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:20260422T212553Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Stéphanie Portet (University of Manitoba) DTSTART:20201203T203000Z DTEND:20201203T213000Z DTSTAMP:20260422T212553Z 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:20210204T203000Z DTEND:20210204T213000Z DTSTAMP:20260422T212553Z 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:20220127T203000Z DTEND:20220127T213000Z DTSTAMP:20260422T212553Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Karen Meagher (University of Regina) DTSTART:20220310T203000Z DTEND:20220310T213000Z DTSTAMP:20260422T212553Z 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:20221124T203000Z DTEND:20221124T213000Z DTSTAMP:20260422T212553Z 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/ END:VEVENT BEGIN:VEVENT SUMMARY:Payman Eskandari (University of Winnipeg) DTSTART:20230126T203000Z DTEND:20230126T213000Z DTSTAMP:20260422T212553Z UID:PrairieMath/7 DESCRIPTION:Title: Periods in number theory and algebraic geometry\nby Payman Eskanda ri (University of Winnipeg) as part of Prairie mathematics colloquium\n\n\ nAbstract\nPeriods are numbers that arise as integrals of rational functio ns with coefficients in $\\mathbb{Q}$ over sets that are cut out by polyno mial inequalities with coefficients in $\\mathbb{Q}$. More conceptually\, periods are numbers that arise from the natural isomorphism between the si ngular and algebraic de Rham cohomologies of algebraic varieties (or more generally\, singular and de Rham realizations of motives) over $\\mathbb{Q }$.\n\nExamples of periods include algebraic numbers\, $\\pi$\, $\\log(2 )$ and other special values of the logarithm function\, and special value s of the Riemann zeta function (or more generally\, multiple zeta values). It is expected that every algebraic relation between periods should "come from geometry": this is the moral of Grothendieck's period conjecture\, a very deep and fascinating conjecture of Grothendieck that connects number theory with geometry.\n\nThe goal of this talk is to give an introduction to periods and Grothendieck's period conjecture. In the final part of the talk we will describe some recent related work (joint with K. Murty).\n LOCATION:https://researchseminars.org/talk/PrairieMath/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Kozdron (University of Regina) DTSTART:20230309T203000Z DTEND:20230309T213000Z DTSTAMP:20260422T212553Z UID:PrairieMath/8 DESCRIPTION:Title: A Quantum Martingale Convergence Theorem\nby Michael Kozdron (Univ ersity of Regina) as part of Prairie mathematics colloquium\n\n\nAbstract\ nIt is well-known in quantum information theory that a positive operator v alued measure (POVM) is the most general kind of quantum measurement. A qu antum probability is a normalised POVM\, namely a function on certain subs ets of a (locally compact and Hausdorff) sample space that satisfies the f ormal requirements for a probability and whose values are positive operato rs acting on a complex Hilbert space. A quantum random variable is an oper ator valued function which is measurable with respect to a quantum probabi lity.\n\nIn this talk\, we will discuss a quantum analogue of the classic Lebesgue dominated convergence theorem and use it to prove a quantum marti ngale convergence theorem (MCT). In contrast with the classical MCT\, the quantum MCT exhibits non-classical behaviour\; even though the limit of th e martingale exists and is unique\, it is not explicitly identifiable. For tunately\, a partial classification of the limit is possible through a stu dy of the space of all quantum random variables having quantum expectation zero. Based on joint work with Kyler Johnson. Note that this general aud ience talk will assume only a basic understanding of undergraduate probabi lity and graduate real analysis (i.e.\, Lebesgue integration).\n LOCATION:https://researchseminars.org/talk/PrairieMath/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Steven Rayan (University of Saskatchewan) DTSTART:20240118T203000Z DTEND:20240118T213000Z DTSTAMP:20260422T212553Z UID:PrairieMath/9 DESCRIPTION:Title: Moduli Spaces and Quantum Matter: From Materials to Pure Mathematics a nd Back\nby Steven Rayan (University of Saskatchewan) as part of Prair ie mathematics colloquium\n\n\nAbstract\nThe advent of topological materia ls\, a form of physical matter with unusual but useful properties\, has br ought with it unexpected new connections between pure mathematics on the o ne side and physics\, chemistry\, and material science on the other side. As the name suggests\, topology has played a significant role in understan ding 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 ma thematician in collaboration with a number of individuals from the physica l sciences over the last three years. This work sees geometry — in parti cular\, the complex algebraic geometry of Riemann surfaces and moduli spac es associated to them — being used to anticipate new models of quantum m atter. There will be lots of pictures.\n\nMeeting ID: 994 8428 6876\nPassc ode: 688175\n LOCATION:https://researchseminars.org/talk/PrairieMath/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Frankland (University of Regina) DTSTART:20241107T203000Z DTEND:20241107T213000Z DTSTAMP:20260422T212553Z UID:PrairieMath/10 DESCRIPTION:Title: Quillen Cohomology of Divided Power Algebras over an Operad\nby M artin Frankland (University of Regina) as part of Prairie mathematics coll oquium\n\n\nAbstract\nIn topology\, cohomology is an invariant we can assi gn to spaces. In algebra\, there are also cohomology theories for various algebraic structures\, such as group cohomology\, Lie algebra cohomology\, and André-Quillen cohomology of commutative rings. Quillen cohomology pr ovides a cohomology theory for any algebraic structure. It has been studie d notably for divided power algebras and restricted Lie algebras\, both of which are instances of divided power algebras over an operad: the commuta tive and Lie operad respectively. I will describe recent work with Ioannis Dokas and Sacha Ikonicoff generalizing this to other operads. My main goa l will be to introduce the three ingredients in the title.\n LOCATION:https://researchseminars.org/talk/PrairieMath/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Shonda Dueck (University of Winnipeg) DTSTART:20250116T203000Z DTEND:20250116T213000Z DTSTAMP:20260422T212553Z UID:PrairieMath/11 DESCRIPTION:Title: Cyclic partitions of complete and almost complete uniform hypergraphs \nby Shonda Dueck (University of Winnipeg) as part of Prairie mathemat ics colloquium\n\n\nAbstract\nPlease click this link to view the abstract: https://a886ca15-3a7f-4e36-808d-76866305dcab.filesusr.com/ugd/661845_f925 979eb1fc4d6b8cb01addc5834b25.pdf\n LOCATION:https://researchseminars.org/talk/PrairieMath/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Clay (University of Manitoba) DTSTART:20250306T203000Z DTEND:20250306T213000Z DTSTAMP:20260422T212553Z UID:PrairieMath/12 DESCRIPTION:Title: Orderable Groups and the L-space Conjecture\nby Adam Clay (Univer sity of Manitoba) as part of Prairie mathematics colloquium\n\n\nAbstract\ nSimilar to how the integers can be equipped with an ordering that is inva riant with respect to addition\, many groups can be equipped with an order ing that is invariant under the group operation. But aside from being a cu rious generalization of a standard algebraic structure\, what role do orde rable groups play in modern mathematics? In this talk\, I will introduce o rderable groups and answer this question by providing a brief overview of connections between orderable groups and areas of current research. The ma in focus\, however\, will be the L-space conjecture from low-dimensional t opology\, its connection with orderable groups\, and how this conjecture h as driven recent advancements in the field. In particular\, I will explain how purely group-theoretic theorems have inspired topological results\, a nd how topology might "give back" to group theory if the L-space conjectur e turns out to be true.\n LOCATION:https://researchseminars.org/talk/PrairieMath/12/ END:VEVENT END:VCALENDAR