result\, do not
explicitly account for time dependencies of the encoded knowledge and are
limited in their ability to simultaneously infer latent time-conditioned
relations among entities. We postulate that such hidden time-conditioned p
roperties may be captured by the tools of multipersistence\, i.e.\, an eme
rging machinery in topological data analysis which allows us to quantify d
ynamics of the data shape along multiple geometric dimensions. We propose
to summarize inherent time-conditioned topological properties of the data
as time-aware multipersistence Euler-Poincaré surface and prove its stabi
lity. We then construct a supragraph convolution module which simultaneous
ly accounts for the extracted intra- and inter-dependencies in the data. W
e illustrate the utility of the proposed approach in application to foreca
sting highway traffic flow\, blockchain Ethereum token prices\, and COVID-
19 hospitalizations.\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:20240715T180145Z
UID:GEOTOP-A/49
DESCRIPTION:Title: Differential Calculus for Modules over Posets\nby Ran Levi (Universi
ty of Aberdeen - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nThe concep
t of a persistence module was introduced in the context of topological dat
a analysis. In its original incarnation a persistence module is defined to
be a functor from the poset of nonnegative real numbers with theory natur
al order to the category of vector spaces and homomorphisms. These are ref
erred to as single parameter persistence modules and are a fundamental and
useful concept in topological data analysis when the source data depends
on a single parameter. The concept naturally lends itself to generalisatio
n\, and one may consider persistence modules as functors from an arbitrary
poset (or more generally an arbitrary small category) to some abelian tar
get category. In other words\, a persistence module is simply a representa
tion of the source category in the target abelian category. As such much r
esearch was dedicated to studying persistence modules in this context. Uns
urprisingly\, it turns out that when the source category is more general t
han a linear order\, then its representation type is generally wild. In pa
rticular\, keeping in mind that persistence module theory is supposed to b
e applicable\, computability of general persistence modules is very limite
d. In this talk I will describe the background and motivation for persiste
nce module theory and introduce a new set of ideas for local analysis of p
ersistence module by methods borrowed from spectral graph theory and multi
variable calculus.\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:20240715T180145Z
UID:GEOTOP-A/50
DESCRIPTION:Title: Singularity-free motion planning for redundant parallel manipulators
\nby Petar Pavešić (University of Ljubljana - Slovenia) as part of GEOTO
P-A seminar\n\n\nAbstract\nSome twenty years ago Michael Farber defined th
e topological complexity of robot motion\nplanning as a measure of the dif
ficulty to construct predictable motion plans for mechanical devices\n(lik
e robots) that are allowed to move in a given work space. More recently\,
we defined the\ncomplexity of a kinematic map that takes into account the
kinematic relation between the internal\nstates of a serial mechanism and
its spatial poses. In our talk we will discuss a more general motion plann
ing for parallel mechanisms. In particular\, we will consider mechanisms t
hat are redundant in\nthe sense that the dimension of their joint space is
strictly bigger than the dimension of their work\nspace. The additional d
egrees of freedom allow motion paths that avoid critical configurations of
\njoints\, and we will discuss how difficult it is to construct predictabl
e singularity-free motion plans that\nperform a given set of tasks. This i
s joint work with Edward Haug and Adrian Peidro.\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:20240715T180145Z
UID:GEOTOP-A/51
DESCRIPTION:Title: Modeling knotted proteins with tangles\nby Isabel Darcy (University
of Iowa - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nWe prove using t
he mathematics of tangles that if a protein terminus passing through a sin
gle loop results in a locally knotted protein\, then Taylor's twisted hair
pin model is the most likely method for creating such knots. In this case
the knotted products will all be twist knots. If we assume a right-handed
chirality bias\, which is common in proteins\, then the majority of these
twist knots will be right-handed trefoils ($+3_1$)\, followed by left-ha
nded trefoils ($-3_1$)\, achiral figure eight knots ($4_1$) and right-hand
ed five crossing twist knots ($-5_2$). An alternative pathway has been obs
erved computationally where a terminus passes through two loops. We use 3
-string tangle analysis to model this pathway. This is joint work with Ga
rrett Jones and Puttipong Pongtanapaisan.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eggers (Bristol\, UK)
DTSTART;VALUE=DATE-TIME:20231006T150000Z
DTEND;VALUE=DATE-TIME:20231006T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/52
DESCRIPTION:Title: Geometrical singularities and free surface cusps\nby Jens Eggers (Br
istol\, UK) as part of GEOTOP-A seminar\n\n\nAbstract\nCusp shapes are wid
ely observed in nature\, most famously as the bright caustic lines on the
inside of a coffee cup. This can be understood from the fact that a cusp a
rises from the smooth deformation of a parameterized curve. Remarkably\, t
he same generic cusp can be formed on the surface of a viscous fluid with
surface tension\, as demonstrated by Jeong and Moffatt [J. Fluid Mech. 241
\, 1\, (1992)]\, using complex mapping techniques. However\, their observa
tion is limited to very specific and idealized geometries. Here we demonst
rate that cusps are indeed local solutions to the Stokes equation with sur
face tension\, regardless of the global flow.\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:20240715T180145Z
UID:GEOTOP-A/53
DESCRIPTION:Title: The Fermat principle in Riemannian geometry\nby Ximena Fernández (D
urham University\, UK) as part of GEOTOP-A seminar\n\n\nAbstract\nIn many
situations in physics\, the path of light is determined not only by spatia
l geometry but also by an underlying local density (e.g.\, mass concentrat
ion in general relativity\, refractive index in optics). Consider a scenar
io where a Riemannian manifold in Euclidean space is shaped by a density f
unction\, with only a finite sample of points available. How can we infer
the original metric and determine the manifold's topology?\n\nThis talk in
troduces a density-based method for estimating topological features from d
ata in high-dimensional Euclidean spaces\, assuming a manifold structure.
