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BEGIN:VEVENT
SUMMARY:Chimere Anabanti (University of Technology (TU Graz) Austria)
DTSTART;VALUE=DATE-TIME:20200611T130000Z
DTEND;VALUE=DATE-TIME:20200611T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/1
DESCRIPTION:Title: On the classification of finite filled groups\nby Chimere Anabanti
(University of Technology (TU Graz) Austria) as part of MESS (Mathematics
Essex Seminar Series)\n\n\nAbstract\nWe give an introduction to product-fr
ee sets in finite groups\, discuss an application to Combinatorics\, and c
onclude with what is known about filled groups.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Savostyanov (University of Essex)
DTSTART;VALUE=DATE-TIME:20200618T130000Z
DTEND;VALUE=DATE-TIME:20200618T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/2
DESCRIPTION:Title: Epidemiological models on networks: Numerical approaches and challenges
(Work in progress)\nby Dmitry Savostyanov (University of Essex) as pa
rt of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nMathematical
modelling of infectious disease is an important area of applied mathematic
s. The Kermack--McKendrick compartmental SIR model is quite simple but als
o quite powerful --- it describes the epidemics with a system of ordinary
differential equations (ODEs)\, which can be easily solved using a suitabl
e numerical method\, and predicts the behaviour of outbreaks very similar
to that observed in many recorded epidemics. Even though compartmental mod
els are almost hundred years old now\, they are still widely used not only
in a classroom\, but also to predict the development of dangerous disease
s and to inform Government strategies in case of emergency. The quality of
a mathematical model\, and our understanding of its assumptions and appli
cability in a particular scenario\, is therefore crucial to make correct d
ecisions to protect public health and respond to epidemics effectively whe
n they occur. The fundamental assumption of a compartmental model is that
the population is well-mixed: there is no firm boundary between susceptibl
e\, infected and recovered individuals. Everyone interacts with everyone a
t once\, similar to chemical molecules in a mixture. Although this assumpt
ion may be appropriate on a later stages of epidemic\, it clearly limits t
he model's capability to accurately describe and predict the early stages\
, when the infection is largely localised in one location and is carried t
o other locations through a network of transport and/or social and communi
ty links. If we consider how a disease progresses through a network\, only
neighbouring nodes can participate in transmission --- the network is not
well-mixed. Hence\, the compartmental model is no longer fit for purpose\
, and has to be replaced with a probabilistic model\, where we estimate th
e probability for each node to be in susceptible\, infected or recovered s
tate at a given time. Importantly\, the states of the neighbours are not
independent --- quite the opposite! --- a susceptible person in direct co
ntact with an infected person is likely to become infected soon. This mean
s that instead of considering individual probabilities\, we have to descri
be the evolution of the joint probability distribution\, accounting for th
e states of all nodes at once. This high--dimensional problem struggles fr
om the curse of dimensionality --- the number of unknowns grows exponentia
lly with the number of nodes\, and traditional ODE solvers can't cope with
he growing complexity when the number of nodes exceeds several tens. For
this reason\, the problem is typically solved using Stochastic Simulation
Algorithms (SSA)\, such as Monte Carlo and its variants. Using our experie
nce with high--dimensional problems\, such as Fokker--Planck\, Chemical Ma
ster Equation and Quantum Spin Dynamics\, we consider applying tensor prod
uct algorithms to solve this high--dimensional ODE with high accuracy\, an
d hence obtain a full probabilistic picture of the disease transfer throug
h the network. In preliminary experiments we find tensor product approach
to be successful in principle. In particular\, it can accurately estimate
the probabilities of rare events\, as well as higher moments of the observ
ed quantities\, where SSA often struggles. This is a work in progress! The
presented results are in preparation for publication. We will appreciate
all feedback and suggestions regarding this work.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Kinnear (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20200626T130000Z
DTEND;VALUE=DATE-TIME:20200626T140000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/3
DESCRIPTION:Title: Teaching mathematics online with STACK\nby George Kinnear (Universi
ty of Edinburgh) as part of MESS (Mathematics Essex Seminar Series)\n\n\nA
bstract\nAt the University of Edinburgh\, we have been increasing our use
of the STACK computer-aided assessment system to provide practice and home
work for students. I will give an overview of the features of STACK\, and
describe different ways it is being used across all years of our programme
. In particular\, I will show how STACK was a key part of the design of a
new optional course for incoming students\, "Fundamentals of Algebra and C
alculus"\, which covers key topics from Advanced Higher and A-Level syllab
uses. The course is delivered almost entirely online\, as a series of STAC
K quizzes which interleave textbook-style exposition with videos of worked
examples\, interactive applets\, and practice questions. I will describe
how ideas from education research and cognitive science (such as spacing a
nd retrieval practice) informed the course design\, from its overall struc
ture to the content of individual questions. I will also show some results
from our evaluation of the course\, including measures of the students' l
earning gains.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Antonopoulos (University of Essex)
DTSTART;VALUE=DATE-TIME:20201015T140000Z
DTEND;VALUE=DATE-TIME:20201015T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/4
DESCRIPTION:Title: An extended SIR model for the spread of COVID-19 in different communiti
es\nby Chris Antonopoulos (University of Essex) as part of MESS (Mathe
matics Essex Seminar Series)\n\n\nAbstract\nIn this paper\, we study the e
ffectiveness of the modelling approach on the pandemic due to the spreadin
g of the novel COVID-19 disease and develop an extended-susceptible-infect
ed-removed (eSIR) model that provides a theoretical framework to investiga
te its spread within a community. The eSIR model is based upon the well-kn
own susceptible-infected-removed (SIR) model with the difference that a to
tal population is not defined or kept constant per se and the number of su
sceptible individuals does not decline monotonically. To the contrary\, as
we show herein\, it can be increased in surge periods! In particular\, we
investigate the time evolution of different populations and monitor diver
se significant parameters for the spread of the disease in various communi
ties\, represented by countries and the state of Texas in the USA. The eSI
R model can provide us with insights and predictions of the spread of the
virus in communities that recorded data alone cannot. Our work shows the i
mportance of modelling the spread of COVID-19 by the eSIR model that we pr
opose here\, as it can help to assess the impact of the disease by offerin
g valuable predictions. Our analysis takes into account data from January
to June\, 2020\, the period that contains the data before and during the i
mplementation of strict and control measures. We propose predictions on va
rious parameters related to the spread of COVID-19 and on the number of su
sceptible\, infected and removed populations until September 2020. By comp
aring the recorded data with the data from our modelling approaches\, we d
educe that the spread of COVID-19 can be under control in all communities
considered\, if proper restrictions and strong policies are implemented to
control the infection rates early from the spread of the disease.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Sophie Kaloghiros (Brunel University)
DTSTART;VALUE=DATE-TIME:20201112T150000Z
DTEND;VALUE=DATE-TIME:20201112T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/5
DESCRIPTION:Title: K-stability of Fano 3-folds\nby Anne-Sophie Kaloghiros (Brunel Univ
ersity) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\n
Fano varieties are geometric shapes which are positively curved. They aris
e in a wide array of fields from theoretical physics to phylogenetic trees
. In fact\, every geometric shape which can be parametrised (or covered )
is - up to surgery - a family of Fano varieties. There are rich interacti
ons between differential geometric and algebro-geometric properties of Fan
o manifolds (and more generally of Kahler manifolds). An instance of this
phenomenon was conjectured by Yau Tian and Donaldson ( and proved by Donal
dson\, Chen and Sun): they proved that on Fano manifolds the existence of
special canonical metrics is equivalent to a stability property. This is
an equivalence between properties that are subtle\, and still little unde
rstood. I will discuss algebro-geometric approaches to this problem and wi
ll present recent developments and their applications to our understanding
of Fano surfaces and 3-folds.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murat Akman (University of Essex)
DTSTART;VALUE=DATE-TIME:20201119T150000Z
DTEND;VALUE=DATE-TIME:20201119T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/6
DESCRIPTION:Title: A Minkowski problem for nonlinear capacity\nby Murat Akman (Univers
ity of Essex) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbst
ract\nThe classical Minkowski problem consists in finding a convex polyhed
ron from data consisting of normals to their faces and their surface areas
. In the smooth case\, the corresponding problem for convex bodies is to f
ind the convex body given the Gauss curvature of its boundary\, as a funct
ion of the unit normal. The proof consists of three parts: existence\, uni
queness and regularity. In this talk\, we study a Minkowski problem for ce
rtain measure associated with a compact convex set E with nonempty interio
r and its A-harmonic capacitary function in the complement of E. Here A-ha
rmonic PDE is a non-linear elliptic PDE whose structure is modeled on the
p-Laplace equation. If \\mu_E denotes this measure\, then the Minkowski
problem we consider in this setting is that\; for a given finite Borel mea
sure \\mu on S^(n-1)\, find necessary and sufficient conditions for which
there exists E as above with \\mu_E =\\mu. We will discuss the existence\,
uniqueness\, and regularity of this problem in this setting. The talk wil
l be related with the following papers: https://arxiv.org/abs/1906.01576\,
https://arxiv.org/abs/1810.03752\, https://arxiv.org/abs/1709.00447.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair Litterick (University of Essex)
DTSTART;VALUE=DATE-TIME:20201126T150000Z
DTEND;VALUE=DATE-TIME:20201126T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/7
DESCRIPTION:Title: Variations on a theme of J.-P. Serre: Complete reducibility in groups\,
representations\, buildings and geometric invariant theory\nby Alasta
ir Litterick (University of Essex) as part of MESS (Mathematics Essex Semi
nar Series)\n\n\nAbstract\nWhen studying modules or other algebraic object
s\, it is common to try and break things up and study the simple pieces. C
omplete reducibility asks the question: Under what conditions do these sim
ple objects fully describe the object we started with? In representation t
heory this becomes: Under what condition is every module a direct sum of i
ts irreducible factors? This question\, which a priori has nothing to do w
ith geometry\, topology or combinatorics\, turns out to have deep connecti
ons with all these other areas. In this talk we will look at these connect
ions\, and we will see how fundamental representation-theoretic results ha
ve analogues and generalisations in other areas of pure mathematics.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Walker (Centre for Environment\, Fisheries and Aquaculture
Science)
DTSTART;VALUE=DATE-TIME:20201203T150000Z
DTEND;VALUE=DATE-TIME:20201203T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/8
DESCRIPTION:Title: Cod on the menu? Using mathematical modelling to provide fisheries mana
gement advice\nby Nicola Walker (Centre for Environment\, Fisheries an
d Aquaculture Science) as part of MESS (Mathematics Essex Seminar Series)\
n\n\nAbstract\nScientific advice on the management of fish stocks is often
informed by mathematical assessment models that fit to information from c
atches\, research surveys and life history. North Sea cod is a high-profil
e and commercially important stock with a long history of highs and lows.
