Events
All upcoming and recent events from the past six months:
Title: A non-local reaction advection-diffusion model for self-interacting species
Speaker: Zongzhi Yue, Universiity of Victoria
Date and time:
01 Aug 2024,
11:00am -
12:00pm
Location: David Strong Building C128
Event type: Graduate dissertations
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Title: Development of a disease analytic model for estimating the hidden population using the stratified-Peterson estimator
Speaker: Siying Ma, University of Victoria
Date and time:
01 Aug 2024,
9:00am -
10:00am
Location: DTB A203
Event type: Graduate dissertations
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Title: Peaceful Colourings
Speaker: Bruce Reed, Academia Sinica
Date and time:
18 Jul 2024,
10:00am -
11:00am
Location: DSB C128
Event type: Discrete math seminar
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A proper conflict-free colouring of a graph is a (vertex-)colouring with no monochromatic edges such that for every nonisolated vertex v, the neighbourhood N(v) contains a vertex w coloured with a colour not appearing on N(v)-{w}. For a real number h, a colouring of a graph with no monochromatic edges is h-conflict-free if for every vertex v, N(v) contains at least min{deg(v), h} vertices coloured with a colour used only once in N(v). For a real number p, we define a p-peaceful colouring to be a colouring f with no monochromatic edges in which for every vertex v,
|{w in N(v) : there exists u in N(v)-{w} with f(u)=f(w)}| ≤ p.
We note that for a d-regular graph, a colouring is an h-conflict-free proper colouring precisely if it is a (d-h)-peaceful colouring. In contrast, if G is an irregular graph of maximum degree Delta then while a p-peaceful colouring and a (\Delta-p)-conflict-free colouring impose the same condition on maximum degree vertices, the peaceful colouring imposes weaker conditions on low degree vertices. We present some results on these three types of colourings. These are joint work with Chun-hung Liu.
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Title: Invariant conic optimization with basis-dependent cones: scaled diagonally dominant matrices and real *-algebra decomposition
Speaker: Khashayar Neshat Taherzadeh, University of Victoria
Date and time:
17 Jul 2024,
9:00am -
10:00am
Location: ECS Room 130
Event type: Graduate dissertations
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Title: IMAGINING UVic Math Camp for Grade 11-12 Girls
Date:
02 Jul
to
05 Jul 2024
Location: University of Victoria
Event type: Education and outreach
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Title: Counting X-free sets
Speaker: Ashna Wright, University of Victoria
Date and time:
13 Jun 2024,
2:30pm -
3:30pm
Location: DSB C108
Event type: Graduate dissertations
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Title: Star and monotone factorizations and Jucys-Murphy elements
Speaker: Amarpreet Rattan, Simon Fraser University
Date and time:
16 May 2024,
10:00am -
11:00am
Location: ECS 104
Event type: Discrete math seminar
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Abstract: For fixed n, consider the symmetric group S_n on the symbols 1,...,n and the set of *star* transpositions, the transpositions that contain the symbol n. A *star factorization* of a permutation b in S_n of length k is the writing of b as the product of k star transpositions. Goulden and Jackson (2009) showed that the number of such factorizations only depends on the conjugacy class of b and not on b itself, a remarkable fact given the special role the symbol n plays amongst star transpositions. We supply the first fully combinatorial proof of this fact that works for all lengths k, and our methods connect star factorizations to monotone factorizations. Star transpositions are connected to Jucys-Murphy elements, and we explain how our result can give expressions for the *transitive* image of certain symmetric functions evaluated at Jucys-Murphy elements.
This is joint work with Jesse Campion Loth (Heilbronn Institute and the University of Bristol).
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Title: Science Rendezvous
Date and time:
11 May 2024,
10:00am -
3:00pm
Location: UVic and Camosun Interurban
Event type: Education and outreach
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Title: Analytic approach to extremal combinatorics
Date and time:
07 May 2024,
10:00am -
11:00am
Location: DSB C118
Event type: Colloquia
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Title: Analytic approach to extremal combinatorics
Date and time:
07 May 2024,
10:00am -
11:00am
Location: DSB C118
Event type: Discrete math seminar
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Title:
Speaker: Mathew Lewis, University of Victoria
Date and time:
03 May 2024,
10:00am -
11:00am
Location: DSB C114 and Zoom
Event type: Graduate dissertations
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Title: The choice of prediction curve method and its effect on the estimated amount of DNA
Speaker: Morgan Magee, University of Victoria
Date and time:
22 Apr 2024,
12:30pm -
1:30pm
Location: David Strong Building Room C126
Event type: Graduate dissertations
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Title: On the Prediction Accuracy of Models Chosen by Constrained Minimum Criterion
Speaker: Xinning Liu, University of Victoria
Date and time:
18 Apr 2024,
4:00pm -
5:00pm
Location: via Zoom
Event type: Graduate dissertations
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Title: Twisting in Hamiltonian flows and prefect fluids
Speaker: Tarek El-Gindi, Duke University
Date and time:
17 Apr 2024,
2:30pm -
3:30pm
Location: DSB C126
Event type: Applied math seminar
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Abstract: We will discuss a recent result joint with In-Jee Jeong and Theo Drivas. We prove that twisting in Hamiltonian flows on annular domains, which can be quantified
by the differential winding of particles around the center of the domain, is stable to general
perturbations. In fact, we prove the all-time stability of the lifted dynamics in an L2
sense (though single particle paths are generically unstable). These stability facts are used to establish several results related to the long-time behavior of inviscid fluid flows.
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Title: A Bayesian Approach to Response Optimization on Data with Multistratum Structure
Speaker: Professor Po Yang, University of Manitoba
Date and time:
17 Apr 2024,
2:00pm -
3:00pm
Location: DSB C114
Event type: Statistics seminar
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Abstract: Response optimization is a process of identifying the input variable settings that optimize the response. Multistratum design arises naturally in industrial experiments due to the inconvenient and impractical completely randomization. Accounting for the model uncertainty, we apply the Bayesian model averaging method and predictive approach to investigate the optimization problem for data with multi-stratum structure. With the posterior probabilities of models as weights, we consider the weighted average of the predictive densities of the response over all potential models. The goal of the optimization is to identify the values of the factors that result in a maximum probability of a response in a given range. The method is illustrated with two examples.
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Title: Comparisons of Ramp Functions and Michaelis-Menten Functions in Biochemical Dynamical Systems
Speaker: Skye Dore-Hall, University of Victoria
Date and time:
12 Apr 2024,
9:00am -
10:00am
Location: Clearihue B021 and Zoom
Event type: Graduate dissertations
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Title: PIMS Data Science Seminar: Data thinning to avoid double dipping
Speaker: Lucy Gao, University of British Columbia
Date and time:
10 Apr 2024,
2:00pm -
3:00pm
Location: DTB A102 and Zoom
Event type: Statistics seminar
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Zoom link.