The key to our approach lies in the Fermat distance\, a sample metric that
robustly infers the deformed Riemannian metric. Theoretical convergence r
esults and implications in the homology inference of the manifold will be
presented. Additionally\, I will show practical applications in time serie
s analysis with examples from real-world data.\n\nThis talk is based on th
e article: X. Fernandez\, E. Borghini\, G. Mindlin\, and P. Groisman. "Int
rinsic Persistent Homology via Density-Based Metric Learning." Journal of
Machine Learning Research 24 (2023) 1-42.\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:20240715T180145Z
UID:GEOTOP-A/54
DESCRIPTION:Title: Simplicial Methods in Distributed Computing\nby Dmitry Feichtner-Koz
lov (University of Bremen - Germany) as part of GEOTOP-A seminar\n\n\nAbst
ract\nWe will give a brief introduction to the subject. The survey of main
ideas and tools will be complemented with applications to specific standa
rd distributed tasks.\n\nWe will conclude with stating an open problem in
combinatorial topology which is related to the complexity of the Weak Symm
etry Breaking distributed task.\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:20240715T180145Z
UID:GEOTOP-A/55
DESCRIPTION:Title: Entanglement and invariants of theta-curves\nby Allison Moore (Virgi
nia Commonwealth University - USA) as part of GEOTOP-A seminar\n\n\nAbstra
ct\nA theta-curve is a spatial embedding of the unique graph with two\nver
tices joined by three parallel edges. Like knots and links\,\ntheta-curves
and their mathematical properties are relevant to the\nmathematical model
ing of biopolymers. In this talk\, we will\ninvestigate unknotting operati
ons and define new invariants of\ntheta-curves. We will also generalize th
e statement that 'unknotting\nnumber one knots are prime' to theta-curves.
This is joint work with\nseveral sets of authors.\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:20240715T180145Z
UID:GEOTOP-A/56
DESCRIPTION:Title: Geometric Approaches to Frame Theory\nby Clayton Shonkwiler (Colorad
o State - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nFrames are overc
omplete systems of vectors in Hilbert spaces. They were originally introdu
ced in the 1950s in the context of non-harmonic Fourier series\, and came
to renewed prominence in the 1980s in signal processing applications. More
recently\, there has been burgeoning interest in frames in finite-dimensi
onal Hilbert spaces\, with applications to signal processing\, quantum inf
ormation\, and compressed sensing.\nIn this talk\, I will describe some wa
ys in which tools from differential\, Riemannian\, and symplectic geometry
can be applied to problems in frame theory. Some key tools that crop up a
re Hamiltonian actions\, the Cartan decomposition\, and geometric invarian
t theory. This is joint work with Tom Needham and partially with Dustin Mi
xon and Soledad Villar.\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:20240715T180145Z
UID:GEOTOP-A/57
DESCRIPTION:Title: Data\, geometry\, and homology\nby Wojciech Chacholski (KTH - Sweden
) as part of GEOTOP-A seminar\n\n\nAbstract\nFor a successful analysis a s
uitable representation of data by objects amenable for statistical methods
is fundamental. There has been an explosion of applications in which homo
logical representations of data played a significant role. I will present
one such representation called stable rank and introduce various novel way
s of using it to encode geometry\, and then analyse\, data. I will provide
several illustrative examples of how to use stable ranks to find meaningf
ul results.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain Goriely (Oxford - UK)
DTSTART;VALUE=DATE-TIME:20231215T160000Z
DTEND;VALUE=DATE-TIME:20231215T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/58
DESCRIPTION:Title: The geometry and mechanics of chirality: from Maxwell's perversion to Fe
ynman's obsession\nby Alain Goriely (Oxford - UK) as part of GEOTOP-A
seminar\n\n\nAbstract\nMany natural structures such as proteins\, climbing
vines\, and seashells exhibit a well defined chirality\, some are left-ha
nded\, some are right-handed\, some are both. The ultimate origin of chira
lity is one of Nature's great mystery. However\, geometry and mechanics pl
ay a fundamental role in assigning chirality and carrying this information
from microscopic to macroscopic scales. In this talk\, I will discuss the
general problem of chirality\, chirality measure\, and chirality transfer
\, trace its history\, and use examples from chemistry and biology to obta
in general principles with some surprising twists.\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:20240715T180145Z
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
BEGIN:VEVENT
SUMMARY:Anthea Monod (Imperial College - UK)
DTSTART;VALUE=DATE-TIME:20240209T160000Z
DTEND;VALUE=DATE-TIME:20240209T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/61
DESCRIPTION:Title: Tropical Geometry of Phylogenetic Tree Space\nby Anthea Monod (Imper
ial College - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nBHV space is
a well-studied moduli space of phylogenetic trees that appears in many sci
entific disciplines\, including computational biology\, computer vision\,
combinatorics\, and category theory. Speyer and Sturmfels identify a homeo
morphism between BHV space and a version of the Grassmannian using tropica
l geometry\, endowing the space of phylogenetic trees with a tropical stru
cture\, which turns out to be advantageous for computational studies. In t