In particular\, the latest assessment estimates that the stock is below sa
fe biological limits\, which comes just two years after the fishery was ce
rtified sustainable. Using North Sea cod as a case study\, Dr Walker will
present the state-space assessment model (SAM) and detail the process of t
urning model outputs into scientific advice for fisheries management. She
will discuss diagnostics for assessing the quality of input data and model
fits and highlight some of the problems facing the assessment of this sto
ck.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Iliopolou (University of Kent)
DTSTART;VALUE=DATE-TIME:20210204T150000Z
DTEND;VALUE=DATE-TIME:20210204T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/9
DESCRIPTION:Title: A discrete Kakeya-type inequality\nby Marina Iliopolou (University
of Kent) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\
nThe Kakeya conjectures of harmonic analysis claim that congruent tubes th
at point in different directions rarely meet. In this talk we discuss the
resolution of an analogous problem in a discrete setting (where the tubes
are replaced by lines)\, and provide some structural information on quasi-
extremal configurations. This is joint work with A. Carbery.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús M. Seoane (Universidad Rey Juan Carlos)
DTSTART;VALUE=DATE-TIME:20210211T150000Z
DTEND;VALUE=DATE-TIME:20210211T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/10
DESCRIPTION:Title: Relativistic chaotic scattering\nby Jesús M. Seoane (Universidad
Rey Juan Carlos) as part of MESS (Mathematics Essex Seminar Series)\n\n\nA
bstract\n"The phenomenon of chaotic scattering is very relevant in differe
nt fields of science and engineering. It has been mainly studied in the co
ntext of Newtonian mechanics\, where the velocities of the particles are l
ow in comparison with the speed of light. In this talk\, we analyze global
properties such as the escape time distribution and the decay law of the
Hénon-Heiles system in the context of special relativity. Our results sho
w that the average escape time decreases with increasing values of the rel
ativistic factor β. As a matter of fact\, we have found a crossover point
for which the KAM islands in the phase space are destroyed when β ≃ 0.
4 [1]. On the other hand\, the study of the survival probability of partic
les in the scattering region shows an algebraic decay for values of β ≤
0.4\, and this law becomes exponential for β >\; 0.4. Surprisingly\, a
scaling law between the exponent of the decay law and the β factor is un
covered where a quadratic fitting between them is found. The results of ou
r numerical simulations agree faithfully with our qualitative arguments. B
esides\, we compute the basin entropy and the fractal dimension of the set
of singularities of the scattering function in function of β [2]. Finall
y\, we apply these results in the scattering in three-body problem in rela
tivistic regime [3]. We expect this work to be useful for a better underst
anding of both chaotic and relativistic systems.\n[1] J. D. Bernal\, J. M.
Seoane\, and M. A. F. Sanjuán. Global relativistic effects in chaotic sc
attering. Phys. Rev. E 95\, 032205 (2017).\n[2] J. D. Bernal\, J. M. Seoan
e\, and M. A. F. Sanjuán. Basin entropy and fractal dimension in relativi
stic chaotic scattering. Phys. Rev. E 97 042214 (2018).\n[3] J. D. Bernal\
, J. M. Seoane\, J. C. Vallejo\, L. Huang\, and M. A. F. Sanjuán. Influen
ce of the gravitational radius o asymptotic behaviour of the relativistic
Sitnikov problem. Phys. Rev. E 102 042204 (2020)."\n
LOCATION:https://researchseminars.org/talk/EssexMaths/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina de Filippis (University of Turin)
DTSTART;VALUE=DATE-TIME:20210225T150000Z
DTEND;VALUE=DATE-TIME:20210225T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/11
DESCRIPTION:Title: Differentiable vs non-differentiable systems\nby Christina de Fili
ppis (University of Turin) as part of MESS (Mathematics Essex Seminar Seri
es)\n\n\nAbstract\n"Nonautonomous\, nonuniformly elliptic functionals are
variational integrals characterized by quite a wild behavior of the ellipt
icity ratio associated to their integrand\, in the sense that it may blow
up as the modulus of the gradient variable goes to infinity. We analyze th
e interaction between the space-depending coefficient of the integrand and
a possible forcing term and derive optimal Lipschitz criteria for minimiz
ers. We catch the main model cases appearing in the literature\, such as f
unctionals with unbalanced power growth or with fast exponential growth. W
e also find new borderline regularity results also in the uniformly ellipt
ic case\, i.e. when the ellipyicity ratio is uniformly bounded. This appro
ach yields optimal regularity results for obstacle problems associated for
instance to iterated exponential models\, which have been treated in [2]
for the first time. Finally\, we look at general nonautonomous integrands
with (p\,q)-growth and show general interpolation properties allowing to g
et basic higher integrability results for either bounded or Hölder contin
uous minimizers under improved bounds for the gap q-p.\nThis talk is based
on papers [1\,2\,3].\nReferences\n[1] C. De Filippis\, G. Mingione\, Inte
rpolative gap bounds for nonautonomous integrals. Preprint (2020)\, submit
ted.\n[2] C. De Filippis\, G. Mingione\, Lipschitz bounds and nonautonomou
s integrals. Preprint (2020)\, submitted. https://arxiv.org/pdf/2007.07469
.pdf\n[3] C. De Filippis\, G. Mingione\, On the regularity of minima of no
n-autonomous functionals. Journal of Geometric Analysis 30:1584-1626\, (20
20). https://doi.org/10.1007/s12220-019-00225-z"\n
LOCATION:https://researchseminars.org/talk/EssexMaths/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Cox (University of Bristol)
DTSTART;VALUE=DATE-TIME:20210304T150000Z
DTEND;VALUE=DATE-TIME:20210304T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/12
DESCRIPTION:Title: Spread and infinite groups\nby Charles Cox (University of Bristol)
as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nMy rece
nt work has involved taking questions asked for finite groups and consider
ing them for infinite groups. There are various natural directions with th
is. In finite group theory\, there exist many beautiful results regarding
generation properties. One such notion is that of spread\, and Scott Harpe
r and Casey Donoven have raised several intriguing questions for spread fo
r infinite groups (in https://arxiv.org/abs/1907.05498). A group G has spr
ead k if for every g_1\, …\, g_k in G we can find an h in G such that <
g_i\, h > = G for i = 1\, ...\, k. For any group we can say that if it has
a proper quotient that is non-cyclic\, then it has spread 0. In the finit
e world there is then the astounding result - which is the work of many au
thors - that this condition on proper quotients is not just a necessary co
ndition for positive spread\, but is also a sufficient one. Harper-Donoven
’s first question is therefore: is this the case for infinite groups? We
ll\, no. But that’s for the trivial reason that we have infinite simple
groups that are not 2-generated (and they point out that 3-generated examp
les are also known). But if we restrict ourselves to 2-generated groups\,
what happens? In this talk we’ll see the answer to this question. The ar
guments will be concrete (*) and accessible to a general audience.\n\n(*)
at the risk of ruining the punchline\, we will find a 2-generated group th
at has every proper quotient cyclic but that has spread zero.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nivedita Viswanathan (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20210318T150000Z
DTEND;VALUE=DATE-TIME:20210318T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/13
DESCRIPTION:Title: Understanding the notion of K-stability using 3-folds\nby Nivedita
Viswanathan (University of Edinburgh) as part of MESS (Mathematics Essex
Seminar Series)\n\n\nAbstract\nThe main objects of study in Algebraic geom
etry are ‘varieties’\, which are basically the geometric counterpart o
f solutions to polynomial equations. One of the most interesting questions
to ask about a variety\, is to determine whether it is ‘K-stable’. A
conjecture by Yau-Tian-Donaldson gives an algebro-geometric way of looking
at the notion of K-stability and many recent developments give very expli
cit ways of determining this property. In this talk\, my goal would be to
give you a rough idea of why this is very interesting to study\, by looki
ng at an explicit example of a Fano 3-fold. We will first look at the basi
c concepts that would be required to do this\, using some simple examples
and then take you through an example of a 3-fold slowly. We will look at
how best to describe the 3-fold using notions that are familiar to us and
then describe how one would determine the K-stability of the same. This
is joint work with Jesus Martinez Garcia\, Ivan Cheltsov\, Costya Shramov
\, Kento Fujita\, Carolina Araujo\, Ana-Maria Castravet\, Anne-Sophie Kalo
ghiros and Hendrick Suess.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Cihan (University of Essex)
DTSTART;VALUE=DATE-TIME:20210325T150000Z
DTEND;VALUE=DATE-TIME:20210325T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/14
DESCRIPTION:Title: Digraph groups and related groups\nby Mehmet Cihan (University of
Essex) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nG
roups can be expressed in terms of a ﬁnite a digraph which vertices cor
respond to the generators and arcs correspond to the relators. Cuno and
Williams investigated when the number of vertices is equal the number of a
rcs\, where the undirected graph is triangle free that means the girth is
at least 4\, and they proved that the corresponding group is either finite
cyclic or infinite. It is known that when the number of vertices is more
than the number of arcs\, then it is infinite. Therefore\, I investigated
when the number of vertices is less than or equal the number of arcs in m
y thesis. But it is more interesting when the undirected graph is with tri
angle and therefore the underlying graph is complete graph. When we direct
ed the complete graph\, then it is known as tournaments. All known example
s are done by Mennicke and Johnson for a strong tournament with 3 vertices
. In 1959\, Mennicke provided an example of a group defined by the present
ation M(a\, b\, c) =〈x\, y\, z | y^−1xy=x^a\, z^−1yz=y^b\, x^−1zx=
z^c〉\, which is finite in the case a=b=c ≥ 3. In 1997\, Johnson provi
ded another group needing exactly three generators with presentation J(a\,
b\, c) =〈x\, y\, z|x^y=y^(b−2)x^−1y^(b+2)\, y^z=z^(c−2)y^−1z^(c
+2)\,z^x=x^(a-2)z^−1x^(a+2)〉 and which is finite in the cases where a\
, b\, and c are non-zero even integers. These are important since they pr
ovide examples of finite groups needing exactly three generators. In this
talk\, I will talk about generalisation of their groups from 3 generators
to n generators for all strong tournaments.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federica Armani (University of Essex)
DTSTART;VALUE=DATE-TIME:20210429T140000Z
DTEND;VALUE=DATE-TIME:20210429T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/15