This is our 5th talk of the PIMS Data Science Seminar Series. PIMS requests all seminar participants to complete the demographics form online at https://ubc.ca1.qualtrics.com/jfe/form/SV_6QcNr2rQcIlQGyy
Abstract
"Double dipping" is the practice of using the same data to fit and validate a model. Problems typically arise when standard statistical procedures are applied in settings involving double dipping. To avoid the challenges surrounding double dipping, a natural approach is to fit a model on one dataset, and then validate the model on another independent dataset. When we only have access to one dataset, we typically accomplish this via sample splitting. Unfortunately, in some problems, sample splitting is unattractive or impossible. In this talk, we are motivated by unsupervised problems that arise in the analysis of single cell RNA sequencing data, where sample splitting does not allow us to avoid double dipping. We first propose Poisson thinning, which splits a single observation drawn from a Poisson distribution into two independent pseudo-observations. We show that Poisson count splitting allows us to avoid double dipping in unsupervised settings. We next generalize the Poisson thinning framework to a variety of distributions, and refer to this general framework as "data thinning". Data thinning is applicable far beyond the context of single-cell RNA sequencing data, and is particularly useful for problems where sample splitting is unattractive or impossible.
Speaker bio
Website Link: https://www.lucylgao.com/
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Title: Triangulating surfaces in Mathematics and in Computer Graphics
Speaker: Joel Hass , U.C. Davis
Date and time:
08 Apr 2024,
3:30pm -
4:30pm
Location: MacLaurin A144
Event type: Colloquia
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Title: On the prevalence of cycles and chaos in natural ecosystems
Speaker: Evan Johnson, Math and Stats, University of Alberta
Date and time:
08 Apr 2024,
3:00pm -
4:00pm
Location: Cornett A225 and Zoom
Event type: Math biology seminar
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https://uvic.zoom.us/j/89487222886
Ecological populations experience booms and busts, with abundances changing by
orders of magnitude within just a few short years. Some of these fluctuations may
be explained by predator-prey cycles or deterministic chaos, two phenomena that
hold immense practical and historical significance in the field of ecology. Here, I
estimate the prevalence of cycles and chaos, using classic time series models, new
tools from nonlinear systems analysis, and a giant database of ecological
time series. Previous assessments find a 6% incidence of cyclical patterns,
whereas my robust model-based procedure indicates that 8-25% of
populations are cyclical. Chaos appears to be rare (with a likely prevalence
of 0%), yet uncertainty remains high (0-18%). In an attempt to control false
positive rates, I devised a surrogate data hypothesis test; however, the test
suffers from low power, indicating that even exceptionally long time series
cannot be reliably classified. Through a sensitivity analysis, I show that high
noise levels, moderate observation errors, and weak density dependence
are the primary obstacles to detecting ecological chaos.
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Title: PIMS Data Science Seminar: Functional Nonlinear Learning
Speaker: Jiguo Cao, Simon Fraser University
Date and time:
05 Apr 2024,
2:00pm -
3:00pm
Location: DTB A102 and Zoom
Event type: Statistics seminar
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Zoom link.
This is our 6th talk of the PIMS Data Science Seminar Series. PIMS requests all seminar participants to complete the demographics form online at https://ubc.ca1.qualtrics.com/jfe/form/SV_6QcNr2rQcIlQGyy
Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual curves. The existing representation learning approaches in functional data analysis usually use linear mapping in parallel to those from multivariate analysis, e.g., functional principal component analysis (FPCA). However, functions, as infinite-dimensional objects, sometimes have nonlinear structures that cannot be uncovered by linear mapping. Linear methods will be more overwhelmed by multivariate functional data. For that matter, this paper proposes a functional nonlinear learning (FunNoL) method to sufficiently represent multivariate functional data in a lower-dimensional feature space. Furthermore, we merge a classification model for enriching the ability of representations in predicting curve labels. Hence, representations from FunNoL can be used for both curve reconstruction and classification. Additionally, we have endowed the proposed model with the ability to address the missing observation problem as well as to further denoise observations. The resulting representations are robust to observations that are locally disturbed by uncontrollable random noises. We apply the proposed FunNoL method to several real data sets and show that FunNoL can achieve better classifications than FPCA, especially in the multivariate functional data setting. Simulation studies have shown that FunNoL provides satisfactory curve classification and reconstruction regardless of data sparsity.
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Title: Cops and Robber on surfaces of constant curvature
Date and time:
04 Apr 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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In 2021, Mohar introduced the game of Cops and Robber on geodesic spaces. The game captures the behavior of the Cops and Robber game played on graphs and that of continuous pursuit-evasion games. Analogous to one of the main open problems for the Cops and Robber game on graphs, Mohar conjectured that the cop number of a geodesic surface of genus $g$ is at most $O(\sqrt{g})$. Surprisingly, this upper bound can be significantly improved on surfaces of constant curvature which will be the main focus of this talk.
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It turns out that the cop number of compact spherical and Euclidean surfaces is at most $2$. Even more surprisingly, the cop number of compact hyperbolic surfaces is also at most $2$, independently of their genus. We will also consider the strong cop number of these surfaces and present several generalizations to higher-dimensions.
Joint work with Bojan Mohar and Alexandra Wesolek.
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Title: Computable Gelfand duality (2 of 2)
Speaker: Chris Eagle, University of Victoria
Date and time:
03 Apr 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
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Abstract: One of the foundational results about C*-algebras is Gelfand's theorem establishing a duality between commutative unital C*-algebras and compact Hausdorff spaces. I will discuss the question of how effectively computable this duality is; specifically, is there an algorithm that takes as input a description of a commutative unital C*-algebra and produces as output a description of the spectrum of A? In the first talk I will provide all the necessary background from computability theory to be able to make this question precise, and also describe previous work on computable dualities. In the second talk I will outline a proof that the Gelfand duality is computable.
These talks are based on joint work with P. Burton, A. Fox, I. Goldbring, M. Harrison-Trainor, T. McNicholl, A. Melnikov, and T. Thewmorakot.
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Title: Stochastic path integrals: classical and new
Speaker: Yu-Ting Chen, University of Victoria
Date and time:
02 Apr 2024,
2:30pm -
3:30pm
Location: DSB C108
Event type: Probability and Dynamics seminar
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Title: Sidorenko-type inequalities for Trees
Speaker: Lina Simbaqueba, University of Victoria
Date and time:
28 Mar 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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Given two graphs H and G, the homomorphism density t(H,G) represents the likelihood that a random mapping from V(H) to V(G) is a homomorphism. Sidorenko Conjecture states that for any bipartite graph H, t(H,G) is greater or equal to t(K_2,G)^{e(H)}.
