BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shaun Fallat (University of Regina) DTSTART:20201105T203000Z DTEND:20201105T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/1 DESCRIPTION:Title: Recent Trends on the Inverse Eigenvalue Problem for Graphs\ nby Shaun Fallat (University of Regina) as part of Prairie mathematics col loquium\n\n\nAbstract\nGiven a simple graph $G=(V\,E)$ with $V = \\{ 1\,2\ , \\ldots\, n \\}$\, we associate a collection of real $n$-by-$n$ symmetri c matrices governed by $G$\, and defined as $S(G)$ where the off-diagonal entry in position $(i\,j)$ is nonzero iff $i$ and $j$ are adjacent.\n\nThe inverse 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 par ticular variant on the IEP-$G$ was born from the research of Parter and Wi ener concerning the eigenvalue of trees and evolved more recently with a c oncentration on related parameters such as: minimum rank\, maximum multipl icity\, minimum number of distinct eigenvalues\, and zero forcing numbers. An exciting aspect of this problem is the interplay with other areas of m athematics and applications. A novel avenue of research on so-called "stro ng properties" of matrices\, closely tied to the implicit function theorem \, provides algebraic conditions on a matrix with a certain spectral prope rty and graph that guarantee the existence of a matrix with the same spect ral property 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 th e work Colin de Verdière\, we will discuss some of these newly developed "strong properties" and present a number of interesting implications perta ining to the IEP-$G$.\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Stéphanie Portet (University of Manitoba) DTSTART:20201203T203000Z DTEND:20201203T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/2 DESCRIPTION:Title: Intracellular transport of intermediate filaments driven by ant agonistic motor proteins\nby Stéphanie Portet (University of Manitoba ) as part of Prairie mathematics colloquium\n\n\nAbstract\nIntermediate fi laments are one of the components of the cytoskeleton\; they are involved in cell mechanics\, signalling and migration. The organisation of intermed iate filaments in networks is the major determinant of their functions in cells. Their spatio-temporal organization in cells results from the interp lay between assembly/disassembly processes and different types of transpor t.\n\nFor instance\, intermediate filaments\, which are long elastic fiber s\, are transported in cells along microtubules\, another component of the cytoskeleton\, by antagonistic motor proteins. How elastic fibers are eff iciently transported by antagonistic motors is not well understood and is difficult to measure with current experimental techniques. Adapting the tu g-of-war paradigm for vesicle-like cargos\, a mathematical model is develo ped to describe the motion of an elastic fiber punctually bound to antagon istic motors. Combining stochastic and deterministic dynamical simulations and qualitative analysis\, we study the asymptotic behaviour of the model \, which defines the mode of transport of fibers [1\,2]. The effects of in itial conditions\, reflecting the intracellular context\, model parameters and functionals\, describing motors and fiber properties\, and noise\, ou tlining other intracellular processes\, are characterized.\n\nThis is work in collaboration with J. Dallon (BYU\, Provo\, Utah\, USA)\, C. Leduc and S. Etienne-Manneville (Institut Pasteur\, Paris\, France).\n\n[1] Dallon\ , J.\, Leduc\, C.\, Etienne-Manneville\, S.\, and Portet\, S. Stochastic m odeling reveals how motor protein and filament properties affect intermedi ate filament transport. J. Theor. Biol. 464: 132-148 (2019).\n\n[2] Portet \, S.\, Leduc\, C.\, Etienne-Manneville\, S.\, Dallon\, J. Deciphering the transport of elastic filaments by antagonistic motor proteins. Phys. Rev. E. 99: 042414 (2019).\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Duffy (University of Saskatchewan) DTSTART:20210204T203000Z DTEND:20210204T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/3 DESCRIPTION:Title: Oriented Graph Colouring - Questions and Answers (but mostly qu estions)\nby Chris Duffy (University of Saskatchewan) as part of Prair ie mathematics colloquium\n\n\nAbstract\nThe simplicity in the standard de finition of graph colouring belies an algebraic interpretation as a homomo rphism. This interpretation can be exploited to provide a definition of gr aph colouring for oriented graphs that\, in some sense\, respects the orie ntations of the arcs. In this talk we'll see how our intuition helps us an d hinders us when we explore well-trodden graph colouring territory for or iented 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://stable.researchseminars.org/talk/PrairieMath/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Kirkland (University of Manitoba) DTSTART:20220127T203000Z DTEND:20220127T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/4 DESCRIPTION:Title: State transfer for paths with weighted loops\nby Steve Kirk land (University of Manitoba) as part of Prairie mathematics colloquium\n\ n\nAbstract\nFaithful transmission of information is an important task in the area of quantum information processing. One approach to that task is t o use a network of coupled spins (which can be modelled as an undirected g raph) and to transfer a quantum state from one vertex to another. We can t hen consider the fidelity of transmission from a source vertex to a target vertex to measure the accuracy of the transmission. The last two decades have seen substantial growth in research on the topic of state transfer in spin networks.