Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
Today
12:00
R. Maria del Rio-Chanona
Abstract

Identifying systemically important countries is crucial for global financial stability. In this work we use (multilayer) network methods to identify systemically important countries. We study the financial system as a multilayer network, where each layer represent a different type of financial investment between countries. To rank countries by their systemic importance, we implement MultiRank, as well a simplistic model of financial contagion. In this first model, we consider that each country has a capital buffer, given by the capital to assets ratio. After the default of an initial country, we model financial contagion with a simple rule: a solvent country defaults when the amount of assets lost, due to the default of other countries, is larger than its capital. Our results show that when we consider that there are various types of assets the ranking of systemically important countries changes. We make all our methods available by introducing a python library. Finally, we propose a more realistic model of financial contagion that merges multilayer network theory and the contingent claims sectoral balance sheet literature. The aim of this framework is to model the banking, private, and sovereign sector of each country and thus study financial contagion within the country and between countries. 

Today
12:45
to
14:00
Michael Negus
Abstract

Recent advances in experimental imaging techniques have allowed us to observe the fine details of how droplets behave upon impact onto a substrate. However, these are highly non-linear, multiscale phenomena and are thus a formidable challenge to model. In addition, when the substrate is deformable, such as an elastic sheet, the fluid-structure interaction introduces an extra layer of complexity.

We present two modeling approaches for droplet impact onto deformable substrates: matched asymptotics and direct numerical simulations. In the former, we use Wagner's theory of impact to derive analytical expressions which approximate the behavior during the early time of impact. In the latter, we use the open source volume-of-fluid code Basilisk to conduct simulations designed to give insight into the later times of impact.

We conclude by showing how these methods are complementary, and a combination of both can give a thorough understanding of the droplet impact across timescales. 

  • Junior Applied Mathematics Seminar
Today
14:00
Carolina Urzua Torres
Abstract


Boundary integral equations (BIEs) are well established for solving scattering at bounded infinitely thin objects, so-called screens, which are modelled as “open surfaces” in 3D and as “open curves” in 2D. Moreover, the unknowns of these BIEs are the jumps of traces across $\Gamma$. Things change considerably when considering scattering at multi-screens, which are arbitrary arrangements of thin panels that may not be even locally orientable because of junction points (2D) or junction lines (3D). Indeed, the notion of jumps of traces is no longer meaningful at these junctions. This issue can be solved by switching to a quotient space perspective of traces, as done in recent work by Claeys and Hiptmair. In this talk, we present the extension of the quotient-space approach to the Galerkin boundary element (BE) discretization of first-kind BIEs. Unlike previous approaches, the new quotient-space BEM relies on minimal geometry information and does not require any special treatment at junctions. Moreover, it allows for a rigorous numerical analysis.
 

  • Numerical Analysis Group Internal Seminar
Today
14:00
Endre Csóka

Further Information: 

We analyze the asymptotic relative size of the largest independent set of a random d-regular graph on n → ∞ vertices. This problem is very different depending on d because of a surprising phase transition. This is somewhat similar to finding the density of ``water'' above and below its freezing point. These phase transitions are related to algorithmic thresholds, mixing properties, counting, graph reconstruction, graph limits and other questions. We are still far from a complete understanding of all these questions. Our tools are partially coming from statistical physics. 

  • Combinatorial Theory Seminar
Today
14:30
Charles Millard
Abstract

The Approximate Message Passing (AMP) algorithm is a powerful iterative method for reconstructing undersampled sparse signals. Unfortunately, AMP is sensitive to the type of sensing matrix employed and frequently encounters convergence problems. One case where AMP tends to fail is compressed sensing MRI, where Fourier coefficients of a natural image are sampled with variable density. An AMP-inspired algorithm constructed specifically for MRI is presented that exhibits a 'state evolution', where at every iteration the image estimate before thresholding behaves as the ground truth corrupted by Gaussian noise with known covariance. Numerical experiments explore the practical benefits of such effective noise behaviour.
 

  • Numerical Analysis Group Internal Seminar
Today
15:30
Bernd Sturmfels
Abstract

Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given 
instance. This lecture illustrates how these two fields complement each other, especially in the light of emerging new applications. We start with a gem from
the 19th century, namely the 3264 conics that are tangent to five given conics in the plane. Thereafter we turn to current problems in statistics, with focus on 
maximum likelihood estimation for linear Gaussian covariance models.
 

  • Algebraic Geometry Seminar
Today
17:00
Abstract

Congruence monoids in the ring of integers are given by certain unions of arithmetic progressions. To each congruence monoid, there is a canonical way to associate a semigroup C*-algebra. I will explain this construction and then discuss joint work with Xin Li on K-theoretic invariants. I will also indicate how all of this generalizes to congruence monoids in the ring of integers of an arbitrary algebraic number field.

  • Functional Analysis Seminar
Tomorrow
15:00
Abstract

In this talk, I will introduce the notion of a sheaf on a topological space. I will then explain why "topological spaces" are an artificial limitation on enjoying life (esp. cohomology) to the fullest and what to do about that (answer: sites). Sheaves also fail our needs, but they have a suitable natural upgrade (i.e. stacks).
This talk will be heavily peppered with examples that come from the world around you (music, torsors, etc.).
 

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