Introducing a binary relation H \geq T if and only if t(H,G)^{e(T)} \geq t(T,G)^{e(H)} for all graphs G, we establish a partial order on the set of non-empty connected graphs. Employing a technique by Kopparty and Rossman, which involves the use of entropy to define a linear program, we derive several necessary and sufficient conditions for two trees T, F satisfy T\geq F. Furthermore, we show how important results and open problems in extremal graph theory can be reframed using this binary relation.
Joint work with Natalie Behage, Gabriel Crudele, and Jonathan Noel.
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Title: Computable Gelfand duality (1 of 2)
Speaker: Chris Eagle, University of Victoria
Date and time:
27 Mar 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
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Abstract: One of the foundational results about C*-algebras is Gelfand's theorem establishing a duality between commutative unital C*-algebras and compact Hausdorff spaces. I will discuss the question of how effectively computable this duality is; specifically, is there an algorithm that takes as input a description of a commutative unital C*-algebra and produces as output a description of the spectrum of A? In the first talk I will provide all the necessary background from computability theory to be able to make this question precise, and also describe previous work on computable dualities. In the second talk I will outline a proof that the Gelfand duality is computable.
These talks are based on joint work with P. Burton, A. Fox, I. Goldbring, M. Harrison-Trainor, T. McNicholl, A. Melnikov, and T. Thewmorakot.
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Title: Lorentz gases on quasicrystals
Speaker: Agnieszka Zelerowicz, UC Riverside
Date and time:
26 Mar 2024,
2:30pm -
3:30pm
Location: DSB C114
Event type: Probability and Dynamics seminar
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Abstract: The Lorentz gas was originally introduced as a model for the movement of electrons in metals.
It consists of a massless point particle (electron) moving through Euclidean space bouncing off a given set of scatterers $\mathcal{S}$ (atoms of the metal) with elastic collisions at the boundaries $\partial \mathcal{S}$. If the set of scatterers is periodic in space, then the quotient system, which is compact, is known as the Sinai billiard.
There is a great body of work devoted to Sinai billiards and in many ways their dynamics is well understood.
In contrast, very little is known about the behavior of the Lorentz gases with aperiodic configurations of scatterers which model quasicrystals and other low-complexity aperiodic sets. This case is the focus of our joint work with Rodrigo Treviño.
We establish some dynamical properties which are common for the periodic and quasiperiodic billiard. We also point out some significant differences between the two. The novelty of our approach is the use of tiling spaces to obtain a compact model of the aperiodic Lorentz gas on the plane.
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Title: Estimating the population size of persons contending with homelessness using electronic health data
Speaker: Gracia Dong, University of Victoria/University of Toronto
Date and time:
25 Mar 2024,
3:00pm -
4:00pm
Location: MacLaurin D283
Event type: Math biology seminar
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Zoom link: https://uvic.zoom.us/j/89487222886.
The majority of attempts to enumerate the homeless population rely on point-in-time or shelter counts, which can be costly and inaccurate. As an alternative, we use electronic health data from the Vancouver Island Health Authority, British Columbia, Canada from 2013 to 2022 to identify adults contending with homelessness based on their self-reported housing status. We estimate the annual population size of this population using a flexible open-population capture-recapture model that takes into account 1) the age and gender structure of the population, including aging across detection occasions, 2) annual recruitment into the population, 3) behavioural-response, and 4) apparent survival in the population, including emigration and incorporating known deaths. With this model, we demonstrate how to perform model selection for the inclusion of covariates. We then compare our estimates of annual population size with reported point-in-time counts of homeless populations on Vancouver Island over the same time period, and find that using data extracts from electronic health records gives comparable estimates. We find similarly comparable results using only a subset of interaction data, when using only ER interactions, suggesting that even if cross-continuum data is not available, reasonable estimates of population size can still be found using our method.
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Title: Counting X-free sets
Speaker: Ashna Wright, University of Victoria
Date and time:
21 Mar 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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Title: Classifying Virtual Pfister Neighbours with Geometric Invariants
Speaker: Khai Quigley, University of Victoria
Date and time:
20 Mar 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
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Abstract: One of the few cases where the Chow groups of quadrics over an arbitrary field are known is that of excellent quadrics, including the special case of Pfister quadrics. The computation of the Chow groups of Pfister quadrics also gives partial information about the Chow groups of Pfister neighbours, the forms stably birational to Pfister forms. By understanding how the Chow groups behave under field extensions, we can obtain important information about the quadric over the ground field, and by extending to an algebraic closure, we obtain interesting numerical invariants of quadratic forms such as the J-invariant. It appears the J-invariant can be useful in determining whether a form is a virtual Pfister neighbour (a form which over some extension becomes a Pfister neighbour), and we are currently interested in just how much information can be obtained from it.
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Title: Moment Equations for Liquid, Vapor, and their Interface
Speaker: Henning Struchtrup, Mechanical Engineering, UVic
Date and time:
20 Mar 2024,
2:30pm -
3:30pm
Location: COR B145
Event type: Applied math seminar
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Title:
Speaker: Kesav Krishnan, University of Victoria
Date and time:
20 Mar 2024,
9:30am -
10:30am
Location: via Zoom registration required
Event type: PIMS lectures
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Title: Ergodic Theory on Coded Shifts
Speaker: Tamara Kucherenko, City College of New York
Date and time:
19 Mar 2024,
2:30pm -
3:30pm
Location: via Zoom
Event type: Probability and Dynamics seminar
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Zoom link.
Abstract: We discuss ergodic properties of coded shift spaces. A coded shift is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. It turns out that many well-known classes of shifts are coded including transitive subshifts of finite type, S-gap shifts, generalized gap shifts, transitive Sofic shifts, Beta shifts, and many more. We derive sufficient conditions for the uniqueness of measures of maximal entropy based on the partition of the coded shift into its sequential set (sequences that are concatenations of generating words) and its residual set (sequences added under the closure). Under these conditions we provide a simple explicit description of the measure. (Joint work with M. Schmoll and C. Wolf)
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Title: Environmental controls and phenology of future Arctic biogeochemistry
Speaker: Antoine Haddon, Earth and Ocean Sciences, University of Victoria
Date and time:
18 Mar 2024,
3:00pm -
4:00pm
Location: Cornett A225
Event type: Math biology seminar
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Join Zoom Meeting https://uvic.zoom.us/j/89487222886.