DESCRIPTION:Title: Mathematics Anxiety: general overview\, what has been done and what we
need to do to help learners\nby Federica Armani (University of Essex)
as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nMathema
tical competence is an important ability to master often accompanied by a
feeling of apprehension\, anxiety and fear which influence the achievement
s\, career choices or performance of an individual. This is called Math An
xiety\, a feeling of tension and anxiety that interferes with the manipula
tion of numbers and the solving of mathematical problems in ordinary life
and academic situations. In this seminar I will discuss this problem and s
how how tailored educational approaches in combination with motivational a
nd Mindset Theories can be used to mitigate the negative effects of Math A
nxiety. In the last part I will present the development and initial result
s obtained from a mathematical puzzle I am using in research which relies
on counting abilities\, spatial reasoning\, working memory and exploits ba
sic mathematical knowledge adapted and used in a different and more engagi
ng way in order to solve a series of puzzles.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Logares (Universidad Complutense de Madrid)
DTSTART;VALUE=DATE-TIME:20210520T140000Z
DTEND;VALUE=DATE-TIME:20210520T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/16
DESCRIPTION:by Marina Logares (Universidad Complutense de Madrid) as part
of MESS (Mathematics Essex Seminar Series)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EssexMaths/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Dolgov (University of Bath)
DTSTART;VALUE=DATE-TIME:20210617T140000Z
DTEND;VALUE=DATE-TIME:20210617T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/17
DESCRIPTION:Title: Deep tensor decompositions for sampling from high-dimensional distribu
tions\nby Sergey Dolgov (University of Bath) as part of MESS (Mathemat
ics Essex Seminar Series)\n\n\nAbstract\nCharacterising intractable high-d
imensional random variables is one of the fundamental challenges in stocha
stic computation\, for example\, in the solution of Bayesian inverse probl
ems. The recent surge of transport maps offers a mathematical foundation a
nd new insights for tackling this challenge by coupling intractable random
variables with tractable reference random variables. In this talk I will
present a nested coordinate transformation framework inspired by deep neur
al networks but driven by functional tensor-train approximation of tempere
d probability density functions instead. This bypasses slow gradient desce
nt optimisation by a direct inverse Rosenblatt transformation. The resulti
ng deep inverse Rosenblatt transport significantly expands the capability
of tensor approximations and transport maps to random variables with compl
icated nonlinear interactions and concentrated density functions. We demon
strate the efficiency of the proposed approach on a range of applications
in uncertainty quantification\, including parameter estimation for dynamic
al systems and inverse problems constrained by partial differential equati
ons.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Amanatidis (University of Essex)
DTSTART;VALUE=DATE-TIME:20201105T150000Z
DTEND;VALUE=DATE-TIME:20201105T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/18
DESCRIPTION:Title: Rapid mixing of the switch Markov chain for strongly stable degree seq
uences\nby Georgios Amanatidis (University of Essex) as part of MESS (
Mathematics Essex Seminar Series)\n\n\nAbstract\nThe switch Markov chain h
as been extensively studied as the most natural Markov Chain Monte Carlo a
pproach for sampling graphs with prescribed degree sequences. We show that
the switch chain for sampling simple undirected graphs with a given degre
e sequence is rapidly mixing when the degree sequence is so-called strongl
y stable. Strong stability is satisfied by all degree sequences for which
the switch chain was known to be rapidly mixing based on Sinclair's multic
ommodity flow method up until a recent manuscript of Erd\\H{o}s et al. (20
19). Our approach relies on an embedding argument\, involving a Markov cha
in defined by Jerrum and Sinclair (1990). This results in a much shorter p
roof that unifies (almost) all the rapid mixing results for the switch cha
in in the literature\, and extends them up to sharp characterizations of P
-stable degree sequences. In particular\, our work resolves an open proble
m posed by Greenhill and Sfragara (2017).\n
LOCATION:https://researchseminars.org/talk/EssexMaths/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anouchah Latifi (University of Qom)
DTSTART;VALUE=DATE-TIME:20201029T150000Z
DTEND;VALUE=DATE-TIME:20201029T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/20
DESCRIPTION:Title: Labyrinth walk: A chaotic non Hamiltonian conservative system that doe
s not admit an energy function\nby Anouchah Latifi (University of Qom)
as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nLabyrin
th Chaos and it conservative version\, Labyrinth walk are generic and mini
mal models of a dynamical system discovered by Otto Rossler and Rene Thoma
s in order to identify the necessary mathematical conditions for the appea
rance of chaotic and hyperchaotic motion in continuous flows. It turned ou
t that in spite of its extreme simplicity these systems are full of surpri
sing properties. Simple and elegant as it is\, it still holds great promis
e for elucidating aspects of chaotic dynamics that are not evident in othe
r systems. Our work highlights the incredible riches of this system in its
disconcerting simplicity and its importance in the context of dynamical s
ystems and in other fields. This is joint work with Chris G. Antonopoulos
and Vasileios Basios.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Blackburn (Royal Holloway\, University of London)
DTSTART;VALUE=DATE-TIME:20201210T150000Z
DTEND;VALUE=DATE-TIME:20201210T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/21
DESCRIPTION:Title: How many finite rings are there?\nby Simon Blackburn (Royal Hollow
ay\, University of London) as part of MESS (Mathematics Essex Seminar Seri
es)\n\n\nAbstract\nFor a positive integer $n$\, write $f(n)$ for the numbe
r of isomorphism classes of rings of order $n$. What can we say about $f(n
)$? Determining $f(n)$ exactly for all $n$ looks unrealistic\, but in 1970
Kruse and Price (J LMS) stated an asymptotic result that gives the growth
rate of $f(n)$ as $n\\rightarrow\\infty$. Sadly\, there are problems wit
h their proof. I will talk about recent joint work with K. Robin McLean (U
niversity of Liverpool) in which we fix the problems\, and improve the err
or terms\, of the Kruse--Price result. No knowledge of ring theory above a
first undergraduate course will be assumed!\n
LOCATION:https://researchseminars.org/talk/EssexMaths/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Lee (University of Auckland)
DTSTART;VALUE=DATE-TIME:20201217T090000Z
DTEND;VALUE=DATE-TIME:20201217T100000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/22
DESCRIPTION:Title: The hunt for regular orbits of almost quasisimple groups\nby Melis
sa Lee (University of Auckland) as part of MESS (Mathematics Essex Seminar
Series)\n\n\nAbstract\nLet $G$ be a permutation group on $\\Omega$. We sa
y that $G$ has a regular orbit on $\\Omega$ if there exists $x \\in \\Omeg
a$ that is fixed only by the identity permutation. Regular orbits arise in
a number of applications including the study of Frobenius groups and the
proof of the celebrated $k(GV)$-theorem\, which gives an upper bound on th
e number of conjugacy classes of certain affine groups where $|G|$ and $|V
|$ are coprime. One of the major cases in the proof of the $k(GV)$-theore
m was a study of regular orbits of the so-called almost quasisimple groups
$G$ (i.e.\,$ G/F(G)$ is an almost simple group). In this talk\, after giv
ing some background and motivation\, I will discuss progress in my quest t
o finish classifying all pairs $(G\,V)$ where $G$ is an almost quasisimple
group with a regular orbit on its irreducible module $V$. By the proof of
the $k(GV)$-problem\, this boils down to the cases where $(|G|\,|V|) >1$.
I will also briefly discuss techniques used for this classification\, whi
ch involve some algebraic group theory\, character theory and computationa
l methods.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Marcos Batista (State University of Ponta Grossa\, Paraná
\, Brazil)
DTSTART;VALUE=DATE-TIME:20210128T150000Z
DTEND;VALUE=DATE-TIME:20210128T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/23
DESCRIPTION:Title: Extreme events in nonlinear wave interactions (dragon king)\nby An
tonio Marcos Batista (State University of Ponta Grossa\, Paraná\, Brazil)
as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nExtreme
events are by definition rare and exhibit unusual values of relevant ob
servables. In literature\, it is possible to find many studies about the p
redictability and suppression of extreme events. In this work\, we show
the existence of dragon-kings extreme events in nonlinear three-wave
interactions. Dragon-king extreme events\, identified by phase transi
tions\, tipping points and catastrophes\, affects fluctuating systems. We
show that these events can be avoided by adding a perturbing small ampli
tude wave to the system.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kelly Iarosz (Universidade Tecnológica Federal do Paraná UTFPR F
aculdade de Telêmaco Borba FATEB)
DTSTART;VALUE=DATE-TIME:20210218T150000Z
DTEND;VALUE=DATE-TIME:20210218T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/24
DESCRIPTION:Title: Our brain is not static\nby Kelly Iarosz (Universidade Tecnológic
a Federal do Paraná UTFPR Faculdade de Telêmaco Borba FATEB) as part of
MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nThe connections bet
ween brain neurons have the characteristic of being modified over time due
to several causes such as new experiences\, lesions\, brain pathologies\,
etc. This fenomenon is known as synaptic plasticity. We study the capacit
y of neurons in a network to change temporarily or permanently their conne
ctions and behavior\, as a function of their synchronous behavior. Specifi
cally\, an initial all-to-all topology evolves to a complex topology. More
over\, external perturbations can induce co-existence of clusters\, those
whose neurons are synchronous and those whose neurons are desynchronous. W
hen the delay is increased the network presents a non-trivial topology. Re
garding the synchronization\, only for small values of the synaptic delay
this phenomenon is observed.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Creaser (University of Exeter)
DTSTART;VALUE=DATE-TIME:20210311T150000Z
DTEND;VALUE=DATE-TIME:20210311T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/25
DESCRIPTION:Title: Domino effects on networks of bistable oscillatory nodes\nby Jenni
fer Creaser (University of Exeter) as part of MESS (Mathematics Essex Semi
nar Series)\n\n\nAbstract\nMultistability has been identified as a key mec
hanism in a diverse range of brain functions at different spatial scales.