his talk\, I will present the coincidence between BHV space and the tropic
al Grassmannian. I will then give an overview of some recent work I have d
one that studies the tropical Grassmannian as a metric space and the pract
ical implications of these results on probabilistic and statistical studie
s on sets of phylogenetic trees.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Morozov (Lawrence Berkeley National Laboratory - USA)
DTSTART;VALUE=DATE-TIME:20240216T170000Z
DTEND;VALUE=DATE-TIME:20240216T180000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/62
DESCRIPTION:Title: From Descriptive to Operational Topological Data Analysis\nby Dmitri
y Morozov (Lawrence Berkeley National Laboratory - USA) as part of GEOTOP-
A seminar\n\n\nAbstract\nTopological data analysis evolved over the past t
wo decades into a primarily descriptive field. Almost all applications aim
to quantify the topology of data and use the resulting descriptors to bui
ld a model for classification or regression. Recently\, a new line of appl
ications emerged\, one that uses topology to guide optimization and thus m
odify the data or the model directly. After reviewing the descriptive view
of TDA\, we will discuss the structure of the optimization problem and de
monstrate how understanding it leads to better optimization algorithms.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörn Dunkel (Mathematics\, MIT - USA)
DTSTART;VALUE=DATE-TIME:20240301T160000Z
DTEND;VALUE=DATE-TIME:20240301T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/63
DESCRIPTION:Title: Topological packing statistics of living and non-living matter\nby J
örn Dunkel (Mathematics\, MIT - USA) as part of GEOTOP-A seminar\n\n\nAbs
tract\nComplex disordered matter is of central importance to a wide range
of disciplines\, from bacterial colonies and embryonic tissues in biology
to foams and granular media in materials science to stellar configurations
in astrophysics. Because of the vast differences in composition and scale
\, comparing structural features across such disparate systems remains cha
llenging. Here\, by using the statistical properties of Delaunay tessellat
ions\, we introduce a mathematical framework for measuring topological dis
tances between two- or three-dimensional point clouds. The resulting syste
m-agnostic metric reveals subtle structural differences between bacterial
biofilms as well as between zebrafish brain regions\, and it recovers temp
oral ordering of embryonic development. We apply the metric to construct a
universal topological atlas encompassing bacterial biofilms\, snowflake y
east\, plant shoots\, zebrafish brain matter\, organoids\, and embryonic t
issues as well as foams\, colloidal packings\, glassy materials\, and stel
lar configurations. Living systems localize within a bounded island-like r
egion of the atlas\, reflecting that biological growth mechanisms result i
n characteristic topological properties.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Soteros (Mathematics U Saskatchewan - Canada)
DTSTART;VALUE=DATE-TIME:20240315T160000Z
DTEND;VALUE=DATE-TIME:20240315T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/64
DESCRIPTION:Title: Establishing that Knots and Links are Localized for Ring polymers in nan
ochannels\nby Chris Soteros (Mathematics U Saskatchewan - Canada) as p
art of GEOTOP-A seminar\n\n\nAbstract\nLattice models have proved useful f
or studying the entanglement complexity of polymers. In 1988 Sumners and W
hittington used a lattice model to prove that knotting is inevitable for s
ufficiently long ring polymers and that knot complexity increases with pol
ymer length. In the lattice model\, a ring polymer is represented by a pol
ygon on the simple cubic lattice. Subsequently\, Monte Carlo simulations o
f lattice polygons led to a 1996 conjecture consistent with the idea that
knots occur in a localized way in fixed knot-type polygons. That is\, the
"knotted part" is expected to be small relative to the length of the polyg
on. Recently a first proof of this conjecture has been established for the
special case of polygons confined to an infinity x 2 x 1 lattice tube. Th
e proof relies on a combination of novel knot theory and lattice combinato
rics\, and the results also extend to non-split links. Monte Carlo simulat
ions support that the conjecture also holds for larger lattice tubes. Thus
one expects that knots and links will also be localized for DNA in nano c
hannel experiments. A lattice tube model has also been used to study the e
ntanglement complexity of two polygons which both span the tube\, a scenar
io for which it is known that linking is inevitable. In this case\, eviden
ce suggest that knots are still localized but the linked part is not. I wi
ll review some of the proofs and Monte Carlo results for these lattice tub
e models and highlight some of the remaining open questions.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Vaccarino (Politecnico di Torino - Italy)
DTSTART;VALUE=DATE-TIME:20240405T160000Z
DTEND;VALUE=DATE-TIME:20240405T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/65
DESCRIPTION:Title: Three easy pieces for Hodge Laplacian and higher order interactions\
nby Francesco Vaccarino (Politecnico di Torino - Italy) as part of GEOTOP-
A seminar\n\n\nAbstract\nFirstly\, we present a cross-order Laplacian reno
rmalization group (X-LRG) scheme for arbitrary higher-order networks. The
renormalization group is a fundamental concept in the physics theory of sc
aling\, scale-invariance\, and universality. An RG scheme was recently int
