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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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
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:20220816T042833Z
UID:GEOTOP-A/22
DESCRIPTION:by Martina Scolamiero (KTH Royal Institute of Technology - Swe
den) as part of GEOTOP-A seminar\n\nAbstract: TBA\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:20220816T042833Z
UID:GEOTOP-A/23
DESCRIPTION:by Alexandru Baltag (Universiteit van Amsterdam - Netherlands)
as part of GEOTOP-A seminar\n\nAbstract: TBA\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:20220816T042833Z
UID:GEOTOP-A/24
DESCRIPTION:by Jérémy Ledent (University of Strathclyde - UK) as part of
GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Bubenik (University of Florida - USA)
DTSTART;VALUE=DATE-TIME:20221007T150000Z
DTEND;VALUE=DATE-TIME:20221007T160000Z
DTSTAMP;VALUE=DATE-TIME:20220816T042833Z
UID:GEOTOP-A/25
DESCRIPTION:by Peter Bubenik (University of Florida - USA) as part of GEOT
OP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/25/
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:20220816T042833Z
UID:GEOTOP-A/26
DESCRIPTION:by Chad Giusti (University of Delaware - USA) as part of GEOTO
P-A seminar\n\nAbstract: TBA\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:20220816T042833Z
UID:GEOTOP-A/27
DESCRIPTION:by Marc Lackenby (University of Oxford - UK) as part of GEOTOP
-A seminar\n\nAbstract: TBA\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:20220816T042833Z
UID:GEOTOP-A/28
DESCRIPTION:by Carlo Barenghi (Newcastle University - UK) as part of GEOTO
P-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reidun Twarock (The University of York - UK)
DTSTART;VALUE=DATE-TIME:20221202T160000Z
DTEND;VALUE=DATE-TIME:20221202T170000Z
DTSTAMP;VALUE=DATE-TIME:20220816T042833Z
UID:GEOTOP-A/29
DESCRIPTION:by Reidun Twarock (The University of York - UK) as part of GEO
TOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Bronstein (University of Oxford - UK)
DTSTART;VALUE=DATE-TIME:20221209T160000Z
DTEND;VALUE=DATE-TIME:20221209T170000Z
DTSTAMP;VALUE=DATE-TIME:20220816T042833Z
UID:GEOTOP-A/30
DESCRIPTION:by Michael Bronstein (University of Oxford - UK) as part of GE
OTOP-A seminar\n\nAbstract: TBA\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:20220816T042833Z
UID:GEOTOP-A/31
DESCRIPTION:by John Baez (UC Riverside - USA) as part of GEOTOP-A seminar\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/31/
END:VEVENT
END:VCALENDAR