### UBC Congregation Ceremony [2012_05_30_0830]

University Of British Columbia Ceremonies And Events Office

### Amenability of quasi-lattice ordered groups

Astrid An Huef
Quasi-lattice ordered groups and their Toeplitz algebras were introduced by Nica in 1992. A quasi-lattice ordered group is amenable if the concrete Toeplitz subalgebra acting on $l^2(P)$ is isomorphic to the universal one. Laca-Raeburn used "controlled maps" to find sufficient conditions for amenability. Here I will discuss a more general notion of controlled map. This is joint work with Ilija Tolich and Iain Raeburn.

### Bootstrap Robust Prescriptive Analytics

Bart Paul Gerard Van Parys
We discuss prescribing optimal decisions in a framework where their cost depends on uncertain problem parameters that need to be learned from supervised data. Prescriptive analytics consists in making optimal decisions specific to a particular covariate context. Prescriptive methods need to factor in additional observed contextual information on a potentially large number of covariates as opposed to static decision methods who only use sample data. Any naive use of training data may, however, lead to...

### Entropy decay for the Kac master equation

Michael Loss
The Kac master equation models the behavior of a large number of randomly colliding particles. Due to its simplicity it allows, without too much pain, to investigate a number of issues. E.g., Mark Kac, who invented this model in 1956, used it to give a simple derivation of the spatially inhomogeneous Boltzmann equation. One important issue is the rate of approach to equilibrium, which can be analyzed in various ways, using, e.g., the gap or...

### UBC Congregation Ceremony [2002_11_27_1000]

University Of British Columbia Ceremonies And Events Office

### Stratifying multi-parameter persistent homology

Nina Otter
In their paper "The theory of multidimensional persistence", Carlsson and Zomorodian write "Our study of multigraded objects shows that no complete discrete invariant exists for multidimensional persistence. We still desire a discriminating invariant that captures persistent information, that is, homology classes with large persistence." In this talk I will discuss how tools from commutative algebra give computable invariants able to capture homology classes with large persistence. Specifically, multigraded associated primes provide a stratification of the...

### Decomposition Methods For Solving Distributionally Robust Two-Stage Stochastic Integer Programs

Sanjay Mehrotra
We introduce and study a two-stage distributionally robust mixed binary problem (TSDR-MBP) where the random parameters follow the worst-case distribution belonging to an uncertainty set of probability distributions. We present a decomposition algorithm, which utilizes distribution separation procedure and parametric cuts within Benders’ algorithm or L-shaped method, to solve TSDR-MBPs with binary variables in the first stage and mixed binary programs in the second stage. We refer to this algorithm as distributionally robust integer (DRI)...

### Lioville Equations and Functional Determinants

Andrea Malchiodi
Liouville equations have interest in spectral theory, as they arise when extremizing so-called Functional Determinants. These are constructed out of spectra of conformally covariant operators, and are explicit in dimension two and four, due to formulas by Polyakov and Branson-Oersted. We discuss some existence, uniqueness, non-uniqueness results and some open problems.

### UBC Congregation Ceremony [2012_05_28_1100]

University Of British Columbia Ceremonies And Events Office

### A new continuum theory for incompressible swelling materials

Pierre Degond
Swelling media (e.g. gels, tumors) are usually described by mechanical constitutive laws (e.g. Hooke or Darcy laws). However, constitutive relations of real swelling media are not well-known. Here, we take an opposite route and consider a simple heuristics relying on the following rule: (i) particles are at packing density; (ii) any two particles cannot swap their position; (iii) motion should be as slow as possible. These heuristics determine the medium velocity uniquely. In general, this...

### UBC Congregation Ceremony [2014_05_23_1600]

University Of British Columbia Ceremonies And Events Office

### UBC Congregation Ceremony [2008_05_22_1330]

University Of British Columbia Ceremonies And Events Office

Christoph Keller

Frieda Granot

### How to account for intracellular dynamics [the cytoskeleton] in developmental processes

Francois Nedelec
The cytoskeleton drives many essential processes in the cell, such as division, the specification of the division axis, movements, polarization and changes in cell shape. These fundamental processes are naturally essential in the development of any organism, and are on their own already complicated to model or understand. What is the correct level of description of intracellular state if one wants to model the development of multiple cells It is possible to capture the dynamics...

Juan Fuxman Bass

### Arithmetic of rational points and zero-cycles on Kummer varieties

Rachel Newton
Yongqi Liang has shown that for rationally connected varieties over a number field K, sufficiency of the Brauer-Manin obstruction to the existence of rational points over all finite extensions of K implies sufficiency of the Brauer-Manin obstruction to the existence of zero-cycles of degree 1 over K. I will discuss joint work with Francesca Balestrieri where we extend Liang's result to Kummer varieties.

### Diophantine inequalities for ternary diagonal forms

Damaris Schindler
We discuss small solutions to ternary diagonal inequalities of any degree where all of the variables are assumed to be of size P. We study this problem on average over a one-parameter family of forms and discuss a generalization of work of Bourgain on generic ternary diagonal quadratic forms to higher degree. In particular we discuss how these Diophantine inequalities are related to counting rational points close to varieties.

Hoang Tran

### Asymptotical analysis of a weighted very fast diffusion equation arising in quantization of measures via the JKO scheme

Mikaela Iacobelli
In this talk I would like to present some recent results on the asymptotic behavior of a very fast diffusion PDE with periodic boundary conditions. This equation is motivated by the gradient flow approach to the problem of quantization of measures. I prove exponential convergence to equilibrium under minimal assumptions on the data, and I also provide sufficient conditions for W2-stability of solutions. Moreover, I will present a work in progress with Filippo Santambrogio and...

### Why plants make puzzle-shaped cells

Richard Smith
The shape and function of plant cells are thought to be closely related. The puzzle-shaped epidermal cells that appear in the epidermis of many plants are a striking example of a complex cell shape, however their functional benefit has remained elusive. We propose that these intricate forms provide an effective strategy to reduce mechanical stress in the cell wall. When tissue-level growth is isotropic, we hypothesize that lobes emerge at the cellular level to prevent...

### Modelling collisions with and between plants

Mik Cieslak
L-systems are widely used for modelling the growth and development of plants. However, until now L-systems did not simulate mechanical collisions between plant parts and entire plants. We show that L-systems can be combined with the position-based collision detection and resolution method, originally devised in computer graphics and subsequently extended to plant modelling. To this end, we extend turtle interpretation by creating a persistent geometric representation of a plant and updating it after each simulated...

### Stable, high-order finite difference methods for nonlinear wave-structure interaction in a moving reference frame

Harry Bingham
This talk will focus on high-order finite difference methods for solving potential flow approximations of nonlinear surface waves interacting with marine structures. Of special interest is the loading and wave-induced response of sailing ships, where it is convenient to work in a reference frame which is translating at constant speed. This introduces non-linear convective terms into the free-surface boundary conditions which are found to require nonlinear numerical schemes to achieve robust and stable solutions. The...