roduced for complex networks with dyadic interactions based on diffusion d
ynamics. However\, we still lack a general RG scheme for higher-order netw
orks despite the mounting evidence of the importance of polyadic interacti
ons. Our approach uses a diffusion process to group nodes or simplices\, w
here information can flow between nodes and between simplices (higher-orde
r interactions).\n\nSecondly\, we discuss simplicial Kuramoto models\, whi
ch have emerged as a diverse and intriguing model that describes oscillato
rs on simplices rather than nodes. We present a unified framework to descr
ibe different variants of these models\, which are categorized into three
main groups: "simple" models\, "Hodge-coupled" models\, and "order-coupled
" (Dirac) models. We explore a potential application in reconstructing bra
in functional connectivity from structural connectomes. We find that simpl
e edge-based Kuramoto models perform competitively or outperform complex e
xtensions of node-based models.\n\nLastly\, we consider associated games i
n cooperative game theory\, which allows for the meaningful characterizati
on of solution concepts. Moreover\, generalized values allow computing eac
h coalition's influence or power index in a game. We view associated games
through the lens of game maps and graph Laplacian\, thus defining the nov
el Hodge Generalized Value (HGV). We characterize HGV via an axiomatic app
roach as a generalized value. Finally\, we show how HGV is linked to the s
olution of the Poisson equation derived from the Hodge decomposition of th
e direct graph associated with the poset of coalitions in the game.\n\nRef
erences and coauthor list:\n\nNurisso\, M.\, Morandini\, M.\, Lucas\, M.\,
Vaccarino\, F.\, Gili\, T.\, & Petri\, G. (2024). Higher-order Laplacian
Renormalization. arXiv preprint arXiv:2401.11298.\n\nNurisso\, M.\, Arnaud
on\, A.\, Lucas\, M.\, Peach\, R. L.\, Expert\, P.\, Vaccarino\, F.\, & Pe
tri\, G. (2023). A unified framework for Simplicial Kuramoto models. arXiv
e-prints\, arXiv-2305.\n\nMastropietro\, Antonio\, and Francesco Vaccarin
o. "The Shapley-Hodge Associated Game." arXiv preprint arXiv:2303.17151(20
23).\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iris Yoon (Wesleyan University - USA)
DTSTART;VALUE=DATE-TIME:20240419T160000Z
DTEND;VALUE=DATE-TIME:20240419T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/66
DESCRIPTION:Title: Topological tracing of encoded circular coordinates between neural popul
ations\nby Iris Yoon (Wesleyan University - USA) as part of GEOTOP-A s
eminar\n\n\nAbstract\nRecent developments in in vivo neuroimaging in anima
l models have made possible the study of information coding in large popul
ations of neurons and even how that coding evolves in different neural sys
tems. Topological methods\, in particular\, are effective at detecting per
iodic\, quasi-periodic\, or circular features in neural systems. Once we d
etect the presence of circular structures\, we face the problem of assigni
ng semantics: what do the circular structures in a neural population encod
e? Are they reflections of an underlying physiological activity\, or are t
hey driven by an external stimulus? If so\, which specific features of the
stimulus are encoded by the neurons? To address this problem\, we introdu
ced the method of analogous bars (Yoon\, Ghrist\, Giusti 2023). Given two
related systems\, say a stimulus system and a neural population\, or two r
elated neural populations\, we utilize the dissimilarity between the two s
ystems and Dowker complexes to find shared features between the two system
s. We then leverage this information to identify related features between
the two systems. In this talk\, I will briefly explain the mathematics und
erlying the analogous bars method. I will then present applications of the
method in studying neural population coding and propagation on simulated
and experimental datasets. This work is joint work with Gregory Henselman-
Petrusek\, Lori Ziegelmeier\, Robert Ghrist\, Spencer Smith\, Yiyi Yu\, an
d Chad Giusti.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Suárez Serrato (UNAM - Mexico)
DTSTART;VALUE=DATE-TIME:20240426T160000Z
DTEND;VALUE=DATE-TIME:20240426T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/67
DESCRIPTION:Title: Topics in Geometric Learning\nby Pablo Suárez Serrato (UNAM - Mexic
o) as part of GEOTOP-A seminar\n\n\nAbstract\nSimilarly to the growth of A
pplied Topology\, the uses and applications of Geometry are now expanding
into scientific\, computational\, and engineering domains. First\, we'll r
eview the recent history of this expanding Applied Geometry area. I'll men
tion several collaborations. Developing and implementing algorithms inspir
ed by the marked length spectrum that classifies complex networks (with El
iassi-Rad and Torres) and analyzing digital images using a variant of curv
e-shortening flow (with Velazquez Richards). As well as a definition I pro
posed of a global convolution on manifolds of arbitrary topology\, relevan
t for deep learning on manifolds. Furthermore\, I'll present our joint wor
k with Evangelista and Ruiz Pantaleón on computational Poisson geometry.
This work includes a practical application in learning symbolic expression
s of Hamiltonian systems. We've developed and released two Python packages
that are instrumental in this process. These packages enable symbolic and
numerical computations of objects in Poisson geometry\, and they're compa
tible with the deep learning frameworks NumPy\, TensorFlow\, and PyTorch.