It is well known that the addition of noise in a multistable system can in
duce random transitions between states. In a network\, the presence of cou
pling introduces dependence between nodes leading to sequences of noise-in
duced transitions in a so called domino effect. The timing and order of th
ese domino cascades are emergent properties of the network. Analysis of th
e transient dynamics responsible for these transitions is crucial to under
stand the drivers of neurological disorders such as epilepsy. We consider
a general model of coupled bi-stable oscillators. Each node has two stable
states\; oscillating (active) and non-oscillating (quiescent). Escape fro
m the quiescent state is driven by additive noise and we assume the timesc
ale of transitions back again is long enough to be ignored. Escapes are af
fected by changes in node dynamics\, coupling strength and synchronisation
. Using numerical and theoretical techniques we explore the interplay betw
een synchronisation and noise-induced escape. We consider amplitude and ph
ase-amplitude coupled motifs. In particular\, we find and investigate exam
ples of three node symmetric networks where sequences of noise-induced esc
apes are associated with various types of partial synchrony during the seq
uence.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyle Wedgwood (University of Exeter)
DTSTART;VALUE=DATE-TIME:20210506T140000Z
DTEND;VALUE=DATE-TIME:20210506T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/26
DESCRIPTION:Title: The curious case of rapid entrainment after jet lag\, and\, how to get
a single neuron to remember\nby Kyle Wedgwood (University of Exeter)
as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\n"This ta
lk will cover two stories involving mathematical modelling (and some exper
iments) in neural systems.\n\nIn the first\, we will discuss the re-entrai
nment problem of how our bodies synchronise with the external environment
following travel across time zones or shift work. To do so\, we analyse a
two-dimensional variant of the Forgers-Jewett-Kronauer model\, which descr
ibes changes in core body temperature and neural activity in the brain reg
ion responsible for circadian rhythms\, forced by a 24-hour light/dark cyc
le. This model\, which has previously been used to explain the East-West a
symmetry in jet lag severity after travel\, predicts a counter-intuitive r
apid re-entrainment for sufficiently bright daylight. We explain this phen
omenon via continuation of invariant manifolds of fixed points of a 24-hou
r stroboscopic map and explore the consequence of the arrangement of such
manifolds on re-entrainment in a variety of scenarios.\n\nIn the second st
ory\, we will explore the capability of a neuron that is synaptically coup
led to itself\, to store and repeat patterns of precisely timed spikes\, w
hich we regard as single cell 'memories'. Drawing on analogies from semico
nductor lasers\, we append a delayed self-coupling term to the oft studied
Morris-Lecar model of neuronal excitability and use bifurcation analysis
to predict the number and type of memories the neuron can store. These res
ults highlight the delay period as an important period parameter controlli
ng the storage capacity of the cell. Finally\, we use the dynamic clamp pr
otocol to introduce self-coupling to a mammalian cell and confirm the exis
tence of the spiking patterns predicted by the model analysis."\n
LOCATION:https://researchseminars.org/talk/EssexMaths/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constanza Rojas-Molina (CY Tech - Institut des Sciences et Techniq
ues - CY Cergy Paris Université)
DTSTART;VALUE=DATE-TIME:20210513T140000Z
DTEND;VALUE=DATE-TIME:20210513T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/27
DESCRIPTION:Title: Fractional random Schrödinger operators\, integrated density of state
s and localization\nby Constanza Rojas-Molina (CY Tech - Institut des
Sciences et Techniques - CY Cergy Paris Université) as part of MESS (Math
ematics Essex Seminar Series)\n\n\nAbstract\nIn this talk we will review s
ome recent results on the fractional Anderson model\, a random Schrödinge
r operator driven by a fractional laplacian. The interest on the latter li
es in their association to stable Levy processes\, random walks with long
jumps and anomalous diffusion. We discuss in this talk the interplay betwe
en the non-locality of the fractional laplacian and the localization prope
rties of the random potential in the fractional Anderson model\, in both t
he continuous and discrete settings. In the discrete setting we study the
integrated density of states and show a fractional version of Lifshitz tai
ls. This coincides with results obtained in the continuous setting by the
probability community. This is based on joint work with M. Gebert (LMU Mun
ich).\n
LOCATION:https://researchseminars.org/talk/EssexMaths/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Billy Woods (University of Essex)
DTSTART;VALUE=DATE-TIME:20210527T140000Z
DTEND;VALUE=DATE-TIME:20210527T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/28
DESCRIPTION:Title: Iwasawa algebras and skew power series rings\nby Billy Woods (Univ
ersity of Essex) as part of MESS (Mathematics Essex Seminar Series)\n\n\nA
bstract\nIn this talk\, beginning with a faulty proof of Fermat’s Last T
heorem from the 19th century\, I’ll attempt to provide some motivation
for the study of Iwasawa algebras\, which have now become a critical tool
in many significant number-theoretic problems. I’ll give a couple of way
s to think about them algebraically\, contrast them with similar algebraic
objects\, and outline some of what is known (and what is still unknown) a
bout them\, including my own research. This is a talk about noncommutative
algebra\, but I’ll try to keep the technical jargon to a minimum\, so t
hat much of this talk remains accessible even to those who haven’t thoug
ht about abstract algebra in some time!\n
LOCATION:https://researchseminars.org/talk/EssexMaths/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thanos Manos (CY Tech - Institut des Sciences et Techniques - CY C
ergy Paris Université)
DTSTART;VALUE=DATE-TIME:20210603T140000Z
DTEND;VALUE=DATE-TIME:20210603T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/29
DESCRIPTION:Title: Neural networks: desynchronization with synaptic and structural plasti
city\nby Thanos Manos (CY Tech - Institut des Sciences et Techniques -
CY Cergy Paris Université) as part of MESS (Mathematics Essex Seminar Se
ries)\n\n\nAbstract\n"Mathematical modelling is an important tool in under
standing the basic mechanisms of the human brain as well as determining it
s function and operation. In this talk\, I will discuss how such models\,
based on ordinary differential equations can capture and describe the unde
rlying dynamical evolution of interactions between a relatively small numb
er of neurons within some brain area. Several brain diseases are character
ized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimu
lation was computationally designed to specifically counteract abnormal ne
uronal synchronization processes by desynchronization. In the presence of
spike timing-dependent plasticity (STDP) this leads to a decrease of synap
tic weights and ultimately to an anti-kindling\, i.e.\, unlearning of abno
rmal synaptic connectivity and abnormal neuronal synchrony. The long-lasti
ng desynchronizing impact of CR stimulation has been verified in pre-clini
cal and clinical proof of concept studies. However\, as yet it is unclear
how to optimally choose the CR stimulation frequency\, i.e.\, the repetiti
on rate at which the CR stimuli are delivered.\nThe first part of the talk
is dedicated to systems with STDP and the design of optimal CR stimulatio
n protocols. Namely\, protocols that manage to induce global (for differen
t system initiations) desynchronization but also show very good robustness
among different signals and network dependent variations. These findings
can be implemented into stimulation protocols for first in man and proof o
f concept studies aiming at further improvement of CR stimulation.\nIn the
second part\, I will present a computational model which account for comb
ining different time scales with synaptic (STDP) and structural plasticity
. The latter one refers to a mechanism that deletes or generates synapses
in order to homeostatically adapt the firing rates of neurons to a set poi
nt-like target firing rate in the course of days to months. Such a model s
ucceeds to explain a clinically relevant dynamic phenomenon which could no
t be explained in the STDP-only models so far. It also provides a plausibl
e mechanism that explains why CR stimulation may become more effective (i.
e.\, require less stimulation duration) when repeatedly delivered (in the
course of the treatment). This aspect is crucial from a clinical standpoin
t to further optimize dosing (and hence treatment outcome) of CR stimulati
on."\n
LOCATION:https://researchseminars.org/talk/EssexMaths/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helen Christodoulidi (University of Lincoln)
DTSTART;VALUE=DATE-TIME:20210610T140000Z
DTEND;VALUE=DATE-TIME:20210610T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/30
DESCRIPTION:Title: The role of KdV and Toda in the FPUT problem\nby Helen Christodoul
idi (University of Lincoln) as part of MESS (Mathematics Essex Seminar Ser
ies)\n\n\nAbstract\nThe celebrated Fermi-Pasta-Ulam-Tsingou model is a lon
g chain of coupled nonlinear oscillators representing the simplest one-dim
ensional analogue of atoms in a crystal. This system represents a benchmar
k in the history of nonlinear science: The FPUT problem sparked the birth
of both computational mathematics and integrable systems. Most notably\, i
t is the first dynamical system numerically integrated on a computer while
its enigmatic non-ergodic behaviour is puzzling the scientists for over 6
5 years\, with innumerable works published. In this talk I will focus on t
he role of two integrable models\, namely I) the Korteweg-de Vries equatio
n (KdV)\, which describes waves on shallow water surfaces\, and II) the To
da lattice\, in explaining FPUT's non-ergodic behaviour at low energies.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirk McDermott (Slippery Rock University)
DTSTART;VALUE=DATE-TIME:20210624T140000Z
DTEND;VALUE=DATE-TIME:20210624T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/31
DESCRIPTION:Title: On the shift dynamics of groups of Fibonacci type\nby Kirk McDermo
tt (Slippery Rock University) as part of MESS (Mathematics Essex Seminar S
eries)\n\n\nAbstract\nA group is said to be cyclically presented if it adm
its a presentation with a certain cyclic symmetry. Such a symmetry induces
a periodic automorphism of the group called the shift\, and its dynamics
strongly impacts the structure of the group. In this talk\, we investigate
the shift dynamics of the cyclically presented groups of Fibonacci type.
