We thank PIMS for their support which makes this seminar series possible.
Speaker:
Time: 9 September, 2025 2:30-3:20 pm
Location: TBA
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Speaker:
Time: 16 September, 2025 2:30-3:20 pm
Location: TBA
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Speaker:
Time: 23 September, 2025 2:30-3:20 pm
Location: TBA
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Speaker: Romain Panis (Lyon)
Time: 30 September, 2025 10:30-11:30 am (NOTE DIFFERENT TIME!)
Location: https://uvic.zoom.us/j/82117115633?pwd=T18dWUILT2zrhpDhsmMxJdbVkxLpW3.1
Title: A random walk approach to high-dimensional critical phenomena
Abstract: One of the main goals of statistical mechanics is to understand critical phenomena of lattice models. This can be achieved by computing the so-called critical exponents, which govern algebraic scaling near or at the critical point. This task is generally impossible due to the intricate interplay between the specific features of the models and the geometry of the graphs on which they are defined. A striking observation was made in the 20th century: above the upper critical dimension d_c, the geometry becomes inessential and critical exponents adopt their mean-field values (as on Cayley trees or complete graphs).
Classical approaches—renormalization group, differential inequalities with reflection positivity, and the lace expansion—are powerful yet model-specific and technically heavy. We revisit the study of the mean-field regime and introduce a unified, probabilistic framework that applies across perturbative settings, including weakly self-avoiding walk (d>4), spread-out Bernoulli percolation (d>6), and one- and two-component spin models (d>4).
Based on ongoing works with Hugo Duminil-Copin, Aman Markar, and Gordon Slade.
Speaker: Mathew Penrose (Bath, UK)
Time: 7 October, 2025 10:30 -11:30 am
Location: https://uvic.zoom.us/j/82117115633?pwd=T18dWUILT2zrhpDhsmMxJdbVkxLpW3.1
Title: Coverage and connectivity in stochastic geometry
Abstract: Consider a random uniform sample of size $n$ over a bounded
region $A$ in $R^d$, $d \geq 2$, having a smooth boundary.
The coverage threshold $T_n$ is the smallest $r$ such that the union $Z$
of Euclidean balls of radius $r$ centred on the sample points
covers $A$. The connectivity threshold $K_n$ is twice the smallest
$r$ required for $Z$ to be connected. These thresholds are random variables
determined by the sample, and are of interest, for example, in wireless
communications, set estimation, and topological data analysis.
We discuss recent results on the large-$n$ limiting distributions of $T_n$
and $K_n$. When $A$ has unit volume, with $v$ denoting the volume of the
unit ball in $R^d$ and $|dA|$ the perimiter of $A$, these take the form of
weak convergence of $ n v T_n^d - (2-2/d) \log n - a_d \log (\log n) $ to
a Gumbel-type random variable with cumulative distribution function
$$
F(x) = \exp (-b_d e^{-x} - c_d |dA| e^{-x/2}),
$$
for suitable constants $a_d, c_d$ with $b_2 =1$, $b_d =0 $ for $d>2$. The corresponding result for $K_n$ takes the same form with different constants $a_d, c_d$.
If time permits, we may also discuss extensions and related results
concerning (i) Other domains $A$ such as polytopes or manifolds;
(ii) coverage by balls of random radii;
(iii) strong laws
of large numbers for $T_n$ and $K_n$ for non-uniform random samples of points.
Some of the work mentioned here is joint work with Xiaochuan Yang and Frankie Higgs.
Speaker: Luca Michael Makowiec (U Leipzig)
Time: 14 October, 2025 10:30 am (NOTE DIFFERENT TIME!)
Location: https://uvic.zoom.us/j/82117115633?pwd=T18dWUILT2zrhpDhsmMxJdbVkxLpW3.1
Title: Random Spanning Trees in Random Environment
Abstract: We will introduce Random Spanning Trees in Random Environment (RSTRE), a disordered system on spanning trees that interpolates between the Uniform Spanning Tree (UST) and Minimum Spanning Tree (MST) measures. Our primary goal is to study how local and global observables of the RSTRE depend on the inverse temperature beta. Of particular interest is the diameter of a (typical) spanning tree, as it is the first step towards establishing convergence to a non-trivial scaling limit. Furthermore, for the RSTRE on the complete graph with uniform disorder, we discuss a sharp transition of the local limit of the RSTRE to either the UST or MST local limit. This stands in contrast to our conjectured smooth transition of the diameter when beta is inside the so-called intermediate regime.
