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SUMMARY:Shaun Fallat (University of Regina)
DTSTART;VALUE=DATE-TIME:20201105T203000Z
DTEND;VALUE=DATE-TIME:20201105T213000Z
DTSTAMP;VALUE=DATE-TIME:20221209T122813Z
UID:PrairieMath/1
DESCRIPTION:Title: Recent Trends on the Inverse Eigenvalue Problem for Graphs\nby Sha
un Fallat (University of Regina) as part of Prairie mathematics colloquium
\n\n\nAbstract\nGiven a simple graph $G=(V\,E)$ with $V = \\{ 1\,2\, \\ldo
ts\, n \\}$\, we associate a collection of real $n$-by-$n$ symmetric matri
ces governed by $G$\, and defined as $S(G)$ where the off-diagonal entry i
n position $(i\,j)$ is nonzero iff $i$ and $j$ are adjacent.\n\nThe invers
e eigenvalue problem for $G$ (IEP-$G$) asks to determine if a given multi-
set of real numbers is the spectrum of a matrix in $S(G)$. This particular
variant on the IEP-$G$ was born from the research of Parter and Wiener co
ncerning the eigenvalue of trees and evolved more recently with a concentr
ation on related parameters such as: minimum rank\, maximum multiplicity\,
minimum number of distinct eigenvalues\, and zero forcing numbers. An exc
iting aspect of this problem is the interplay with other areas of mathemat
ics and applications. A novel avenue of research on so-called "strong prop
erties" of matrices\, closely tied to the implicit function theorem\, prov
ides algebraic conditions on a matrix with a certain spectral property and
graph that guarantee the existence of a matrix with the same spectral pro
perty for a family of related graphs.\n\nIn this lecture\, we will review
some of the history and motivation of the IEP-$G$. Building\, on the work
Colin de Verdière\, we will discuss some of these newly developed "strong
properties" and present a number of interesting implications pertaining t
o the IEP-$G$.\n
LOCATION:https://researchseminars.org/talk/PrairieMath/1/
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BEGIN:VEVENT
SUMMARY:Stéphanie Portet (University of Manitoba)
DTSTART;VALUE=DATE-TIME:20201203T203000Z
DTEND;VALUE=DATE-TIME:20201203T213000Z
DTSTAMP;VALUE=DATE-TIME:20221209T122813Z
UID:PrairieMath/2
DESCRIPTION:Title: Intracellular transport of intermediate filaments driven by antagonist
ic motor proteins\nby Stéphanie Portet (University of Manitoba) as pa
rt of Prairie mathematics colloquium\n\n\nAbstract\nIntermediate filaments
are one of the components of the cytoskeleton\; they are involved in cell
mechanics\, signalling and migration. The organisation of intermediate fi
laments in networks is the major determinant of their functions in cells.
Their spatio-temporal organization in cells results from the interplay bet
ween assembly/disassembly processes and different types of transport.\n\nF
or instance\, intermediate filaments\, which are long elastic fibers\, are
transported in cells along microtubules\, another component of the cytosk
eleton\, by antagonistic motor proteins. How elastic fibers are efficientl
y transported by antagonistic motors is not well understood and is difficu
lt to measure with current experimental techniques. Adapting the tug-of-wa
r paradigm for vesicle-like cargos\, a mathematical model is developed to
describe the motion of an elastic fiber punctually bound to antagonistic m
otors. Combining stochastic and deterministic dynamical simulations and qu
alitative analysis\, we study the asymptotic behaviour of the model\, whic
h defines the mode of transport of fibers [1\,2]. The effects of initial c
onditions\, reflecting the intracellular context\, model parameters and fu
nctionals\, describing motors and fiber properties\, and noise\, outlining
other intracellular processes\, are characterized.\n\nThis is work in col
laboration with J. Dallon (BYU\, Provo\, Utah\, USA)\, C. Leduc and S. Eti
enne-Manneville (Institut Pasteur\, Paris\, France).\n\n[1] Dallon\, J.\,
Leduc\, C.\, Etienne-Manneville\, S.\, and Portet\, S. Stochastic modeling
reveals how motor protein and filament properties affect intermediate fil
ament transport. J. Theor. Biol. 464: 132-148 (2019).\n\n[2] Portet\, S.\,
Leduc\, C.\, Etienne-Manneville\, S.\, Dallon\, J. Deciphering the transp
ort of elastic filaments by antagonistic motor proteins. Phys. Rev. E. 99:
042414 (2019).\n
LOCATION:https://researchseminars.org/talk/PrairieMath/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Duffy (University of Saskatchewan)
DTSTART;VALUE=DATE-TIME:20210204T203000Z
DTEND;VALUE=DATE-TIME:20210204T213000Z
DTSTAMP;VALUE=DATE-TIME:20221209T122813Z
UID:PrairieMath/3
DESCRIPTION:Title: Oriented Graph Colouring - Questions and Answers (but mostly questions
)\nby Chris Duffy (University of Saskatchewan) as part of Prairie math
ematics colloquium\n\n\nAbstract\nThe simplicity in the standard definitio
n of graph colouring belies an algebraic interpretation as a homomorphism.