In the Arctic, specific microbial communities thrive in and around sea ice, leading to blooms, within, beneath, and at the edge of sea ice. The Arctic Ocean is strongly impacted by climate change, with important modifications of the sea ice environment set to continue during the 21st century, and as a result ice algae are poised to undergo significant changes. Conversely, these primary producers play a role in biogeochemical cycles and the Arctic climate. They produce sulfur compounds, such as dimethylsulfide (DMS) which once emitted to the atmosphere is an aerosol precursor, thereby impacting cloud formation. To examine the future of sea ice algae and the production of DMS at the Arctic scale, a regional ocean and sea ice biogeochemical model has been developed. The complexity of such models raises the issue of analyzing model simulations and understanding the impact of modeling choices. In this talk, I will present diagnostics that help to understand model output, both for the analysis of future projections but also to guide model development. To explore the climate-ocean interactions in the Arctic, diagnostics have been developed that allow to link environmental conditions to the growth and phenology of ice algae as well as the production of DMS. These diagnostics also reveal how the mathematical representation of biogeochemical processes impacts model projections.
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Title: PIMS Data Science Seminar - Representation Learning in Large-scale, Heterogeneous Single-cell Genomics
Speaker: Dr. Lin Zhang, Simon Fraser University
Date and time:
15 Mar 2024,
2:00pm -
3:00pm
Location: Cornett B107 and Zoom
Event type: Statistics seminar
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Zoom link: https://uvic.zoom.us/j/84724365947?pwd=OTRzYml3a29oeTJkNW5ucjhUWmxpdz09
This is our 4th talk of the PIMS Data Science Seminar Series. PIMS requests all seminar participants to complete the demographics form online at https://ubc.ca1.qualtrics.com/jfe/form/SV_6QcNr2rQcIlQGyy
Abstract: Single-cell omics data play a pivotal role in identifying cell-to-cell heterogeneity, understanding cell differentiation, unveiling cell population structures, and ultimately deciphering disease pathogenesis. Due to inherent high-dimensionality, sparsity, noise, and high correlation of single cell data, machine learning (ML) models, known for its assumption-free flexibility, scalability, and predictive power, have surged in analyzing single cell data to address these challenges. In this talk, I will present some of our recent work on ML-based approaches to accurately and efficiently encode single-cell gene expressions and chromatin accessibility. Our proposed method OCAT, One Cell At A Time, is a ML-based method that sparsely encodes single-cell gene expressions to integrate data from heterogeneous sources without highly variable gene selection or explicit batch effect correction (Wang et al., Genome Biology, 2022). We have demonstrated that OCAT efficiently integrates multiple heterogeneous scRNA-seq datasets and achieves the state-of-the-art performance in cell type clustering, especially in challenging scenarios of non-overlapping cell types. In addition, OCAT can efficaciously facilitate a variety of downstream analyses, such as differential gene analysis, trajectory inference, pseudo time inference and cell type inference. OCAT has proven its efficiency and accuracy in characterizing the transcriptomic difference between healthy and diseased kidney samples (McEvoy et al., Nature Communications, 2022). We have further developed OCAT2 that maps multiple complementary single-cell omics to the same domain through multi-modal diffusion mapping. We have demonstrated its accuracy and high computational efficiency on integrating real multi-omics datasets.
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Title:
Speaker: Nina Kamcev, University of Zagreb
Date and time:
14 Mar 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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Title: Crystallization of C*-algebras with almost periodic time evolution. Part 3 of 3
Speaker: Marcelo Laca, University of Victoria
Date and time:
13 Mar 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
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Abstract: Given an almost periodic C*-algebraic dynamical system (A,\sigma) we define a new C*-algebra, the crystal of A, whose states parametrize the ground states of A, and which, in several classes of examples, has the same K-theory as A. This addresses a question of Connes about whether a quantum system can be cooled down until it becomes quasi-classical without losing its main equilibrium and topological features. Our work generalizes the two main classes of motivating examples: equilibrium states of Toeplitz-Pimsner algebras of correspondences (from work with Neshveyev) and of Toeplitz algebras of ax+b monoids, (from work with Raeburn and with Cuntz and Deninger) for which the K-theory was computed by Cuntz, Echterhoff, and Li. This is joint work with Sergey Neshveyev and Makoto Yamashita at Oslo.
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Title: Predictive modelling, Anomaly Detection, and Empirical Extraction of Variation Patterns within Longitudinal Data
Speaker: Shuai You, University of Victoria
Date and time:
13 Mar 2024,
2:30pm -
3:30pm
Location: via Zoom
Event type: Graduate dissertations
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Title: On the Gaussian asymptotics of the Stochastic Heat Equation and Kardar-Parisi-Zhang equation for spatial dimensions d>=3
Speaker: Te-Chun Wang , University of Victoria
Date and time:
12 Mar 2024,
2:30pm -
3:30pm
Location: DSB C114
Event type: Probability and Dynamics seminar
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Abstract: In this talk, I will introduce my recent work on the asymptotic behaviors of the stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation for spatial dimensions d >== 3. The former describes the dynamics of non-equilibrium growth processes arising in statistical physics, and the latter is connected with the directed polymer model, which describes the evolution of a hydrophilic polymer chain wafting in water. As an application, the asymptotic structures of the partition function and the free energy of the continuous directed polymer will be clarified.
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Title: Evolution of selfish sex chromosomes and their suppressors
Speaker: Steve Perlman, Biology, University of Victoria
Date and time:
11 Mar 2024,
3:00pm -
4:00pm
Location: Cornett A225
Event type: Math biology seminar
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Selfish genes break the rules of Mendelian inheritance in order to increase in frequency, often at the expense of the fitness of the organism. Many selfish genes hijack transmission during meiosis, and among the most striking examples are selfish X chromosomes that destroy sperm or pollen that carry a Y-chromosome, resulting in highly female-biased sex ratios. Left unchecked, selfish sex chromosomes can drive populations to extinction and a major question has been to understand the forces that enable their persistence, including the evolution of genes that can suppress them. In this talk, I will discuss experimental and theoretical approaches that aim to understand the evolution and persistence of a selfish X chromosome that we recently discovered in a common woodland fly, Drosophila testacea, along with a gene on an autosome (i.e a chromosome that is not a sex chromosome) that can suppress it.
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Title: Conflict-free hypergraph matchings and generalized Ramsey numbers
Speaker: Emily Heath, Iowa State University
Date and time:
07 Mar 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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Title: Crystallization of C*-algebras with almost periodic time evolution. Part 2
Speaker: Marcelo Laca, Universiity of Victoria
Date and time:
06 Mar 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
Read full description
Abstract: Given an almost periodic C*-algebraic dynamical system (A,\sigma) we define a new C*-algebra, the crystal of A, whose states parametrize the ground states of A, and which, in several classes of examples, has the same K-theory as A. This addresses a question of Connes about whether a quantum system can be cooled down until it becomes quasi-classical without losing its main equilibrium and topological features. Our work generalizes the two main classes of motivating examples: equilibrium states of Toeplitz-Pimsner algebras of correspondences (from work with Neshveyev) and of Toeplitz algebras of ax+b monoids, (from work with Raeburn and with Cuntz and Deninger) for which the K-theory was computed by Cuntz, Echterhoff, and Li. This is joint work with Sergey Neshveyev and Makoto Yamashita at Oslo.