Speaker:
Time: 21 October, 2025 2:30-3:20 pm
Location: TBA
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Speaker: Frederik R. Klausen (Princeton)
Time: 28 October, 2025 2:30-3:20 pm
Location: https://uvic.zoom.us/j/82117115633?pwd=T18dWUILT2zrhpDhsmMxJdbVkxLpW3.1
Meeting ID: 821 1711 5633
Password: 469174
Title: Title: Phase transitions of graphical representations of the Ising model
Abstract: Much of the recent rigorous progress on the classical Ising model was driven by new detailed understanding of its stochastic geometric representations.
Motivated by the problem of establishing exponential decay of truncated correlations of the supercritical Ising model in any dimension,Duminil-Copin posed the question in 2016 of determining the (percolative) phase transition of the single random current.
Using that the loop O(1) model is the uniform even graph of the random cluster model, we prove polynomial lower bounds for path probabilities (and infinite expectation of cluster sizes of 0) for both the single random current and loop O(1) model corresponding to any supercritical Ising model on the hypercubic lattice. The method partly extends to all positive integers q, where the analogue of the loop O(1) model is the q-flow model.
In this talk, I will introduce graphical representations of the Potts and Ising model and their many couplings followed by a discussion of new results whose surprising proof takes inspiration from the toric code in quantum theory.
Based on : https://link.springer.com/article/10.1007/s00220-025-05297-3 and https://arxiv.org/abs/2506.10765
Speaker: Ratul Biswas (NITMB)
Time: 4 November, 2025 2:30-3:20 pm
Location: TBA
Title:
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Speaker: Lina Li
Time: 11 November, 2025 2:30-3:20 pm
Location: https://uvic.zoom.us/j/82117115633?pwd=T18dWUILT2zrhpDhsmMxJdbVkxLpW3.1
Meeting ID: 821 1711 5633
Password: 469174
Title:
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Speaker: Caelan Atamanchuk
Time: 18 November, 2025 2:30-3:20 pm
Location: https://uvic.zoom.us/j/82117115633?pwd=T18dWUILT2zrhpDhsmMxJdbVkxLpW3.1
Meeting ID: 821 1711 5633
Password: 469174
Title - The largest common subtree of two random trees
Abstract - Given two trees, what is the size and structure of their largest common shared subtree? This question has been a growing topic of interest in the probability/combinatorics community in recent years, with the problem having been discussed for a few different models of random trees. In this talk, we will discuss the case where the two trees are independent Bienaymé-Galton-Watson trees with finite-variance offspring distributions, conditioned to have size n. The main result will be a scaling limit for the size of the largest common subtrees of two such Bienaymé trees under some light assumptions. The talk is based on joint work with Omer Angel, Anna Brandenberger, Serte Donderwinkel, and Robin Khanfir.
Speaker: Hannah Cairns (McGill)
Time: 25 November, 2025 2:30-3:20 pm
Location: https://uvic.zoom.us/j/82117115633?pwd=T18dWUILT2zrhpDhsmMxJdbVkxLpW3.1
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Time: 2 December, 2025 2:30-3:20 pm
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Time: 9 December, 2025 2:30-3:20 pm
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Time: 6 january, 2026 2:30-3:20 pm
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Time: 13 january, 2026 2:30-3:20 pm
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Time: 20 january, 2026 2:30-3:20 pm
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Time: 27 january, 2026 2:30-3:20 pm
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Speaker:
Time: 3 February, 2026 2:30-3:20 pm
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Speaker: Shirshendu Ganguly (Berkeley)
Time: 12 February, 2026 3:30-4:20 pm (NOTE UNUSUAL DATE and TIME)
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Time: 17 February, 2026 2:30-3:20 pm
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Time: 24 February, 2026 2:30-3:20 pm
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Time: 3 March, 2026 2:30-3:20 pm
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Speaker:
Time: 10 March, 2026 2:30-3:20 pm
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Speaker: Francesco Tosello (UBC)
Time: 17 March, 2026 2:30-3:20 pm
Location: TBA
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Speaker:
Time: 24 March, 2026 2:30-3:20 pm
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Speaker:
Time: 3 April, 2026 2:30-3:20 pm
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