We've utilized these packages to train neural networks\, particularly hybr
ids with CNN and LSTM components\, that learn symbolic expressions of Hami
ltonian vector fields. I'll present a tutorial on our computational Poisso
n Geometry modules if time allows.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuanan Diao (UNC Charlote -USA)
DTSTART;VALUE=DATE-TIME:20240503T160000Z
DTEND;VALUE=DATE-TIME:20240503T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/68
DESCRIPTION:Title: Braid index and Ropelength of alternating knots\nby Yuanan Diao (UNC
Charlote -USA) as part of GEOTOP-A seminar\n\n\nAbstract\nA long standing
conjecture states that the ropelength of any alternating link is at least
proportional to its crossing number. That is\, there exists a constant $b
_0>0$ such that $R(K)\\ge b_0Cr(K)$ for any alternating link $K$\, where $
R(K)$ is the ropelength of $K$ and $Cr(K)$ is the crossing number of $K$.
This conjecture has been recently proved affirmatively for the case of alt
ernating knots. In this talk I will present the main results/ideas leading
to the proof of this result\, where the braid index served as the key bri
dge between the minimum crossing number and the ropelength of the knot.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamas Kalman (Mathematics\, Tokyo Institute of Technology - Japan)
DTSTART;VALUE=DATE-TIME:20240517T150000Z
DTEND;VALUE=DATE-TIME:20240517T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/69
DESCRIPTION:Title: Knotted and branching defects in ordered media\nby Tamas Kalman (Mat
hematics\, Tokyo Institute of Technology - Japan) as part of GEOTOP-A semi
nar\n\n\nAbstract\nI will discuss a homotopy classification of the global
defect in ordered media\, with a particular emphasis on the example of bia
xial nematic liquid crystals. These are systems in which the order paramet
er space is the quotient of the $3$-sphere $S^3$ by the quaternion group $
Q$\, and an important feature of them is that disclination lines may branc
h and form graphs. Therefore as a model\, I will consider continuous maps
from complements of spatial graphs to $S^3/Q$ modulo a certain equivalence
relation\, and find that the equivalence classes are enumerated by the si
x subgroups of $Q$. Via monodromy around meridional loops\, the edges of o
ur spatial graphs are marked by conjugacy classes of $Q$\; once one passes
to planar diagrams\, these labels can be refined to elements of $Q$ assoc
iated to each arc. The same classification scheme applies not only in the
case of $Q$ but also to arbitrary groups. This research is joint with Yuta
Nozaki\, Yuya Koda\, and Masakazu Teragaito.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Goubault (Ecole Polytechnique - France)
DTSTART;VALUE=DATE-TIME:20240531T160000Z
DTEND;VALUE=DATE-TIME:20240531T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/70
DESCRIPTION:Title: Directed homology and persistence modules\nby Eric Goubault (Ecole P
olytechnique - France) as part of GEOTOP-A seminar\n\n\nAbstract\nIn this
talk\, I will give a self-contained account of a construction for a direct
ed homology theory based on modules over algebras\, linking it to both per
sistence homology and natural homology.\n\nPersistence modules have been i
ntroduced originally for topological data analysis\, where the data set se
en at different « resolutions » is organized as a filtration of spaces.
This has been further generalized to multidimensional persistence and « g
eneralized » persistence\, where a persistence module was defined to be a
ny functor from a partially ordered set\, or more generally a preordered s
et\, to an arbitrary category (in general\, a category of vector spaces).\
n\nThis talk will be concerned with a more « classical » construction of
directed homology\, mostly for precubical sets here\, based on (bi)module
s over (path) algebras\, making it closer to classical homology with value
in modules over rings\, and of the techniques introduced for persistence
modules. Still\, this construction retains the essential information that
natural homology is unveiling. Of particular interest will be the role of
restriction and extension of scalars functors\, that will be central to th
e discussion of Kunneth formulas\, Mayer-Vietoris and relative homology se
quences. If time permits as well\, we will discuss some « tameness » iss
ues\, for dealing with practical calculations.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman (University of Illinois at Chicago)
DTSTART;VALUE=DATE-TIME:20240111T210000Z
DTEND;VALUE=DATE-TIME:20240111T220000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/71
DESCRIPTION:Title: Reconnection Numbers of Knotted Vortices\nby Louis H Kauffman (Unive
rsity of Illinois at Chicago) as part of GEOTOP-A seminar\n\n\nAbstract\nK
notted vortices such as those produced in water by Kleckner and Irvine ten
d to transform by reconnection to collections of unknotted and unlinked ci
rcles. The reconnection number $R(K)$ of an oriented knot of link $K$ is t
he least number of reconnections (oriented re-smoothings) needed to unknot
/unlink $K$. Putting this problem into the context of knot cobordism\, we
show\, using Rasmussen's Invariant that the reconnection number of a posit
ive knot is equal to twice the genus of its Seifert spanning surface. In p
articular an (a\,b) torus knot has $R=(a−1)(b−1)$. For an arbitrary un
splittable positive knot or link $K$\, $R(K)=c(K)−s(K)+1$ where $c(K)$ i
s the number of crossings of K and $s(K)$ is the number of Seifert circles
of $K$. Examples of vortex dynamics are illustrated in the talk.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Micheletti (International School for Advanced Studies (SI
SSA))
DTSTART;VALUE=DATE-TIME:20240108T210000Z
DTEND;VALUE=DATE-TIME:20240108T220000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/72
DESCRIPTION:Title: Dynamics and mechanics of knotted DNA and RNAs: insights from molecular
dynamics simulations\nby Cristian Micheletti (International School for
Advanced Studies (SISSA)) as part of GEOTOP-A seminar\n\n\nAbstract\nI wi
ll report on a series of studies where we used molecular dynamics simulati
ons and various models to study how the properties of DNA and RNAs are aff
ected by the presence of knots and other forms of structural entanglement[
1]. I will first consider model DNA plasmids that are both knotted and sup
ercoiled\, and discuss how the simultaneous presence of knots and supercoi
ling creates long-lived multi-strand interlockings that might may be relev
ant for the simplifying action of topoisomerases. I next consider how enta
ngled nucleic acids behave when driven through narrow pores[2-4]\, a setti
ng that models translocation through the lumen of enzymes\, and discuss th
e biological implication for a certain class of viral RNAs[4].\n\n \n[1] L
. Coronel\, A. Suma and C. Micheletti\, "Dynamics of supercoiled DNA with
complex knots"\, Nucleic Acids Res. (2018) 46 \, 7533 \n\n[2] A. Suma\, V.