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Title: Coupled Opinion-Disease Dynamics in YT and BC Interior
Speaker: Mijanur Rahman, UBC Okanagan
Date and time:
06 Mar 2024,
2:30pm -
3:30pm
Location: COR B145
Event type: Applied math seminar
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Title: Local weighted optimizations and open problems
Speaker: Benoit Corsini, Eindhoven
Date and time:
05 Mar 2024,
2:30pm -
3:30pm
Location: via Zoom
Event type: Probability and Dynamics seminar
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Zoom link.
Abstract: In this talk, I will present a recent work in which two co-authors and myself studied the behaviour of a local algorithm optimizing the weight of a graph. More precisely, the process starts with a given subgraph H of the complete graph with uniform weights and a maximal weight W, and inductively replaces a subgraph of H and of weight less than W by the minimum spanning tree on the corresponding set of vertices. Our main result shows that there is a sharp threshold for W regarding the asymptotic behaviour of this algorithm (i.e. with high probability): if W is less than 1, it is impossible to reach the global minimum spanning tree, whereas it is possible when W is larger than 1. Since this work introduces a new type of local algorithm, I will also present some related open problems. In particular, our results prove when such algorithms can reach the global minimum spanning tree and it is then only natural to ask how fast they can do so when possible. The answer to this question actually relates to efficiently packing sets of uniforms into a special type of partition and leads to a surprisingly difficult open question.
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Title: Intraguild Predation in homogeneous and heterogeneous landscapes
Speaker: Silas Poloni Lyra, Math and Stats, University of Victoria
Date and time:
04 Mar 2024,
3:00pm -
4:00pm
Location: Cornett A225
Event type: Math biology seminar
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Intraguild predation (IGP) consists of two (or more) consumers of the same shared resource exhibiting a predator-prey relation among themselves, and is a very present phenomena in terrestrial, freshwater and marine ecological systems. Theoretical works show that IGP allows for coexistence between two consumers of the same guild, as long as IG prey is a more effective consumer than IG predator, revealing an important mechanism for consumer coexistence in food chains. Here we explore biological invasions forming IGP communities, by either introducing IG prey or IG predator to established (single) Consumer-Resource populations in homogeneous and heterogeneous landscapes. We use reaction-diffusion equations as our modeling framework, and explore them through numerical simulations and homogenization techniques. In homogeneous landscapes, we find that asymptotic spreading speeds are linearly determinate and also that the formation of traveling wave solutions and dynamical stabilization regimes are possible. On heterogeneous landscapes, we find that coexistence regimes in highly heterogeneous landscapes can occur regardless of IG-Prey being the least effective consumer, or be hindered even when IG-Prey remains as the dominant competitor, depending on habitat preferences of each of the species involved. We provide some conclusions of the work and venues of future research.
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Title: PIMS Network-Wide Colloquium Series - Complex dynamics: the real story
Speaker: Sarah Koch, University of Michigan
Date and time:
29 Feb 2024,
1:30pm -
2:30pm
Location: via Zoom Registration required
Event type: PIMS lectures
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Abstract:
We will introduce the research area of complex dynamics by studying the family of (complex) quadratic polynomials, $z->z^2+c$. Historically, mathematicians first studied the dynamics of {\em real} quadratic polynomials and then moved to the complex realm. Recently, there has been a resurgence of mathematical activity surrounding real quadratic polynomials. We will explore some well known features and some rather new features of real polynomials in contrast with those enjoyed by their complex counterparts.
Speaker Biography:
Sarah Koch is a an Arthur F. Thurnau Professor in the Department of Mathematics at the University of Michigan. Her research incorporates topology, algebraic geometry, complex analysis, and Teichmueller theory to better understand complex dynamical systems (in one and several variables) and their associated dynamical moduli spaces from both analytic and algebraic points of view.
Click here to Register for the Series.
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Title: Oriented Colouring Graphs of Bounded Euler Genus
Speaker: Alexander Clow, SFU
Date and time:
29 Feb 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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Abstract: In this talk we consider the oriented colouring problem for graphs with bounded Euler genus. That is we consider the smallest $k$ such that all oriented graphs embeddable on surfaces of Euler genus at most $g$ necessarily have an oriented homomorphism to a graph of order $k$. For convenience given a fixed $g$ and $k$, we let $\chi_o(g) = k$. We will discuss our proofs that $\Omega((\frac{g^2}{\log{g}})^{\frac{1}{3}}) \leq \chi_o(g) \leq (1+o(1))g^{6400}$, which improves the prior upper bound of order $2^{O(g^{\frac{1}{2}+o(1)})}$ and lower bound of order $\Omega(\sqrt{g})$, as well as exploring how our bounds might be improved in future work.
Joint work with Peter Bradshaw (University of Illinois Urbana Champaign), and Jingwei Xu (University of Illinois Urbana Champaign).
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Title: Crystallization of C*-algebras with almost periodic time evolution
Speaker: Marcelo Laca, University of Victoria
Date and time:
28 Feb 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
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Abstract: Given an almost periodic C*-algebraic dynamical system (A,\sigma) we define a new C*-algebra, the crystal of A, whose states parametrize the ground states of A, and which, in several classes of examples, has the same K-theory as A. This addresses a question of Connes about whether a quantum system can be cooled down until it becomes quasi-classical without losing its main equilibrium and topological features. Our work generalizes the two main classes of motivating examples: equilibrium states of Toeplitz-Pimsner algebras of correspondences (from work with Neshveyev) and of Toeplitz algebras of ax+b monoids, (from work with Raeburn and with Cuntz and Deninger) for which the K-theory was computed by Cuntz, Echterhoff, and Li. This is joint work with Sergey Neshveyev and Makoto Yamashita at Oslo.
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Title: Estimating the effect of contact tracing during the early stage of an epidemic
Speaker: Manting Wang, University of Victoria
Date and time:
28 Feb 2024,
2:30pm -
3:30pm
Location: COR B145
Event type: Applied math seminar
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Abstract: The epidemic curve is generally exponential during the early stage of an epidemic, presenting a challenge in identifying parameters of mathematical models that incorporate multiple control measures. This presents a major hurdle in disentangling and evaluating the effectiveness of contact tracing and other non-pharmaceutical public health interventions (NPIs) separately. In this presentation, we show how to use a novel contact tracing model and a simulation study to determine the dataset required for such an assessment. Our results show that the daily counts of new cases, cases diagnosed via contact tracing, and symptom onsets are necessary for this evaluation. We apply our method to the early stage of the Covid-19 pandemic in Ontario, Canada.