These groups have a rich history and have been studied from a variety of p
erspectives\, from combinatorial group theory to 3-manifold topology. We u
se these perspectives to study the shift dynamics and go on to introduce t
opological and computational techniques for identifying fixed points.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ihechukwu Chinyere (University of Essex)
DTSTART;VALUE=DATE-TIME:20210701T140000Z
DTEND;VALUE=DATE-TIME:20210701T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/32
DESCRIPTION:Title: Hyperbolicity of certain cyclically presented groups\nby Ihechukwu
Chinyere (University of Essex) as part of MESS (Mathematics Essex Seminar
Series)\n\n\nAbstract\nIn his 1992 article titled “A funny property of
sphere and equations over groups” Klyachko used the car-crash lemma to e
stablish the Kervaire conjecture for torsion-free groups. Inspired by this
construction we use ant-lane argument to prove that certain cyclically pr
esented groups are hyperbolic.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Logares (Universidad Complutense de Madrid)
DTSTART;VALUE=DATE-TIME:20211021T140000Z
DTEND;VALUE=DATE-TIME:20211021T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/33
DESCRIPTION:Title: The many facets of Higgs bundles\nby Marina Logares (Universidad C
omplutense de Madrid) as part of MESS (Mathematics Essex Seminar Series)\n
\n\nAbstract\nSince their origin in the late 80’s\, Higgs bundles manife
st as fundamental objects which are ubiquitous in contemporary mathematics
and theoretical physics. Some prominent examples of this ubiquity are the
ir role as integrable systems\, in Langlands duality and Mirror Symmetry\,
and in representation theory as character varieties. In this talk we shal
l give an introduction to Higgs bundles\, together with a glimpse of how t
hey play all these roles mentioned above.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrios Mitsotakis (Victoria University of Wellington)
DTSTART;VALUE=DATE-TIME:20220224T150000Z
DTEND;VALUE=DATE-TIME:20220224T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/34
DESCRIPTION:Title: Nonlinear and dispersive waves in a basin\nby Dimitrios Mitsotakis
(Victoria University of Wellington) as part of MESS (Mathematics Essex Se
minar Series)\n\n\nAbstract\nSurface water waves of significant interest s
uch as tsunamis and solitary waves are nonlinear and dispersive waves. Unl
uckily\, the equations describing the propagation of surface water waves k
nown as Euler’s equations are immensely hard to solve. In this presentat
ion we show that among the so many simplified systems of PDEs proposed as
alternative approximations to Euler’s equations there is only one proven
to be well-posed (in Hadamard’s sense) in bounded domains with slip-wal
l boundary conditions. We also show that the system obeys most of the phys
ical laws that acceptable water waves equations must obey. Validation with
laboratory data is also presented.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernd Sturmfels (MPI Leipzig)
DTSTART;VALUE=DATE-TIME:20211014T140000Z
DTEND;VALUE=DATE-TIME:20211014T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/35
DESCRIPTION:Title: Linear PDE with Constant Coefficients\nby Bernd Sturmfels (MPI Lei
pzig) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nWe
discuss practical methods for computing the space of solutions to an arbi
trary homogeneous linear system of partial differential equations with con
stant coefficients. These rest on the Fundamental Principle of Ehrenpreis-
-Palamodov from the 1960s. We develop this further using recent advances i
n computational commutative algebra.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Vernitski (University of Essex)
DTSTART;VALUE=DATE-TIME:20211028T140000Z
DTEND;VALUE=DATE-TIME:20211028T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/36
DESCRIPTION:Title: Looking for ways of presenting knots which help artificial intelligenc
e to learn to manipulate knots\nby Alexei Vernitski (University of Ess
ex) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nKnot
s (like the one presented in the picture) are difficult to begin to study
mathematically because mathematical notation works well with words or matr
ices\, and a knot diagram cannot be easily represented as either. This is
why in knot theory much effort is invested in representing knots in the fo
rm of words or matrices (for example\, you might have heard of Gauss words
or Goeritz matrices). Now suppose we want the computer to work with knots
\; then we face a different kind of problem\, namely\, the computer does n
ot possess human 2D and 3D intuition. To enable the computer to start expl
oring knots\, we need to trawl through existing representations of knots (
or invent new ones) looking for those which will compensate for the comput
er not possessing human spatial intuition.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnid Banerjee (Tata Institute of Fundamental Research)
DTSTART;VALUE=DATE-TIME:20211104T150000Z
DTEND;VALUE=DATE-TIME:20211104T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/37
DESCRIPTION:Title: Strong unique continuation for heat operator with Hardy type potentia
l\nby Agnid Banerjee (Tata Institute of Fundamental Research) as part
of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nI will talk abou
t strong unique continuation for the heat operator with Hardy type potenti
al. This is. based on a recent joint work with Nicola Garofalo and Ramesh
Manna. A strong unique continuation property for the heat operator with H
ardy type potential. J. Geom. Anal. 31 (2021)\, no. 6\, 5480–5504.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Kleer (Tilburg University)
DTSTART;VALUE=DATE-TIME:20211118T150000Z
DTEND;VALUE=DATE-TIME:20211118T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/39
DESCRIPTION:Title: MCMC methods for sampling graphs with given degree constraints\nby
Pieter Kleer (Tilburg University) as part of MESS (Mathematics Essex Semi
nar Series)\n\n\nAbstract\n"Efficiently sampling graphs with given degree
constraints is an important open problem\, both in theory and practice. In
this talk\, I will give an overview of some Markov Chain Monte Carlo algo
rithms for various type of degree constraints: Hard degree constraints\, d
egree interval constraints and joint degree distribution constraints.\nThe
se algorithms are based on making small random changes (to a given initial
graph) that preserve the desired constraints. The goal is to understand h
ow many of these small changes are needed until the resulting distribution
\, over the set of all graphs satisfying the given constraints\, is close
to the (uniform) stationary distribution of the induced Markov chain.\nBas
ed on joint work with Georgios Amanatidis (University of Essex)."\n
LOCATION:https://researchseminars.org/talk/EssexMaths/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Katzourakis (University of Reading)
DTSTART;VALUE=DATE-TIME:20211125T150000Z
DTEND;VALUE=DATE-TIME:20211125T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/40
DESCRIPTION:Title: Generalised vectorial $\\infty$-eigenvalue nonlinear problems for $L^\
\infty$ functionals\nby Nikos Katzourakis (University of Reading) as p
art of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\n"Let $\\Omeg
a \\Subset \\mathbb R^n$\, $f \\in C^1(\\mathbb R^{N\\times n})$ and $g\\i
n C^1(\\mathbb R^N)$\, where $N\,n \\in \\mathbb N$. In this talk I will d
iscuss the minimisation problem of finding $u \\in W^{1\,\\infty}_0 (\\Ome
ga\; \\mathbb R^N)$ that satisfies\n$$\\big\\| f(\\mathrm D u) \\big\\|_{L
^\\infty(\\Omega)} \\! = \\inf \\Big\\{\\big\\| f(\\mathrm D v) \\big\\|_{
L^\\infty(\\Omega)} \\! : \\ v \\! \\in W^{1\,\\infty}_0(\\Omega\;\\mathbb
R^N)\, \\\, \\| g(v) \\|_{L^\\infty(\\Omega)}\\! =1\\Big\\}\,$$\nunder na
tural assumptions on $f\,g$. This includes the $\\infty$-eigenvalue proble
m as a special case. I will describe the existence of a minimiser $u_\\inf
ty$ with extra properties\, derived as the limit of minimisers of approxim
ating constrained $L^p$ problems as $p\\to \\infty$. A central contributi
on and novelty of this work is that $u_\\infty$ is shown to solve a diverg
ence PDE with measure coefficients\, whose leading term is a divergence co
unterpart equation of the non-divergence $\\infty$-Laplacian. The results
are new even in the scalar case of the $\\infty$-eigenvalue problem. The t
alk is based on the preprint https://arxiv.org/abs/2103.15911."\n
LOCATION:https://researchseminars.org/talk/EssexMaths/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Livia Campo (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20211209T150000Z
DTEND;VALUE=DATE-TIME:20211209T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/41
DESCRIPTION:Title: Morphing shapes: a guide to birational surgeries\nby Livia Campo (
University of Birmingham) as part of MESS (Mathematics Essex Seminar Serie
s)\n\n\nAbstract\n"Algebraic Geometry studies geometric shapes (algebraic
varieties) that are defined as solutions of polynomial equations in many v
ariables. Such shapes can be distinguished according to their curvature: p
ositive\, zero\, or negative. In this talk I will focus on those with posi
tive curvature\, called Fano varieties.\nThe Minimal Model Program offered
a novel approach to the classification of Fano varieties. As a consequenc
e\, many of them can be transformed into one another by performing sequenc
es of specific (birational) modifications. During my talk I will give an a
ccount of these birational surgeries carrying out a basic example\, and I
will describe a picture that illustrates this procedure in a more complica
ted setting."\n
LOCATION:https://researchseminars.org/talk/EssexMaths/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodoros Papazachariou (University of Essex)
DTSTART;VALUE=DATE-TIME:20211216T150000Z
DTEND;VALUE=DATE-TIME:20211216T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/42
DESCRIPTION:Title: GIT and K-stability for Fano varieties\nby Theodoros Papazachariou
(University of Essex) as part of MESS (Mathematics Essex Seminar Series)\
n\n\nAbstract\nIn algebraic geometry\, one studies varieties which occur a
s solutions to polynomial equations. In particular\, we deal with projecti
ve varieties which are the solution spaces of homogeneous polynomials. An
important category of geometric objects in algebraic geometry is smooth Fa
no varieties\, which are varieties with positive curvature. As such they c
an be thought of as higher dimensional analogues of the sphere. These have
been classified in 1\, 8 and 105 families for curves\, surfaces and three
folds respectively\, while in higher dimensions the number of Fano familie
s is yet unknown\, although we know that their number is bounded. An impor
tant current problem is compactifying these families into moduli spaces\,
i.e.\, spaces which parametrise objects with some common properties. The a
im for the above is so that we can study these families into more details.