Carnevale and C. Micheletti\, Nonequilibrium thermodynamics of DNA nanopo
re unzipping\, Phys. Rev. Lett.\, (2023)\, 130 048101\n\n[3] A. Suma\, A.
Rosa and C. Micheletti\, Pore translocation of knotted polymer chains: how
friction depends on knot complexity\, ACS Macro Letters\, (2015)\, 4 \, 1
420-1424\n\n[4] A. Suma\, L. Coronel\, G. Bussi and C. Micheletti\, "Direc
tional translocation resistance of Zika xrRNA” Nature Communications (20
20)\, 11 \, art no. 3749\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuliy Baryshnikov (University of Illinois at Urbana-Champaign)
DTSTART;VALUE=DATE-TIME:20240109T000000Z
DTEND;VALUE=DATE-TIME:20240109T010000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/73
DESCRIPTION:Title: On Spaces of Coverings\nby Yuliy Baryshnikov (University of Illinois
at Urbana-Champaign) as part of GEOTOP-A seminar\n\n\nAbstract\nConsider
a relation $R\\subset X\\times Y$ between two topological spaces. A finite
collection $C=(x_1\,\\ldots\,x_n)\\in X^n$ is a covering if for any $y\\i
n Y$\, one has $(x_k\,y)\\in R$ for one of the points $x_k$ in $C$. (For
example\, if $X=Y$ is a metric space\, and $R$ is the relation of being a
t the distance $<\\epsilon$\, then $C$ is a covering if the union of $\\ep
silon$-balls around $x_k$'s cover $Y$.) The topology of the space of cover
ings $C_R(n)$ is important\, if unexplored\, topic in several applied disc
iplines\, from multi-agent systems to sociology. In this talk we discuss s
ome examples where the homotopy type of these spaces can be explicitly com
puted.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ismar Volić (Wellesley College)
DTSTART;VALUE=DATE-TIME:20240109T150000Z
DTEND;VALUE=DATE-TIME:20240109T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/74
DESCRIPTION:Title: Simplicial complexes and political structures\nby Ismar Volić (Well
esley College) as part of GEOTOP-A seminar\n\n\nAbstract\nSimplicial compl
exes and their topology are a natural tool for modeling interactions in a
system and revealing its deeper underlying structures. We will discuss how
simplicial complexes can be used to study political systems in which coal
itions are represented by simplices. Some basic topological constructions
can then easily be translated into political situations such as merging of
parties\, introduction of mediators\, or delegation of power. The topolog
ical point of view also supplies a refined point of view on game-theoretic
notions like the Banzhaf and Shapley-Shubik power indices of agents in a
political system. We will also present a generalization to hypergraphs whi
ch captures an even richer collection of political dynamics concepts. Time
permitting\, a recasting of some classical results from social choice the
ory in topological and category-theoretic terms will also be mentioned.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Soberón (City University of New York)
DTSTART;VALUE=DATE-TIME:20240109T210000Z
DTEND;VALUE=DATE-TIME:20240109T220000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/75
DESCRIPTION:Title: New results on envy-free distributions\nby Pablo Soberón (City Univ
ersity of New York) as part of GEOTOP-A seminar\n\n\nAbstract\nSimilarly t
o the growth of Applied Topology\, the uses and applications of Geometry a
re now expanding into scientific\, computational\, and engineering domains
. First\, we'll review the recent history of this burgeoning Applied Geome
try area. I'll mention a couple of collaborations\, developing and impleme
nting algorithms inspired by the marked length spectrum that classify comp
lex networks (with Eliassi-Rad and Torres) and analyzing digital images u
sing a variant of curve-shortening flow (with Velazquez Richards). Then\,
I'll present joint work with Evangelista and Ruiz Pantaleón on computatio
nal Poisson geometry and its applications to learning symbolic expressions
of Hamiltonian systems. We developed and released two Python packages tha
t perform symbolic and numerical computation of objects in Poisson geometr
y. We then used them to train neural networks (hybrids with CNN and LSTM c
omponents) that learn symbolic expressions of Hamiltonian vector fields. F
inally\, I'll briefly mention the theoretical limitations of computational
ly analyzing Hamiltonian dynamics. I recently constructed an example of a
Hamiltonian flow on the 4-sphere that is Turing complete. Therefore the mo
st general cases of Hamiltonian learning problems are undecidable.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Dranishnikov (University of Florida)