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Title: Random optimization problems at fixed temperatures
Speaker: Partha Dey, University of Illinois at Urbana-Champaign
Date and time:
27 Feb 2024,
2:30pm -
3:30pm
Location: via Zoom
Event type: Probability and Dynamics seminar
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Zoom link.
Abstract: We consider a class of disordered mean-field combinatorial optimization problems, focusing on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a general distribution. We prove Central Limit Theorems for the log-partition function, the weight of a typical configuration, and the Gibbs average in both quenched and annealed forms. We also derive quenched Poisson convergence for the size of the intersection of two independent samples, yielding replica symmetry of the model. Applications cover popular models from the literature, such as the Minimal Matching Problem, Traveling Salesman Problem, and Minimal Spanning Tree Problem, on a sequence of deterministic and random dense block graphs of increasing size. Joint work with Grigory Terlov.
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Title: Application of Bayesian Hierarchical Models for Acoustic Telemetry Data
Speaker: Inesh Munaweera, Math and Stats, University of Alberta
Date and time:
26 Feb 2024,
3:00pm -
4:00pm
Location: Cornett A225
Event type: Math biology seminar
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Bayesian hierarchical models have gained popularity for analyzing complex ecological data gathered through contemporary animal tracking technologies, including acoustic telemetry. Their widespread use is attributed to several advantages such as remarkable flexibility, the capacity to integrate prior knowledge, and enhanced precision. Acoustic telemetry systems are increasingly employed to investigate fish movement patterns, habitat utilization, and demographic parameter estimation. Nonetheless, the data produced by omnidirectional acoustic telemetry studies are intricate, characterized by multiple sources of variability. In this presentation, we explore several applications of Bayesian hierarchical modeling for acoustic telemetry data, focusing on estimating individual-level Walleye movement paths in Lake Winnipeg and examining survival probability variations of Arctic Char in the Cambridge Bay area. Additionally, we confront the practical challenges encountered in modeling such data and underscore the benefits of the Bayesian approach compared to traditional methods.
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Title: Pseudoku: A Sudoku Adjacency Algebra and Fractional Completion Threshold
Speaker: Kate Nimegeers, University of Victoria
Date and time:
26 Feb 2024,
10:30am -
11:30am
Location: DSB C124
Event type: Graduate dissertations
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Title: PIMS Data Science Seminar: Functional spherical autocorrelation: robust autocorrelation estimation of a functional time series
Speaker: Chi-Kuang Yeh, University of Waterloo
Date and time:
23 Feb 2024,
2:00pm -
3:00pm
Location: Cornett B107 and Zoom
Event type: Statistics seminar
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Zoom link.
PIMS requests all seminar participants to complete the demographics form online at https://ubc.ca1.qualtrics.com/jfe/form/SV_6QcNr2rQcIlQGyy
Abstract:
Measuring the serial dependence across time is critical in model identification and diagnosis in time series (TS) analysis. In classic TS analysis, the autocorrelation function is perhaps the most widely used method to examine the temporal relationship of the scalar or vector-valued observations. In functional TS (FTS), which refers to TS of functional data, their dependence is best summarised by an autocovariance operator. Evaluating the size and information contained in such an object can be difficult. Existing methods are relatively constrained and unable to capture certain characteristics contained in the FTS objects, such as the "direction" of dependence. We develop a new method to address this problem by projecting lagged pairs unit sphere and computing the angle between them, which we refer to as spherical autocorrelation. We establish the asymptotic properties of the empirical spherical autocorrelation, and we study its use in an application to European electricity data.
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Title: Frontiers in Mathematical Modeling: Celebrating Roderick Edwards' Contributions
Date:
17 Feb
to
18 Feb 2024
Location: Clearihue A127 and Zoom
Event type: Conferences and workshops
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In recognition of Rod Edwards' remarkable contributions to the field of Mathematical Modeling, we are inviting Rod's current and former students, postdocs, close collaborators, friends and colleagues to attend this event, scheduled to take place on campus on February 17th and 18th, 2024.
See the Program for more details
.
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Title: Broadcast Independence and Broadcast Packing in Various Subclasses of Trees
Speaker: Kiara McDonald, University of Victoria
Date and time:
15 Feb 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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Title: Morita equivalence of C*-correspondences (Part 2)
Speaker: Tyler Schulz, University of Victoria
Date and time:
14 Feb 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
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Abstract: "(Strong) Morita equivalence of C*-algebras was introduced by M. Rieffel as a generalization of Morita equivalence of rings, and is an extremely useful tool in studying K-theory, ideals and representations of C*-algebras. It was generalized by Combes ('84) to 'Morita equivalence of C*-algebras with a group action' (i.e. equivariant Morita equivalence). One of Combes results is that, if C*-dynamical systems are Morita equivalent, then their (full/reduced) crossed-product C*-algebras are Morita equivalent.
In this talk, I will introduce another generalization to 'Morita equivalence of C*-correspondences.' I show that if two C*-correspondences are Morita equivalent, then the Toeplitz algebras are Morita equivalent. This will start with some background on C*-correspondences and Toeplitz algebras, a proof-sketch of the main result, and some examples."
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Title: Reproductive value, prevalence, and perturbation theory of Perron vectors
Speaker: Eric Foxall, University of British Columbia Okanagan
Date and time:
14 Feb 2024,
2:30pm -
3:30pm
Location: COR B145
Event type: Applied math seminar
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Title: Some uses of ordered representations in finite-population exchangeable ancestry models
Speaker: Eric Foxall, UBC Okanagan
Date and time:
13 Feb 2024,
2:30pm -
3:30pm
Location: DSB C114
Event type: Probability and Dynamics seminar
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Title:
Speaker: Virgelot Virgile, University of Victoria
Date and time:
13 Feb 2024,
8:30am -
9:30am
Location: via Zoom
Event type: Graduate dissertations
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Title: A retrospective modelling analysis on the effects of control measures on SARS-CoV-2 transmission in Canada
Speaker: Tanya Philippsen, Math and Stats, University of Victoria
Date and time:
12 Feb 2024,
3:00pm -
4:00pm
Location: Cornett A225
Event type: Math biology seminar
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Zoom link.
We consider the SARS-CoV-2 pandemic, between March 2020 and February 2021, in three Canadian regions: Greater Vancouver, Greater Toronto, and Calgary. This period was dominated by the wild-type strain of SARS-CoV-2 and occurred prior to widespread vaccination roll-out. To assess the effectiveness of age-specific control measures on viral transmission, we construct a Susceptible-Exposed-Infectious-Recovered (SEIR) deterministic model with two age groups: youth (0-19 years), and adults (20+ years). We fit this model to SARS-CoV-2 case data over sequential time frames that capture the changes in public health control measures in each region. The age-specific control parameters of the fitted model are then adjusted to simulate alternative policy scenarios and assess their relative potential effectiveness in reducing the Fall/Winter epidemic peaks.