In this talk I will discuss how one can obtain such compactifications usi
ng Geometric Invariant Theory (GIT)\, which studies (algebraic) group acti
ons on varieties. I will also discuss how one can get similar compactifica
tions using the theory of K-stability\, and the links this has to GIT.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:CANCELED DUE TO STRIKE
DTSTART;VALUE=DATE-TIME:20211202T150000Z
DTEND;VALUE=DATE-TIME:20211202T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/43
DESCRIPTION:Title: CANCELED DUE TO STRIKE\nby CANCELED DUE TO STRIKE as part of MESS
(Mathematics Essex Seminar Series)\n\n\nAbstract\nThis week's seminar is c
ancelled due to industrial action on higher education.\nPlease see https:/
/www.theguardian.com/education/2021/nov/16/uk-universities-and-colleges-fa
ce-three-days-of-strikes-in-december for more details.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zulkarnain (University of Essex)
DTSTART;VALUE=DATE-TIME:20220120T150000Z
DTEND;VALUE=DATE-TIME:20220120T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/44
DESCRIPTION:Title: Localisation of energy in the FPUT-a system with variability and its c
haotic behaviour\nby Zulkarnain (University of Essex) as part of MESS
(Mathematics Essex Seminar Series)\n\n\nAbstract\nFermi\, Pasta\, Ulam\, a
nd Tsingou studied one-dimensional lattices to model the crystal evolution
towards thermal equilibrium. They expected to observe the equipartition o
f energy as predicted by the Boltzmann-Gibbs (BG) statistics due to nonlin
earities in their model. However\, they noticed that almost all energy was
back to its initial state after some period of steady state. This phenome
non\, well-known as the FPUT recurrences\, led to numerous discoveries in
mathematics and physics. A recent study by Nelson et al. shows that if var
iability is incorporated in the FPUT system\, it will limit the observance
of recurrences. They numerically show that this variability can prevent r
ecurrences in this system. In this talk\, I will discuss two-modes approxi
mations in the normal mode coordinate to explain the localisation of energ
y for large enough variabilities. Moreover\, we also investigate the chaot
ic behaviour of the FPUT-α system for different numbers of particles as w
e increase the variabilities by computing the maximum Lyapunov exponent an
d the SALI of this system.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huseyin Yildirim (University of Essex)
DTSTART;VALUE=DATE-TIME:20220127T150000Z
DTEND;VALUE=DATE-TIME:20220127T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/45
DESCRIPTION:Title: Network re-construction for the complex data generated from the discre
te and continuous models\nby Huseyin Yildirim (University of Essex) as
part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nNetwork In
ference for complex systems is crucial to infer connectivity among variabl
es in many subject areas\, ranging from finance to health sciences. Theref
ore\, it is a rapidly developing area with newly proposed methods. In this
seminar talk\, I will present the Mutual Information (MI)\, double normal
ised Mutual Information Rate (MIR) methods and their lagged versions to re
construct the initial network for artificial data generated by the coupled
logistic map\, coupled circle map\, and coupled Hindmarsh-Rose (HR) model
of neuronal activity. The authors in [1] have already showed that the dou
ble normalised MIR can capture all links in the original network for discr
ete and continuous dynamical models when specific conditions are met. Our
study proposes that the lagged versions of MI and double normalised MIR ca
n infer network topology 100% successfully for small time series. Finally\
, our results show that the latter methods have better performance when us
ing the instantaneous frequency of the membrane potential in the HR model
as a probe to infer network structure.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valerij Romanovskij (University of Maribor)
DTSTART;VALUE=DATE-TIME:20220203T150000Z
DTEND;VALUE=DATE-TIME:20220203T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/46
DESCRIPTION:Title: Integrability and limit cycles in polynomial systems of ODEs\nby V
alerij Romanovskij (University of Maribor) as part of MESS (Mathematics Es
sex Seminar Series)\n\n\nAbstract\n"We discuss two problems related to the
theory of olynomial plane differential systems\, that is\, systems of
the form \n$$\\frac{dx}{dt}=P_{n}(x\,y)\, \\ \\ \\ \n\\frac{dy}{dt}=Q_{n}(
x\,y)\,\n$$\nwhere $P_{n}(x\,y)\, Q_{n}(x\,y)$ are polynomials of degree $
n$\, $x$ and $y$ are real unknown functions.\n\nThe first one is the prob
lem of local integrability\, that is\, the problem of finding local analy
tic integrals in a neighborhood of singular points of system (1). We pres
ent a computational approach to find integrable systems within given par
ametric families of systems and describe some mechanisms of integrability.
\n\n\nThe second problem is called the cyclicity problem\, or the local 1
6th Hilbert problem\, and is related to the stimation of the number of li
mit cycles arising in system (1) after perturbations of integrable systems
. The approach is algorithmic and is based on algorithms of computational
commutative algebra relying on the Groebner bases theory. \n"\n
LOCATION:https://researchseminars.org/talk/EssexMaths/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitra Kosta (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20220210T150000Z
DTEND;VALUE=DATE-TIME:20220210T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/47
DESCRIPTION:by Dimitra Kosta (University of Edinburgh) as part of MESS (Ma
thematics Essex Seminar Series)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EssexMaths/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zihui Zhao (University of Chicago)
DTSTART;VALUE=DATE-TIME:20220217T150000Z
DTEND;VALUE=DATE-TIME:20220217T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/48
DESCRIPTION:Title: Quantitative unique continuation\nby Zihui Zhao (University of Chi
cago) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nUn
ique continuation theorem is a fundamental property of harmonic functions\
, as well as solutions to a large class of elliptic and parabolic PDEs. It
says that if a harmonic function vanishes to infinite order at a point\,
the function must vanish everywhere. In the same spirit\, there is a large
class of quantitative unique continuation theorems\, which use the local
information about the growth rate of a harmonic function to deduce global
information. In particular\, I will talk about how to estimate the size of
the singular set $\\{u=0=|\\nabla u|\\}$ of a harmonic function u. This i
s joint work with Carlos Kenig.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alyssa Genschaw (Milwaukee School of Engineering)
DTSTART;VALUE=DATE-TIME:20220303T150000Z
DTEND;VALUE=DATE-TIME:20220303T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/49
DESCRIPTION:Title: Hausdorff Dimension of Caloric Measure\nby Alyssa Genschaw (Milwau
kee School of Engineering) as part of MESS (Mathematics Essex Seminar Seri
es)\n\n\nAbstract\nCaloric measure is a probability measure supported on t
he boundary of a domain in R^{n+1} = R^n × R (space × time) that is rela
ted to the Dirichlet problem for the heat equation in a fundamental way. E
quipped with the parabolic distance\, R^{n+1} has Hausdorff dimension n+ 2
. We prove that (even on domains with geometrically very large boundary)\,
the caloric measure is carried by a set of Hausdorff dimension at most n
+ 2 − beta_n for some beta_n > 0. The corresponding theorem for harmonic
measure is due to Bourgain (1987)\, but the proof in that paper contains
a gap. Additionally\, we prove a caloric analogue of Bourgain’s alternat
ive. I will briefly discuss the results\, including how we fix the gap in
the original proof. This is joint work with Matthew Badger.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Bick (University of Exeter)
DTSTART;VALUE=DATE-TIME:20220310T150000Z
DTEND;VALUE=DATE-TIME:20220310T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/50
DESCRIPTION:Title: Coupled Oscillator Networks: Structure\, Interactions\, and Dynamics\nby Christian Bick (University of Exeter) as part of MESS (Mathematics
Essex Seminar Series)\n\n\nAbstract\nThe collective dynamics of coupled os
cillatory processes govern many aspects crucial to our lives\, whether it
is the synchronous beating of our heart cells\, collective activity of neu
rons in the brain\, or power grid networks that operate in a stable freque
ncy regime. In this talk we discuss how the collective network dynamics ar
e shaped by the network structure (what oscillator is coupled to what othe
r oscillator) and the network interactions (how one oscillator is coupled
to another). We discuss in particular how ""higher-order"" interactions\,
which have attracted tremendous attention in recent years\, give rise to h
eteroclinic and chaotic dynamics.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitra Kosta (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20220317T150000Z
DTEND;VALUE=DATE-TIME:20220317T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/51
DESCRIPTION:Title: Unboundedness of Markov complexity of monomial curves in for n ≥
4\nby Dimitra Kosta (University of Edinburgh) as part of MESS (Math
ematics Essex Seminar Series)\n\n\nAbstract\nComputing the complexity of M
arkov bases is an extremely challenging problem\; no formula is known in g
eneral and there are very few classes of toric ideals for which the Markov
complexity has been computed. A monomial curve $C$ in $ \\mathbb{A}^3$ ha
s Markov complexity $m(C)$ two or three. Two if the monomial curve is a c
omplete intersection and three otherwise. Our main result shows that there
is no $d \\in \\mathbb{N}$ such that $m(C) \\leq d$ for all monomial cu
rves C in $ \\mathbb{A}^4$. The same result is true even if we restrict t
o complete intersections. We extend this result to all monomial curves in
$ \\mathbb{A}^n$\, where $n \\geq 4$.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eabhnat Ni Fhloinn and Aidan Fitzsimons (Dublin City University)
DTSTART;VALUE=DATE-TIME:20220324T150000Z
DTEND;VALUE=DATE-TIME:20220324T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/52
DESCRIPTION:Title: Problem-solving Potential within the field of mathematics\nby Eabh
nat Ni Fhloinn and Aidan Fitzsimons (Dublin City University) as part of ME
SS (Mathematics Essex Seminar Series)\n\n\nAbstract\nProblem-solving Poten
tial (PsP) is a triad construct\, developed as part of a doctoral study\,
that encompasses a student's mindset\, their mathematical resilience\, and
their problem-solving skills\; which together influence the student's pot
ential in mathematical problem-solving. In this talk\, I will outline that
theory that underlines PsP\, its relevance to the teaching of mathematics
\, and the context and environment in which the PsP has been studied thus
far.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantinos Zygalakis (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20220428T140000Z
DTEND;VALUE=DATE-TIME:20220428T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/53
DESCRIPTION:Title: Connections Between Optimization and Sampling Algorithms\nby Konst
antinos Zygalakis (University of Edinburgh) as part of MESS (Mathematics E
ssex Seminar Series)\n\n\nAbstract\nOptimization and Sampling problems lie
in the heart of Bayesian inverse problems. The ability to solve such inve
rse problems depends crucially on the efficient calculation of quantities
relating to the posterior distribution\, giving thus rise to computational
ly challenging high dimensional optimization and sampling problems. In thi
s talk\, we will connect the corresponding optimization and sampling probl
ems to the large time behaviour of solutions to (stochastic) differential
equations. Establishing such a connection allows to utilise existing knowl
edge from the field of numerical analysis of differential equations. In pa
rticular\, two very important concepts are numerical stability and numeric
al contractivity. In the case of linear differential equations these two c
oncepts coincide\, but with the exception of some very simple Runge-Kutta
methods such the Euler method in the non-linear case numerical stability d
oesn’t imply numerical contractivity [1]. However\, the recently introdu
ced framework of integral quadratic constraints and Lyapunov functions [2\
, 3] allows for bridging this gap between linearity and non-linearity in t
he case of (strongly) convex functions. We will use this framework to stud
y a large class of strogly convex optimization methods and give an alterna