\n\nIn this talk\, we consider a spin network consisting of an unweighted path on $n$ vertices\, to which a loop of weight $w$ has be en added at each end vertex. Let $f(t)$ denote the fidelity of state trans fer from one end vertex to the other at time $t$\; it turns out that for a ny $t$\, $0 \\leq f(t) \\leq 1$\, and that $f(t)$ close to $1$ corresponds to high 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 made close to $1$ via suitable choices of $w$\, $n$ and $t$. Throughou t\, the results rely on a detailed analysis of the eigenvalues and eigenve ctors of the associated adjacency matrix.\n\nThis talk is based on joint w ork with Christopher van Bommel.\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Karen Meagher (University of Regina) DTSTART:20220310T203000Z DTEND:20220310T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/5 DESCRIPTION:Title: The Intersection Density of Permutation Groups\nby Karen Me agher (University of Regina) as part of Prairie mathematics colloquium\n\n \nAbstract\nTwo permutations are intersecting if they both map some $i$ to the same point\, equivalently\, permutations $\\sigma$ and $\\pi$ are int ersecting if and only if $\\pi^{-1}\\sigma$ has a fixed point. A set of pe rmutations is called intersecting if any two permutations in the set are i ntersecting. For any transitive group the stabilizer of a point is an inte rsecting set. The intersection density of a permutation group is th e 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 si ze. Such groups are said to have the Erdős-Ko-Rado property. \n\nO ne effective way to determine the intersection density of a group is build a graph so that the cocliques (or the independent sets) in the graph are exactly the intersecting sets in the group. This graph is called the de rangement graph for the group. The eigenvalues of these graphs can be found using the representation theory of the group and using tools from al gebraic graph theory these eigenvalues can be used to bound the size of an intersecting set.\n\nIn this talk I will show that large families of subg roups have the Erdős-Ko-Rado property. But I will also give examples of g roups that have a large intersection density\, and so are very far from ha ving this property. I will also give a general upper bound on the intersec tion density of a group and show some extremal examples.\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ebrahim Samei (University of Saskatchewan) DTSTART:20221124T203000Z DTEND:20221124T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/6 DESCRIPTION:Title: Hermitian groups are amenable\nby Ebrahim Samei (University of Saskatchewan) as part of Prairie mathematics colloquium\n\n\nAbstract\ nIn this talk\, we will first review the concept of inverse-closedness for a pair of algebras and its connection with an important property of group s known as being Hermitian (or symmetric). This property appears when one considers inverse-closedness for a particular pair of algebras associated to a group $G$. After recalling and reviewing some known facts\, we will a im to show how this concept relates to another important property of group s known as amenability. Our final goal is to give an affirmative answer to the long-standing conjecture that Hermitian groups are amenable. This sol ution is a based on a joint work with Matthew Wiersma (University of Winni peg).\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Payman Eskandari (University of Winnipeg) DTSTART:20230126T203000Z DTEND:20230126T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/7 DESCRIPTION:Title: Periods in number theory and algebraic geometry\nby Payman Eskandari (University of Winnipeg) as part of Prairie mathematics colloqui um\n\n\nAbstract\nPeriods are numbers that arise as integrals of rational functions with coefficients in $\\mathbb{Q}$ over sets that are cut out by polynomial inequalities with coefficients in $\\mathbb{Q}$. More conceptu ally\, periods are numbers that arise from the natural isomorphism between the singular and algebraic de Rham cohomologies of algebraic varieties (o r more generally\, singular and de Rham realizations of motives) over $\\m athbb{Q}$.\n\nExamples of periods include algebraic numbers\, $\\pi$\, $ \\log(2)$ and other special values of the logarithm function\, and specia l values of the Riemann zeta function (or more generally\, multiple zeta v alues). It is expected that every algebraic relation between periods shoul d "come from geometry": this is the moral of Grothendieck's period conject ure\, a very deep and fascinating conjecture of Grothendieck that connects number theory with geometry.\n\nThe goal of this talk is to give an intro duction to periods and Grothendieck's period conjecture. In the final part of the talk we will describe some recent related work (joint with K. Murt y).