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Title: Clique number of Paley graphs and Paley-like graphs
Speaker: Kyle Yip, UBC
Date and time:
08 Feb 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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Abstract: Let q=1 mod 4 be a prime power and let F_q be the finite field of q elements. The Paley graph of order q is the graph with vertex set F_q, such that two vertices are adjacent if and only if their difference is a square in F_q. Paley graphs play an important role in many branches of combinatorics and number theory. Among many exciting questions related to Paley graphs, estimating their clique number is of importance. In this talk, I will report recent progress on the lower bounds and upper bounds on the clique number of Paley graphs and Paley-like graphs. Joint work with Seoyoung Kim, Jozsef Solymosi, and Semin Yoo.
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Title: Morita equivalence of C*-correspondences
Speaker: Tyler Schulz, University of Victoria
Date and time:
07 Feb 2024,
3:00pm -
4:00pm
Location: CLE A221
Event type: Operator theory seminar
Read full description
Abstract: "(Strong) Morita equivalence of C*-algebras was introduced by M. Rieffel as a generalization of Morita equivalence of rings, and is an extremely useful tool in studying K-theory, ideals and representations of C*-algebras. It was generalized by Combes ('84) to 'Morita equivalence of C*-algebras with a group action' (i.e. equivariant Morita equivalence). One of Combes results is that, if C*-dynamical systems are Morita equivalent, then their (full/reduced) crossed-product C*-algebras are Morita equivalent.
In this talk, I will introduce another generalization to 'Morita equivalence of C*-correspondences.' I show that if two C*-correspondences are Morita equivalent, then the Toeplitz algebras are Morita equivalent. This will start with some background on C*-correspondences and Toeplitz algebras, a proof-sketch of the main result, and some examples."
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Title: Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations
Speaker: Wojciech Ozanski, Florida State University
Date and time:
07 Feb 2024,
2:30pm -
3:30pm
Location: Zoom
Event type: Applied math seminar
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Abstract: We will discuss local well-posedness and ill-posedness results of some active scalar equations, including 2D incompressible Euler equations and the SQG equation. We will discuss how one can obtain instantaneous growth of solutions using a perturbation of a steady initial data as well as making use of unboundedness of the Riesz transform in $L^\infty$. We will then discuss the first result of an instantaneous gap loss of Sobolev regularity for 2D Euler. Namely, we will describe a construction of initial vorticity for the 2D Euler equations that belongs to the Sobolev space $H^\beta$, $\beta \in (0,1)$ which gives rise to a unique global-in-time solution that instantaneously leaves not only $H^\beta$, but also $H^{\beta'}$ for every $\beta' >(2-\beta )\beta /(2-\beta^2)$. This is joint work with Diego Cordoba and Luis Martinez-Zoroa.
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Title: Understanding the lifting phenomena (exporting our understanding from weak models of computation to strong models) and the underlying pseudo-random properties
Speaker: Sajin Koroth, UVic Computer Science
Date and time:
06 Feb 2024,
2:30pm -
3:30pm
Location: DSB C114
Event type: Probability and Dynamics seminar
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Title: Spatial transcriptomics and Spatial Statistics as Tools to Study Anti-Tumour Immunity in High Grade Serous Ovarian Cancer
Speaker: Shreena Kalaria, University of Victoria
Date and time:
05 Feb 2024,
3:00pm -
4:00pm
Location: Cornett A225
Event type: Math biology seminar
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Zoom link.
Areas in which B cells, T cells and macrophages assemble in close spatial proximity to each other, known as lympho-myeloid aggregates (LMAs), are prognostic for patients with High Grade Serous Ovarian Cancer (HGSC), yet there is still much to be discovered about their vital role in anti-tumour immunity. This includes quantitative descriptors of their cellular makeup; the specifics of the interactions and collaborations within these communities; and the immunomodulatory and immunostimulatory factors that promote and prevent their formation. We are investigating spatial distributions of the immune cells that comprise LMAs, their gene expression profiles, and their receptor (ie. T-Cell receptor - TCR, and B-Cell receptor - BCR) sequences via modification of the 10X genomics Visium technology for this purpose. We are identifying LMAs, their subtypes, and the specific role these subtypes pose in anti-tumour immunity using kernel density analysis, clustering, and spatial point process statistics. We are also leveraging our data to identify pairs of collaborating T and B cells. Specifically, we used (i) cross-K functions and simulation envelopes to evaluate spatial dependence, and (ii) number of pixels shared to flag putative sites of direct contact between B and T cells. Overall, we aim to understand how location, phenotype and antigen specificity of tumor-infiltrating T-Cells and B-Cells contribute to antitumor immunity. This information is essential for understanding the clinical benefits of immune cells and LMAs, and maximizing their functionality for therapeutic purposes.
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Title:
Date and time:
01 Feb 2024,
10:00am -
11:00am
Location: COR A128
Event type: Discrete math seminar
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Since suggested by Tur\'an in 1941, determining the Tur\'an density of hypergraphs has been a notoriously difficult problem at the center of extremal combinatorics.
Subsequently, several natural variants of this problem have been suggested, most prominently the uniform Tur\'an density by Erd\H{o}s and S\'os and the codegree Tur\'an density by Mubayi and Zhao.
Roughly speaking, the Tur\'an density is the threshold of the edge density above which large hypergraphs are guaranteed to contain a copy of a fixed hypergraph~$F$.
Similarly, the uniform Tur\'an density and the codegree Tur\'an density are the thresholds of the local density and the minimum codegree, respectively, above which large hypergraphs are guaranteed to contain a copy of~$F$.
In this talk, we will discuss recent results which determine several variants of the Tur\'an density in new instances and make progress towards a problem of Erd\H{o}s and S\'os.
Further, we will present our recent result with Piga which states that there are hypergraphs with arbitrarily small codegree Tur\'an density.
This is in contrast to the behaviour of the classical Tur\'an density and the uniform Tur\'an density due to results by Erd\H{o}s and by Reiher, R\"odl, and Schacht, respectively.
Based on joint works with Chen, Conlon, Piga, and Sales.
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Title: Dimension groups and dynamical systems (Part 2 of 2)
Speaker: Ian Putnam, University of Victoria
Date and time:
31 Jan 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
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Abstract: I will start with a short review of dimension groups (no background needed) and show how, in the case of a minimal action of the group of integers on a Cantor set, how they arise in a natural way (helped, in part, by the associated crossed product C*-algebra). This further leads to a complete model for such systems. In the second talk, I will discuss how these ideas can be extended, in a surprising way, to minimal actions of the group Z^2. This is joint work with Thierry Giordano (Ottawa) and Christian Skau (Oslo).