This interpretation can be exploited to provide a definition of graph col
ouring for oriented graphs that\, in some sense\, respects the orientation
s of the arcs. In this talk we'll see how our intuition helps us and hinde
rs us when we explore well-trodden graph colouring territory for oriented
graph colouring. In particular\, we'll see how oriented versions of Brooks
' Theorem\, the Four-Colour Theorem and Chromatic Polynomials give rise to
unexpected results when recast in the context of oriented graphs.\n
LOCATION:https://researchseminars.org/talk/PrairieMath/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Kirkland (University of Manitoba)
DTSTART;VALUE=DATE-TIME:20220127T203000Z
DTEND;VALUE=DATE-TIME:20220127T213000Z
DTSTAMP;VALUE=DATE-TIME:20221209T122813Z
UID:PrairieMath/4
DESCRIPTION:Title: State transfer for paths with weighted loops\nby Steve Kirkland (U
niversity of Manitoba) as part of Prairie mathematics colloquium\n\n\nAbst
ract\nFaithful transmission of information is an important task in the are
a of quantum information processing. One approach to that task is to use a
network of coupled spins (which can be modelled as an undirected graph) a
nd to transfer a quantum state from one vertex to another. We can then con
sider the fidelity of transmission from a source vertex to a target vertex
to measure the accuracy of the transmission. The last two decades have se
en substantial growth in research on the topic of state transfer in spin n
etworks.\n\nIn this talk\, we consider a spin network consisting of an unw
eighted path on $n$ vertices\, to which a loop of weight $w$ has been adde
d at each end vertex. Let $f(t)$ denote the fidelity of state transfer fro
m one end vertex to the other at time $t$\; it turns out that for any $t$\
, $0 \\leq f(t) \\leq 1$\, and that $f(t)$ close to $1$ corresponds to hig
h accuracy of transmission\, while $f(t)$ close to $0$ corresponds to poor
accuracy. We give upper and lower bounds on $f(t)$ in terms of $w$\, $n$
and $t$\; further\, given $a > 0$ we discuss the values of $t$ for which $
f(t) > 1-a$. In particular\, the results show that the fidelity can be mad
e close to $1$ via suitable choices of $w$\, $n$ and $t$. Throughout\, the
results rely on a detailed analysis of the eigenvalues and eigenvectors o
f the associated adjacency matrix.\n\nThis talk is based on joint work wit
h Christopher van Bommel.\n
LOCATION:https://researchseminars.org/talk/PrairieMath/4/
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BEGIN:VEVENT
SUMMARY:Karen Meagher (University of Regina)
DTSTART;VALUE=DATE-TIME:20220310T203000Z
DTEND;VALUE=DATE-TIME:20220310T213000Z
DTSTAMP;VALUE=DATE-TIME:20221209T122813Z
UID:PrairieMath/5
DESCRIPTION:Title: The Intersection Density of Permutation Groups\nby Karen Meagher (
University of Regina) as part of Prairie mathematics colloquium\n\n\nAbstr
act\nTwo permutations are intersecting if they both map some $i$ to the sa
me point\, equivalently\, permutations $\\sigma$ and $\\pi$ are intersecti
ng if and only if $\\pi^{-1}\\sigma$ has a fixed point. A set of permutati
ons is called intersecting if any two permutations in the set are intersec
ting. For any transitive group the stabilizer of a point is an intersectin
g set. The **intersection density** of a permutation group is the ratio
of the size of the largest intersecting set in the group\, to the size of
the stabilizer of a point. If the intersection density of a group is 1\,
then the stabilizer of a point is an intersecting set of maximum size. Suc
h groups are said to have the **Erdős-Ko-Rado property**. \n\nOne effe
ctive way to determine the intersection density of a group is build a grap
h so that the cocliques (or the independent sets) in the graph are exactly
the intersecting sets in the group. This graph is called the **derangeme
nt graph** for the group. The eigenvalues of these graphs can be found u
sing the representation theory of the group and using tools from algebraic
graph theory these eigenvalues can be used to bound the size of an inters
ecting set.\n\nIn this talk I will show that large families of subgroups h
ave the Erdős-Ko-Rado property. But I will also give examples of groups t
hat have a large intersection density\, and so are very far from having th
is property. I will also give a general upper bound on the intersection de
nsity of a group and show some extremal examples.\n
LOCATION:https://researchseminars.org/talk/PrairieMath/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ebrahim Samei (University of Saskatchewan)
DTSTART;VALUE=DATE-TIME:20221124T203000Z
DTEND;VALUE=DATE-TIME:20221124T213000Z
DTSTAMP;VALUE=DATE-TIME:20221209T122813Z
UID:PrairieMath/6
DESCRIPTION:Title: Hermitian groups are amenable\nby Ebrahim Samei (University of Sas
katchewan) as part of Prairie mathematics colloquium\n\n\nAbstract\nIn thi
s talk\, we will first review the concept of inverse-closedness for a pair
of algebras and its connection with an important property of groups known
as being Hermitian (or symmetric). This property appears when one conside
rs inverse-closedness for a particular pair of algebras associated to a gr
oup $G$. After recalling and reviewing some known facts\, we will aim to s
how how this concept relates to another important property of groups known
as amenability. Our final goal is to give an affirmative answer to the lo
ng-standing conjecture that Hermitian groups are amenable. This solution i
s a based on a joint work with Matthew Wiersma (University of Winnipeg).\n
LOCATION:https://researchseminars.org/talk/PrairieMath/6/
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