\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Kozdron (University of Regina) DTSTART:20230309T203000Z DTEND:20230309T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/8 DESCRIPTION:Title: A Quantum Martingale Convergence Theorem\nby Michael Kozdro n (University of Regina) as part of Prairie mathematics colloquium\n\n\nAb stract\nIt is well-known in quantum information theory that a positive ope rator valued measure (POVM) is the most general kind of quantum measuremen t. A quantum probability is a normalised POVM\, namely a function on certa in subsets of a (locally compact and Hausdorff) sample space that satisfie s the formal requirements for a probability and whose values are positive operators acting on a complex Hilbert space. A quantum random variable is an operator valued function which is measurable with respect to a quantum probability.\n\nIn this talk\, we will discuss a quantum analogue of the c lassic Lebesgue dominated convergence theorem and use it to prove a quantu m martingale convergence theorem (MCT). In contrast with the classical MCT \, the quantum MCT exhibits non-classical behaviour\; even though the limi t of the martingale exists and is unique\, it is not explicitly identifiab le. Fortunately\, a partial classification of the limit is possible throug h a study of the space of all quantum random variables having quantum expe ctation zero. Based on joint work with Kyler Johnson. Note that this gene ral audience talk will assume only a basic understanding of undergraduate probability and graduate real analysis (i.e.\, Lebesgue integration).\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Steven Rayan (University of Saskatchewan) DTSTART:20240118T203000Z DTEND:20240118T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/9 DESCRIPTION:Title: Moduli Spaces and Quantum Matter: From Materials to Pure Mathem atics and Back\nby Steven Rayan (University of Saskatchewan) as part o f Prairie mathematics colloquium\n\n\nAbstract\nThe advent of topological materials\, a form of physical matter with unusual but useful properties\, has brought with it unexpected new connections between pure mathematics o n the one side and physics\, chemistry\, and material science on the other side. As the name suggests\, topology has played a significant role in un derstanding and classifying these materials. In this talk\, I will offer a brief look at a vast extension to this story\, arising from my work as a pure mathematician in collaboration with a number of individuals from the physical sciences over the last three years. This work sees geometry — i n particular\, the complex algebraic geometry of Riemann surfaces and modu li spaces associated to them — being used to anticipate new models of qu antum matter. There will be lots of pictures.\n\nMeeting ID: 994 8428 6876 \nPasscode: 688175\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Frankland (University of Regina) DTSTART:20241107T203000Z DTEND:20241107T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/10 DESCRIPTION:Title: Quillen Cohomology of Divided Power Algebras over an Operad\nby Martin Frankland (University of Regina) as part of Prairie mathemati cs colloquium\n\n\nAbstract\nIn topology\, cohomology is an invariant we c an assign to spaces. In algebra\, there are also cohomology theories for v arious algebraic structures\, such as group cohomology\, Lie algebra cohom ology\, and André-Quillen cohomology of commutative rings. Quillen cohomo logy provides a cohomology theory for any algebraic structure. It has been studied notably for divided power algebras and restricted Lie algebras\, both of which are instances of divided power algebras over an operad: the commutative and Lie operad respectively. I will describe recent work with Ioannis Dokas and Sacha Ikonicoff generalizing this to other operads. My m ain goal will be to introduce the three ingredients in the title.\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Shonda Dueck (University of Winnipeg) DTSTART:20250116T203000Z DTEND:20250116T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/11 DESCRIPTION:Title: Cyclic partitions of complete and almost complete uniform hype rgraphs\nby Shonda Dueck (University of Winnipeg) as part of Prairie m athematics colloquium\n\n\nAbstract\nPlease click this link to view the ab stract: https://a886ca15-3a7f-4e36-808d-76866305dcab.filesusr.com/ugd/6618 45_f925979eb1fc4d6b8cb01addc5834b25.pdf\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Clay (University of Manitoba) DTSTART:20250306T203000Z DTEND:20250306T213000Z DTSTAMP:20260404T094319Z UID:PrairieMath/12 DESCRIPTION:Title: Orderable Groups and the L-space Conjecture\nby Adam Clay (University of Manitoba) as part of Prairie mathematics colloquium\n\n\nAb stract\nSimilar to how the integers can be equipped with an ordering that is invariant with respect to addition\, many groups can be equipped with a n ordering that is invariant under the group operation. But aside from bei ng a curious generalization of a standard algebraic structure\, what role do orderable groups play in modern mathematics? In this talk\, I will intr oduce orderable groups and answer this question by providing a brief overv iew of connections between orderable groups and areas of current research. The main focus\, however\, will be the L-space conjecture from low-dimens ional topology\, its connection with orderable groups\, and how this conje cture has driven recent advancements in the field. In particular\, I will explain how purely group-theoretic theorems have inspired topological resu lts\, and how topology might "give back" to group theory if the L-space co njecture turns out to be true.\n LOCATION:https://stable.researchseminars.org/talk/PrairieMath/12/ END:VEVENT END:VCALENDAR