tive explanation for the good properties of Nesterov method\, as well as h
ighlight the reasons behind the failure of the heavy ball method [2]. In a
ddition\, using similar ideas [4]\, we will present a general framework fo
r the non-asymptotic study of the 2-Wasserstein distance between the invar
iant distribution of an ergodic stochastic differential equation and the d
istribution of its numerical approximation in the strongly log-concave cas
e. This allows us to study in a unified way a number of different integrat
ors proposed in the literature for the overdamped and underdamped Langevin
dynamics.\n\n\n[1] J. M. Sanz Serna and K. C. Zygalakis\, Contractivity o
f Runge–Kutta Methods for Convex\nGradient Systems\, SIAM Journal on Num
erical Analysis 58(4):2079-2092\, 2020.\n\n[2] L. Lessard\, B. Recht\, and
A. Packard\, Analysis and design of optimization algorithms via integral
quadratic constraints\, SIAM Journal on Optimization\, 26(1):57–95\, 201
6.\n\n[3] M. Fazlyab\, A. Ribeiro\, M. Morari\, and V. M. Preciado\, Analy
sis of optimization algorithms via integral quadratic constraints: nonstro
ngly convex problems\, SIAM Journal on Optimization\, 28(3):2654–2689\,
2018.\n\n[4] J. M. Sanz Serna and K. C. Zygalakis\, Wasserstein distance e
stimates for the distributions of numerical approximations to ergodic stoc
hastic differential equations\, Journal of Machine Learning Research\, 22
\, 1--37\, 2021\n
LOCATION:https://researchseminars.org/talk/EssexMaths/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riikka Kangaslampi (Tampere University)
DTSTART;VALUE=DATE-TIME:20220519T140000Z
DTEND;VALUE=DATE-TIME:20220519T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/54
DESCRIPTION:Title: Ollivier--Ricci curvature on graphs\nby Riikka Kangaslampi (Tamper
e University) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbst
ract\nCurvature is a fundamental notion in the study of smooth Riemannian
manifolds. This notion has been generalized in various ways from the smoot
h setting of manifolds to more general metric spaces. Several adaptations
of Ricci curvature such as Bakry-Emery curvature\, Ollivier-Ricci curvatur
e\, entropic curvature introduced by Erbar and Maas\, and Forman curvature
\, have emerged on graphs in recent years\, and there is very active resea
rch on these notions. These discrete Ricci curvature notions have also bee
n shown to play significant roles in various applied fields.\n\nIn this ta
lk I will focus on the Ollivier-Ricci curvature in the discrete setting of
combinatorial graphs. This curvature notion\, based on optimal transporta
tion\, is due to Yann Ollivier. I will introduce the Ollivier-Ricci curvat
ure and present some examples\, basic properties and applications. I will
also discuss a few results like the classification of cubic graphs with no
n-negative Ollivier-Ricci curvature and of cubic graphs with girth five th
at have zero curvature\, as well as the behaviour of the Ollivier-Ricci cu
rvature under graph products.\n\nThe talk is based on joint work with D. C
ushing\, S. Kamtue\, V. Lipiäinen\, S. Liu\, N. Peyerimhoff\, and G.W. St
agg.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Istvan Kiss (University of Sussex)
DTSTART;VALUE=DATE-TIME:20220526T140000Z
DTEND;VALUE=DATE-TIME:20220526T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/55
DESCRIPTION:Title: Epidemics on networks: from exact to mean-field models including resul
ts and challenges\nby Istvan Kiss (University of Sussex) as part of ME
SS (Mathematics Essex Seminar Series)\n\n\nAbstract\nThe contact structure
of a population plays an important role in the transmission of infectio
us diseases. Often individuals are represented by nodes and contacts betwe
en them by links. This gives rise to a network/graph which allows us to de
part from the homogeneous random mixing assumption implied by the widely u
sed population dynamic models based on ordinary differential equations. Wh
ile networks offer a great deal of flexibility to model heterogeneity in i
ndividuals and their contacts/mixing\, they lead to high-dimensional model
s even when the number of nodes is small. Such network-based models are di
fficult to analyse both analytically and numerically. In this talk\, I wil
l start from the exact formulation of an epidemic model on a network and s
how how the exact model can be reduced to various mean-field models (syste
ms with a few ordinary differential equations). In particular\, I will di
scuss the pairwise and edge-based compartmental models and will show how t
he network manifest itself in these models and what analytic insights can
be gained from these simplified approximations. I will briefly touch upon
the relationship between these and the exact model. Finally\, I will prese
nt a number of further extensions\, such as for non-Markovian epidemic dyn
amics and adaptive networks\, and discuss future challenges.\n\n[1] I Z K
iss\, J C Miller\, and P L Simon. Mathematics of Epidemics on Networks: fr
om exact to approximate models. Springer\, 2017.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esmaeel Asadi (Institute for Advanced Studies in Basic Science\, Z
anjan\, Iran)
DTSTART;VALUE=DATE-TIME:20220512T140000Z
DTEND;VALUE=DATE-TIME:20220512T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/56
DESCRIPTION:Title: geometry of integrable systems\; introduction by examples\nby Esma
eel Asadi (Institute for Advanced Studies in Basic Science\, Zanjan\, Iran
) as part of MESS (Mathematics Essex Seminar Series)\n\n\nAbstract\nIf a c
urve moves in a certain way In a geometric space\, what would be the evol
ution of its invariants? In this talk we focus on some curve flow in low d
imensional Euclidean space and see how it is related to evolution of its c
lassical curvature and torsion in the form of integrable PDEs and discuss
the possible extension of the idea behind some multi-components integrable
systems.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Abban (Loughborough University)
DTSTART;VALUE=DATE-TIME:20220609T140000Z
DTEND;VALUE=DATE-TIME:20220609T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/57
DESCRIPTION:Title: Fano varieties: their geometry\, classification\, and parametrisation<
/a>\nby Hamid Abban (Loughborough University) as part of MESS (Mathematics
Essex Seminar Series)\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EssexMaths/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theresa Smith (University of Bath)
DTSTART;VALUE=DATE-TIME:20220623T140000Z
DTEND;VALUE=DATE-TIME:20220623T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/58
DESCRIPTION:Title: https://essex-university.zoom.us/j/97080588123\nby Theresa Smith (
University of Bath) as part of MESS (Mathematics Essex Seminar Series)\n\n
\nAbstract\nIn this talk\, I will present ongoing research I am carrying o
ut following a productive Knowledge Transfer Partnership with Mayden\, a B
ath-based company that develops the most widely used electronic patient re
cord system in NHS psychological therapies services. The key statistical c
hallenge in this project is predicting the likelihood of multiple competin
g outcomes while incorporating new data on subjects as it becomes availabl
e so that these predictions can be updated dynamically throughout a course
of psychological therapy. I will discuss two existing paradigms for dynam
ic prediction: joint modelling and landmarking\, focusing on the trade-off
s in computational challenges and the statistical properties of the two ap
proaches. I will also discuss practical barriers to embedding these approa
ches within decision support tools in a patient records systems.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baha Tamimi (University of Essex)
DTSTART;VALUE=DATE-TIME:20220630T140000Z
DTEND;VALUE=DATE-TIME:20220630T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/59
DESCRIPTION:Title: The sandpile & Smith groups of certain classes of graphs\nby Baha
Tamimi (University of Essex) as part of MESS (Mathematics Essex Seminar Se
ries)\n\n\nAbstract\nThe Smith group and the sandpile group are graph inva
riants. It is common to calculate these groups algorithmically using the S
mith normal form. We show an alternative combinatorial approach using Tiet
ze transformation and apply it to calculate a subset of known graph famili
es like integral circulant graphs and walk regular graphs.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Duarte-Guerreiro (University of Essex)
DTSTART;VALUE=DATE-TIME:20221013T140000Z
DTEND;VALUE=DATE-TIME:20221013T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/60
DESCRIPTION:Title: Non-solidity of Uniruled Varieties\nby Tiago Duarte-Guerreiro (Uni
versity of Essex) as part of MESS (Mathematics Essex Seminar Series)\n\nLe
cture held in NTC.1.04.\n\nAbstract\nThe minimal model program (MMP) is a
far-reaching conjecture in birational geometry that says that any complex
algebraic variety is built up from 3 basic building blocks: Mori fibre spa
ces\, Calabi-Yau fibrations and Canonically polarised varieties. Although
the MMP is still conjectural\, in the seminal paper of Birkar\, Cascini\,
Hacon and Mckernan\, (BCHM)\, the authors prove\, among other important re
sults\, that varieties covered by rational curves (uniruled varieties) are
birational to Mori fibre spaces. In this talk we give a criterion to esta
blish when such a Mori fibre space is a strict fibration\, that is\, a Mor
i fibre space with strictly positive dimensional basis. Moreover\, there
are usually many different possible outcomes when applying the MMP to a un
iruled variety\, so it becomes natural to study their relations. If time a
llows\, I will explain how to obtain explicit birational maps between cert
ain Mori fibre spaces.\n\nThis is joint work with Livia Campo.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Hynd (Penn University)
DTSTART;VALUE=DATE-TIME:20221020T140000Z
DTEND;VALUE=DATE-TIME:20221020T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/61
DESCRIPTION:Title: The Blaschke–Lebesgue theorem revisited\nby Ryan Hynd (Penn Univ
ersity) as part of MESS (Mathematics Essex Seminar Series)\n\nLecture held
in STEM 3.1.\n\nAbstract\nA curve of constant width has the property that
any two parallel supporting lines are the same distance apart in all dire
ctions. It turns out that a circle encloses the most area and a Reuleaux
triangle encloses the least area among all curves of a given width. The la
tter fact was proved independently by Blaschke and Lebesgue. We will disc
uss this theorem\nand what is thought to be true for the analogous shapes
in three-dimensions.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sema Gunturkun (University of Essex)
DTSTART;VALUE=DATE-TIME:20221027T140000Z
DTEND;VALUE=DATE-TIME:20221027T150000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/62
DESCRIPTION:Title: Growth of the Hilbert function of ideals containing a regular sequence
\nby Sema Gunturkun (University of Essex) as part of MESS (Mathematics
Essex Seminar Series)\n\nLecture held in STEM 3.1.\n\nAbstract\nFamous Ma
caulay’s theorem describes the growth of Hilbert functions of homogeneou
s ideals in $K[x_1\,\\ldots\, x_n]$. Eisenbud\, Green and Harris conjectu
red a finer bound on the Hilbert function so that it associates with the s
tructure of the ideal such as the degrees of a regular sequence it contain
s. In this talk\, we discuss the current state of this conjecture\, and e
specially focus on the ideal containing a regular sequence of quadratic fo
rms.\n\nhttps://findyourway.essex.ac.uk/bcdc98e0-e3c3-11eb-b52e05a67b7792f
c/search/projects/23/60ef1a882031e800c230405d\n
LOCATION:https://researchseminars.org/talk/EssexMaths/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annalisa Calini (College of Charleston\, USA)
DTSTART;VALUE=DATE-TIME:20221103T150000Z
DTEND;VALUE=DATE-TIME:20221103T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/63
DESCRIPTION:Title: Knotted solutions of the Vortex Filament Equation and their stability
properties\nby Annalisa Calini (College of Charleston\, USA) as part o
f MESS (Mathematics Essex Seminar Series)\n\nLecture held in STEM 3.1.\n\n
Abstract\nThe Vortex Filament Equation (VFE) or binormal flow–a localize
d induction approximation of the Biot-Savart law–describes the self-indu
ced dynamics of a vortex filament in a 3-dimensional ideal fluid. Its conn
ection with the focusing cubic Nonlinear Schrödinger Equation (NLS) throu
gh the Hasimoto map allows the use of tools from soliton theory to constru
ct large classes of solutions. \n\nIn this first part of this talk I will
focus on the construction of a family of knotted vortex filaments coming
from finite-genus solutions of the NLS\, including torus and cable knots.