DTSTART;VALUE=DATE-TIME:20240110T150000Z
DTEND;VALUE=DATE-TIME:20240110T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/76
DESCRIPTION:Title: On some variations of TC and the LS-category\nby Alexander Dranishni
kov (University of Florida) as part of GEOTOP-A seminar\n\n\nAbstract\nDat
asets can be viewed as mathematical objects (e.g.\, point clouds\, matrice
s\, graphs\, images\, fields/functions) that have shape. This shape can de
scribe the space that data populates (e.g.\, data that lies on a manifold)
or can be used to understand the complex structures contained within data
(e.g.\, the multi-scale organization of self-assembled materials). Data s
hape can be exploited to improve the effectiveness of data analysis method
s or provide connections between complex materials and their physical and
chemical properties. However\, quantifying shape is difficult to do with c
ommon methods based on statistics\, signal processing\, or with the use of
machine learning. Topology and geometry are fields of mathematics that p
rovide tools for the characterization and quantification of the shape of d
ata directly.\n\nIn this talk I will discuss how data taken from industria
l processes\, such as time series and images\, can be represented as a sha
pe and how that shape can be analyzed through topological and geometrical
methods such as the Euler characteristic (EC) and Riemannian manifold geom
etry. I will provide a brief overview of these methods and illustrate how
exploiting the topology and geometry of data can provide improvements in d
ata-centric tasks such as dimensionality reduction\, anomaly detection\, a
nd statistical process control in the context of textile production\, chem
ical process systems\, and granular material manufacturing.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Jackson (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20240111T150000Z
DTEND;VALUE=DATE-TIME:20240111T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/77
DESCRIPTION:Title: The What\, Where\, How and Why of Topological Knots in Proteins\nby
Sophie Jackson (University of Cambridge) as part of GEOTOP-A seminar\n\n\n
Abstract\nFor decades it was thought that topological knots would never be
formed by the polypeptide chain of any protein\, knotting being incompati
ble with folding mechanisms. However\, we now know that many proteins fol
d and form three-dimensional structures in which the chain crosses itself
and threads through loop(s) to form knots. Proteins with very deep knots\,
i.e.\, a large part of the chain has passed through a knotting loop to fo
rm the knot have been identified\, and four different classes of knots hav
e been found embedded in protein strucutres: 3-1\, 4-1\, 5-2\, and 6-1 kn
ots. In addition\, recently it has been established that a single polypept
ide chain can contain more than one knot - several examples of tandem tref
oil knotted proteins have been characterised. With the advent of the mach
ine-learning based protein structure algorithm AlphaFold\, several new cla
sses of knotted protein have been predicted although their knotted structu
res have not yet been verified experimentally. Over twenty years\, numero
us experimental and computational studies on knotted proteins have investi
gated how such structures might form\, in addition\, to the properties of
the knotted structure and whether they differ significantly or not from un
knotted proteins. In this talk\, I will review the field and explain 1) w
hat knots are found in proteins and where they are within the folded struc
tures\, 2) the mechanisms by which knotted may fold\, i.\, how the knots g
et there\, and 3) why proteins may have evolved to form knotted structures
. The talk will provide background on twenty years of research as well as
discussing some state-of-the-art studies on designing proteins with novel
knotted folds\, as well as watching knotted proteins unfold and transloca
te through narrow pores.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitchell Berger (University of Exeter)
DTSTART;VALUE=DATE-TIME:20240108T150000Z
DTEND;VALUE=DATE-TIME:20240108T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/78
DESCRIPTION:Title: Continuous topological measures: helicity\, winding\, and higher order w
inding\nby Mitchell Berger (University of Exeter) as part of GEOTOP-A
seminar\n\n\nAbstract\nMany measures of topological complexity are discret
e: for example the linking number between two closed curves is an integer.