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Title: Nonuniqueness phenomena in discontinuous dynamical systems and their regularizations
Speaker: Rod Edwards, University of Victoria
Date and time:
31 Jan 2024,
2:30pm -
3:30pm
Location: COR B145
Event type: Applied math seminar
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Abstract:
In a recent article by Guglielmi and Hairer (SIADS 2015), an analysis in the $\varepsilon\to 0$ limit was proposed of regularized discontinuous ODEs in codimension-2 switching domains (intersections of discontinuity surfaces). This was obtained by studying a certain 2-dimensional system describing the so-called hidden dynamics. In particular, the existence of a unique limit solution was not proved in all cases, a few of which were labeled as ambiguous, and it was not clear whether or not the ambiguity could be resolved. We now show that it cannot be resolved in general. We show that three types of non-uniqueness or ambiguity can occur.
Firstly, we show that the limit solution can depend on the form of the regularization function.
Secondly, we show that behaviour of the hidden dynamics in the structurally ambiguous cases can depend on parameters, with bifurcations between different macroscopic outcomes. Thus the structure does not directly determine the behaviour.
Finally, we investigate the extreme sensitivity of solutions to initial conditions or parameters in the transition from codimension-2 domains to codimension-3 when there is a limit cycle in the hidden dynamics.
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Title: Subshifts with very low word complexity
Speaker: Ronnie Pavlov, University of Denver
Date and time:
30 Jan 2024,
2:30pm -
3:30pm
Location: via Zoom
Event type: Probability and Dynamics seminar
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Zoom link.
Abstract: The word complexity function p(n) of a subshift X measures the number of n-letter words appearing in sequences in X, and X is said to have linear complexity if p(n)/n is bounded. It's been known since work of Ferenczi that linear word complexity highly constrains the dynamical behavior of a subshift. In recent work with Darren Creutz, we show that if X is a transitive subshift with limsup p(n)/n < 3/2, then X is measure-theoretically isomorphic to a compact abelian group rotation. On the other hand, limsup p(n)/n = 3/2 can occur even for X measurably weak mixing. Our proofs rely on a substitutive/S-adic decomposition for such subshifts. I'll give some background/history on linear complexity, discuss our results, and will describe several ways in which 3/2 turns out to be a key threshold (for limsup p(n)/n) for several different types of dynamical behavior.
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Title: Modeling species-rich ecosystems to understand community dynamics and structures emerging from individual plant interactions
Speaker: Julia Schmid, University of Alberta
Date and time:
29 Jan 2024,
3:00pm -
4:00pm
Location: Cornett A225
Event type: Math biology seminar
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Title: PIMS Network-wide Colloquium: Hamilton-Jacobi equations on the Wasserstein space on graphs
Speaker: Wilfrid Gangbo, UCLA
Date and time:
25 Jan 2024,
1:30pm -
2:30pm
Location: via Zoom registration required
Event type: PIMS lectures
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Description:
We consider metric tensors on undirected weighted graphs G, which allows us to treat P(G), the set of probability vectors on G, as a length space. On defines a divergence operator div_\mu(G) for mu in P(G), in such a way that we can use control vectors m to define paths s:[0,T] \to P(G), satisfying the system of ODEs: d\sigma/dt + div_G(m) + \hbar div_\sigma(\nabla_G log \sigma)=0. These paths serve as characteristics for Hamilton-Jacobi equations involving graph-individual noise operators. We propose a well posedness theory on P(G). (This talk is based on a joint work with C. Mou and A. Swiech)
Other Information:
Time:
All network wide colloquia take place at 1:30pm Pacific Time with a few exceptions.
Registration:
Participants register once on Zoom and can attend any of the Colloquium talks. Please remember to download the calendar information to save the dates on your calendar. PIMS will resend the confirmation from Zoom prior to the event date.
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Title: Correspondence Packing Planar Graphs
Speaker: Evelyne Smith-Roberge, Georgia Tech
Date and time:
25 Jan 2024,
10:00am -
11:00am
Location: COR A128 and Zoom
Event type: Discrete math seminar
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Evelyne will be giving her talk remotely (on Zoom). Local participants are still encouraged to come to COR A128 to view it on the projector.
Abstract: Suppose a graph G has list chromatic number k. It is easy to see that if L is a (k+1)-list assignment for G, then G admits two L-colourings f and g where f(v) =/= g(v) for every vertex v in the graph. But what if we want still more disjoint L-colourings? In this talk, I will discuss recent progress towards determining the list packing number of various classes of planar graphs: that is, the smallest number k such that if L is a k-list assignment for an arbitrary graph G in the class under study, then L can be decomposed into k disjoint L-colourings. All results I will discuss also hold in the correspondence colouring framework. Joint work with Daniel Cranston.
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Title: Dimension groups and dynamical systems (Part 2 of 2)
Speaker: Ian Putnam, University of Victoria
Date and time:
24 Jan 2024,
3:30pm -
4:30pm
Location: CLE A221
Event type: Operator theory seminar
Read full description
Abstract: I will start with a short review of dimension groups (no background needed) and show how, in the case of a minimal action of the group of integers on a Cantor set, how they arise in a natural way (helped, in part, by the associated crossed product C*-algebra). This further leads to a complete model for such systems. In the second talk, I will discuss how these ideas can be extended, in a surprising way, to minimal actions of the group Z^2. This is joint work with Thierry Giordano (Ottawa) and Christian Skau (Oslo).
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Title: Minimal spanning arborescence
Speaker: Gourab Ray, University of Victoria
Date and time:
23 Jan 2024,
2:30pm -
3:30pm
Location: DSB C114
Event type: Probability and Dynamics seminar
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Abstract: I will talk about the `minimal spanning arborescence', a directed version of the Minimal spanning tree. I will explain how this naturally leads to a new type of stochastic process which we call `loop contracting random walk'. I will show how this can be analyzed in the setting of trees. I will finish with some simulations and open questions. Joint work with Arnab Sen.
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Title: The outsized influence of the average in environmental research and management
Speaker: Gerald Singh, Environmental Studies, UVic
Date and time:
22 Jan 2024,
3:00pm -
4:00pm
Location: Cornett A225 and Zoom
Event type: Math biology seminar
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Few statistical measures receive as much attention (implicitly or explicitly) as the arithmetic mean. The history for this particular measure is rooted in the historic development of quantitative science and the personalities that influenced it. Today, environmental measures, predictions, and evaluations of environmental and sustainable development interventions and policy are routinely done on mean responses, even when the "average" may not be the best way to understand a system or inform a decision. This talk will be a broad survey of ecological, evolutionary, and sustainable development contexts where measuring the "average" may mislead more than enlighten, and will serve as an exploration and an invitation to openly question and consider alternatives to the kinds of technical measures we take for granted when doing environmental research.
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