These solutions do not exhibit self-crossing during the VFE evolution\, th
us representing physically plausible models of vortex filaments. In the se
cond part\, I will discuss a framework for studying the stability of finit
e-genus solutions of the VFE and present several interesting examples.\n\n
The seminar presentation of Prof Calini at Essex is partially funded by Is
aac Newton Institute for Mathematical Sciences\, Cambridge.\n\nhttps://fin
dyourway.essex.ac.uk/bcdc98e0-e3c3-11eb-b52e-05a67b7792fc/search/projects/
23/60ef1a882031e800c230405d\n
LOCATION:https://researchseminars.org/talk/EssexMaths/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Poggi (Universitat Autònoma de Barcelona)
DTSTART;VALUE=DATE-TIME:20221110T150000Z
DTEND;VALUE=DATE-TIME:20221110T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/64
DESCRIPTION:Title: $L^p$-solvability of the Poisson problem and its applications to the r
egularity problem.\nby Bruno Poggi (Universitat Autònoma de Barcelona
) as part of MESS (Mathematics Essex Seminar Series)\n\nLecture held in ST
EM 3.1.\n\nAbstract\nWe introduce the concept of $L^p$-solvability of the
Poisson problem\n\\[\n\\left\\{\\begin{array}{ll}-\\operatorname{div}A\\n
abla w=H-\\operatorname{div} F\,&\\text{in }\\Omega\,\\\\w=0\,&\\text{on }
\\partial\\Omega\,\\end{array}\\right.\n\\]\nunder certain natural quantit
ative assumptions on $H$ and $F$\, with its corresponding new estimate (ne
w even for the Laplacian)\, and study several applications. By $L^p$ solva
bility\, we mean uniform bounds on the $L^p$ norm of the non-tangential ma
ximal function of $w$. An analogous concept is classical and central for t
he theory of boundary value problems for \\emph{homogeneous} second-order
elliptic PDEs. Our main application is towards the $L^p$ Dirichlet-regular
ity problem for elliptic operators $-\\operatorname{div} A\\nabla$ whose m
atrix $A$ satisfies the Dahlberg-Kenig-Pipher condition (this is\, roughly
speaking\, a Carleson measure condition on $|\\nabla A|^2\\operatorname{d
ist}(\\cdot\,\\partial\\Omega)$)\, in the geometric generality of bounded
Corkscrew domains with uniformly rectifiable boundaries. This solves an op
en problem from 2001. Other applications include new characterizations of
the $L^p$-solvability of the Dirichlet problem\, and a non-tangential maxi
mal function estimate for the gradient of the Green's function\, in Corksc
rew domains with Ahlfors-regular boundaries. This is joint work with Mihal
is Mourgoglou and Xavier Tolsa.\n\nhttps://findyourway.essex.ac.uk/bcdc98e
0-e3c3-11eb-b52e-05a67b7792fc/search/projects/23/60ef1a882031e800c230405d\
n
LOCATION:https://researchseminars.org/talk/EssexMaths/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Fairbairn (Birbeck University London)
DTSTART;VALUE=DATE-TIME:20221117T150000Z
DTEND;VALUE=DATE-TIME:20221117T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/65
DESCRIPTION:Title: Beauville Surfaces\, Structures and Groups\nby Ben Fairbairn (Birb
eck University London) as part of MESS (Mathematics Essex Seminar Series)\
n\nLecture held in STEM 3.1.\n\nAbstract\nVery roughly speaking\, a Beauvi
lle surface is a complex surface constructed by allowing a finite group G
act on the product of two compact Riemann surfaces. These have numerous ni
ce properties and are easier to study than most complex surfaces since the
entire construction can be internalised into the group which we call a Be
auville group. Numerous questions about constructing these and what proper
ties they can have been posed over the past twenty years or so. In this ta
lk we will discuss a handful of approaches to these objects that have been
taken.\n\nhttps://findyourway.essex.ac.uk/bcdc98e0-e3c3-11eb-b52e-05a67b7
792fc/search/projects/23/60ef1a882031e800c230405d\n
LOCATION:https://researchseminars.org/talk/EssexMaths/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jing Ping Wang (University of Kent)
DTSTART;VALUE=DATE-TIME:20221124T150000Z
DTEND;VALUE=DATE-TIME:20221124T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/66
DESCRIPTION:Title: POSTPONED: Quantisations of the Volterra hierarchy\nby Jing Ping W
ang (University of Kent) as part of MESS (Mathematics Essex Seminar Series
)\n\n\nAbstract\nTHIS TALK IS POSTPONED.\n\nIn this talk\, we’ll discuss
a recently emerged approach to the problem of quantisation based on the n
otion of quantisation ideals. We prove that the nonabelian Volterra togeth
er with the whole hierarchy of its symmetries admit a deformation quantisa
tion\, and that all odd-degree symmetries of the Volterra hierarchy admit
also a non-deformation quantisation. The quantisation problem for periodic
Volterra hierarchy will also be discussed. In particular\, we show that t
he Volterra system with period 3 admits a bi-quantum structure\, which can
be regarded as a quantum deformation of its classical bi-Hamiltonian stru
cture. This is a joint work with S. Carpentier and A.V. Mikhailov recently
published on Letters in Math. Phys.\n
LOCATION:https://researchseminars.org/talk/EssexMaths/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Camassa (University of North Carolina)
DTSTART;VALUE=DATE-TIME:20221201T150000Z
DTEND;VALUE=DATE-TIME:20221201T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/67
DESCRIPTION:Title: Fluid-boundary interaction: confinement effects\, stratification and t
ransport\nby Roberto Camassa (University of North Carolina) as part of
MESS (Mathematics Essex Seminar Series)\n\nLecture held in STEM 3.1.\n\nA
bstract\nArguably some of the most interesting phenomena in fluid dynamics
\, both\nfrom a mathematical and a physical perspective\, stem from the in
terplay\nbetween a fluid and its boundaries. This talk will present some e
xamples of how boundary effects lead to remarkable outcomes. Singularitie
s can form in finite time as a consequence of the continuum assumption whe
n material surfaces are in smooth contact with horizontal boundaries of a
fluid under gravity. For fluids with chemical solutes\, the presence of bo
undaries impermeable to diffusion adds further dynamics which can give ris
e to self-induced flows and the formation of coherent structures out of sc
attered assemblies of immersed bodies. These effects can be analytically a
nd numerically predicted by simple mathematical models and observed in “
simple” experimental setups.\n\n\nThe seminar presentation of Prof Camas
sa at Essex is partially funded by Isaac Newton Institute for Mathematical
Sciences\, Cambridge.\n\nhttps://findyourway.essex.ac.uk/bcdc98e0-e3c3-11
eb-b52e-05a67b7792fc/search/projects/23/60ef1a882031e800c230405d\n
LOCATION:https://researchseminars.org/talk/EssexMaths/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shirsho Mukherjee (University of Essex)
DTSTART;VALUE=DATE-TIME:20221208T150000Z
DTEND;VALUE=DATE-TIME:20221208T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/68
DESCRIPTION:Title: Regularity of quasilinear equations with Hormander vector fields of st
ep two\nby Shirsho Mukherjee (University of Essex) as part of MESS (Ma
thematics Essex Seminar Series)\n\nLecture held in STEM 3.1.\n\nAbstract\n
In this talk\, some recent results on the regularity theory of quasilinear
subelliptic equations shall be presented.\n\nThe main prototype of such e
quations is the $p$-Laplacian equation defined on vector fields which\, to
gether with their commutators\, span the tangent space at every point. I
shall illustrate the proof of weak solutions being locally $C^{1\,\\alpha}
$ for every \n$1 < p < \\infty$.\n\nThis is a joint work with Giovanna Cit
ti.\n\nhttps://findyourway.essex.ac.uk/bcdc98e0-e3c3-11eb-b52e-05a67b7792f
c/search/projects/23/60ef1a882031e800c230405d\n
LOCATION:https://researchseminars.org/talk/EssexMaths/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Argha Mondal (Sidho-Kanho-Birsha University\, India)
DTSTART;VALUE=DATE-TIME:20221215T150000Z
DTEND;VALUE=DATE-TIME:20221215T160000Z
DTSTAMP;VALUE=DATE-TIME:20221209T232059Z
UID:EssexMaths/69
DESCRIPTION:Title: The role of Mathematical pathways in modelling Computational Neuroscie
nces\nby Argha Mondal (Sidho-Kanho-Birsha University\, India) as part
of MESS (Mathematics Essex Seminar Series)\n\nInteractive livestream: http
s://essex-university.zoom.us/j/97080588123\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/EssexMaths/69/
URL:https://essex-university.zoom.us/j/97080588123
END:VEVENT
END:VCALENDAR