However\, some topological invariants can be continuous. The winding numb
er of two curves extending between parallel planes\, with fixed end points
provides a simple example. We will discuss how winding numbers work in mo
re complicated geometries such as spheres\, cubes\, and closed surfaces in
general. On the way\, we will need Gauss-Bonnet. Also we will touch on hi
gher order winding related to the Borromean rings.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusu Wang (UC San Diego)
DTSTART;VALUE=DATE-TIME:20240112T150000Z
DTEND;VALUE=DATE-TIME:20240112T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/79
DESCRIPTION:Title: Graph learning models: theoretical understanding\, limitations and enhan
cements\nby Yusu Wang (UC San Diego) as part of GEOTOP-A seminar\n\n\n
Abstract\nGraph data is ubiquitous in many application domains. The rapid
advancements in machine learning also lead to many new graph learning fram
eworks\, such as message passing (graph) neural networks (MPNNs)\, graph t
ransformers and higher order variants. In this talk\, I will describe some
of our recent journey in attempting to provide better (theoretical) under
standing of these graph learning models (e.g\, their representation power
and limitations in capturing long range interactions in graphs)\, the pros
and cons of different models\, and ways to further enhance them in practi
ce. This talk is based on multiple pieces of work with various collaborato
rs\, whom I will mention in the talk.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radmila Sazdanovic (NC State University)
DTSTART;VALUE=DATE-TIME:20240113T150000Z
DTEND;VALUE=DATE-TIME:20240113T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/80
DESCRIPTION:Title: The shape of relations: knots and other stories\nby Radmila Sazdanov
ic (NC State University) as part of GEOTOP-A seminar\n\n\nAbstract\nTopolo
gical Data Analysis provides tools for discovering relevant features of da
ta by analyzing the shape of a point cloud. In this context we develop too
ls for visualizing maps between high dimensional spaces with the goal of d
iscovering relations between data sets with expected correlations. Additio
nally we are adapting TDA tools to analyzing infinite data sets where rep
resentative sampling is impossible or impractical and using them in synerg
y with ML techniques. Most of the examples will focus on analyzing relatio
ns between knot invariants with additional examples in game theory and can
cer genomics.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pawel Dlotko (Dioscuri Centre in Topological Data Analysis\, Mathe
matical Institute\, Polish Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20240113T230000Z
DTEND;VALUE=DATE-TIME:20240114T000000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/81
DESCRIPTION:Title: Data\, their shape\, and beyond\nby Pawel Dlotko (Dioscuri Centre in
Topological Data Analysis\, Mathematical Institute\, Polish Academy of Sc
iences) as part of GEOTOP-A seminar\n\n\nAbstract\nIn contemporary science
we are exposed to vast amounts of data. Understanding them is often helpf
ul\, sometimes essential\, to make considerable progress in the field. Mat
hematics\, and mathematical statistics\, offer a wealth of tools allowing
for better understanding of data. Most tools concentrate on the quantitati
ve characterization of data\, rather than understanding their layout\, or
shape. To fill in the gap\, in my Dioscuri Centre in Topological Data Anal
ysis\, we are developing new techniques to quantify the shape of data and
provide visualizations which\, in the next step\, deliver new knowledge. O
ur methods apply for a large variety of inputs\, including high dimensiona
l samples\, time series\, images\, correlation patterns and more. In this
talk\, I will give a brief and intuitive overview of our methods with a ho
pe that you may find them beneficial in your research. A showcase of the c
urrent usages of our methodology will provide both an important motivation
for\, and driving force to\, our research.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasha Jonoska (University of South Florida - USA)
DTSTART;VALUE=DATE-TIME:20240823T160000Z
DTEND;VALUE=DATE-TIME:20240823T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/82
DESCRIPTION:by Natasha Jonoska (University of South Florida - USA) as part
of GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucile Vandembroucq (Universidade do Minho - Portugal)
DTSTART;VALUE=DATE-TIME:20240906T160000Z
DTEND;VALUE=DATE-TIME:20240906T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/83
DESCRIPTION:by Lucile Vandembroucq (Universidade do Minho - Portugal) as p
art of GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claus Ernst (Western Kentucky University - USA)
DTSTART;VALUE=DATE-TIME:20240913T160000Z
DTEND;VALUE=DATE-TIME:20240913T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/84
DESCRIPTION:by Claus Ernst (Western Kentucky University - USA) as part of
GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uta Ziegler (Western Kentucky University - USA)
DTSTART;VALUE=DATE-TIME:20240927T160000Z
DTEND;VALUE=DATE-TIME:20240927T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/85
DESCRIPTION:by Uta Ziegler (Western Kentucky University - USA) as part of
GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Lipton (MIT - USA)
DTSTART;VALUE=DATE-TIME:20241011T160000Z
DTEND;VALUE=DATE-TIME:20241011T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/86
DESCRIPTION:by Max Lipton (MIT - USA) as part of GEOTOP-A seminar\n\nAbstr
act: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Brodzki (University of Southampton - United Kingdom)
DTSTART;VALUE=DATE-TIME:20241018T160000Z
DTEND;VALUE=DATE-TIME:20241018T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/87
DESCRIPTION:by Jacek Brodzki (University of Southampton - United Kingdom)
as part of GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Santa Cruz (Penn State University - USA)
DTSTART;VALUE=DATE-TIME:20241025T160000Z
DTEND;VALUE=DATE-TIME:20241025T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/88
DESCRIPTION:by Hannah Santa Cruz (Penn State University - USA) as part of
GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Lesnick (SUNY Albany - USA)
DTSTART;VALUE=DATE-TIME:20241108T160000Z
DTEND;VALUE=DATE-TIME:20241108T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/89
DESCRIPTION:by Mike Lesnick (SUNY Albany - USA) as part of GEOTOP-A semina
r\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Vega (BCAM - Spain)
DTSTART;VALUE=DATE-TIME:20241206T160000Z
DTEND;VALUE=DATE-TIME:20241206T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/90
DESCRIPTION:by Luis Vega (BCAM - Spain) as part of GEOTOP-A seminar\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María José Jiménez Rodríguez (Universidad de Sevilla - Spain)
DTSTART;VALUE=DATE-TIME:20241122T160000Z
DTEND;VALUE=DATE-TIME:20241122T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/91
DESCRIPTION:by María José Jiménez Rodríguez (Universidad de Sevilla -
Spain) as part of GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Soberón (CUNY - USA)
DTSTART;VALUE=DATE-TIME:20241213T160000Z
DTEND;VALUE=DATE-TIME:20241213T170000Z
DTSTAMP;VALUE=DATE-TIME:20240715T180145Z
UID:GEOTOP-A/92
DESCRIPTION:by Pablo Soberón (CUNY - USA) as part of GEOTOP-A seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/92/
END:VEVENT
END:VCALENDAR