Past Seminars

18 June 2021
14:00
Mike Daas
Abstract

It is a well-known fact that Boolean rings, those rings in which $x^2 = x$ for all $x$, are necessarily commutative. There is a short and completely elementary proof of this. One may wonder what the situation is for rings in which $x^n = x$ for all $x$, where $n > 2$ is some positive integer. Jacobson and Herstein proved a very general theorem regarding these rings, and the proof follows a widely applicable strategy that can often be used to reduce questions about general rings to more manageable ones. We discuss this strategy, but will also focus on a different approach: can we also find ''elementary'' proofs of some special cases of the theorem? We treat a number of these explicit computations, among which a few new results.

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  • Junior Algebra and Representation Theory Seminar
18 June 2021
14:00
Abstract

Our society is witnessing an exponential growth of data being generated. Among the various data types being routinely collected, event logs are available in a wide variety of domains. Despite historical and structural digitalisation challenges, healthcare is an example where the analysis of event logs might bring a new revolution.

In this talk, I will present our recent efforts in analysing and exploring temporal event data sequences extracted from event logs. Our visual analytics approach is able to summarise and seamlessly explore large volumes of complex event data sequences. We are able to easily derive observations and findings that otherwise would have required significant investment of time and effort.  To facilitate the identification of findings, we use a hierarchical clustering approach to cluster sequences according to time and a novel visualisation environment.  To control the level of detail presented to the analyst, we use a hierarchical aggregation tree and an Align-Score-Simplify strategy based on an information score.   To show the benefits of this approach, I will present our results in three real world case studies: CUREd, Outpatient clinics and MIMIC-III. These will respectively cover the analysis of calls and responses of emergency services, the efficiency of operation of two outpatient clinics, and the evolution of patients with atrial fibrillation hospitalised in an acute and critical care unit. To finalise the talk, I will share our most recent work in the analysis of clinical events extracted from Electronic Health Records for the study of multimorbidity.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Mathematical Biology and Ecology Seminar
18 June 2021
13:30
to
17:00
Piotr Przytycki, Elia Fioravanti, Rylee Lyman

Further Information: 

Tits Alternative in dimension 2

1:30-2:30PM

Piotr Przytycki (McGill)

A group G satisfies the Tits alternative if each of its finitely generated subgroups contains a non-abelian free group or is virtually solvable. I will sketch a proof of a theorem saying that if G acts geometrically on a simply connected nonpositively curved complex built of equilateral triangles, then it satisfies the Tits alternative. This is joint work with Damian Osajda.

Coarse-median preserving automorphisms

2:45-3:45PM

Elia Fioravanti (Bonn)

We study fixed subgroups of automorphisms of right-angled Artin and Coxeter groups. If Phi is an untwisted automorphism of a RAAG, or an arbitrary automorphism of a RACG, we prove that Fix(Phi) is finitely generated and undistorted. Up to replacing Phi with a power, the fixed subgroup is actually quasi-convex with respect to the standard word metric (which implies that it is separable and a virtual retract, by work of Haglund and Wise). Our techniques also apply to automorphisms of hyperbolic groups and to certain automorphisms of hierarchically hyperbolic groups. Based on arXiv:2101.04415.

Some new CAT(0) free-by-cyclic groups

4:00-5:00PM

Rylee Lyman (Rutgers-Newark)

I will construct several infinite families of polynomially-growing automorphisms of free groups whose mapping tori are CAT(0) free-by-cyclic groups. Such mapping tori are thick, and thus not relatively hyperbolic. These are the first families comprising infinitely many examples for each rank of the nonabelian free group; they contrast strongly with Gersten's example of a thick free-by-cyclic group which cannot be a subgroup of a CAT(0) group.

 

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

18 June 2021
13:00
Abstract

Tendon tissue engineering aims to grow functional tissue in the lab. Tissue is grown inside a bioreactor which controls both the mechanical and biochemical environment. As tendon cells alter their behaviour in response to mechanical stresses, designing suitable bioreactor loading regimes forms a key component in ensuring healthy tissue growth.  

Linking the forces imposed by the bioreactor to the shear stress experienced by individual cell is achieved by homogenisation using multiscale asymptotics. We will present a continuum model capturing fluid-structure interaction between the nutrient media and the fibrous scaffold where cells grow. Solutions reflecting different experimental conditions will be discussed in view of the implications for shear stress distribution experienced by cells across the bioreactor.  

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Junior Applied Mathematics Seminar
18 June 2021
12:45
Gabriel Wong
Abstract

The holographic entanglement entropy formula identifies the generalized entropy of the bulk AdS spacetime with the entanglement entropy of the boundary CFT. However the bulk microstate interpretation of the generalized entropy remains poorly understood. Progress along this direction requires understanding how to define Hilbert space factorization and entanglement entropy in the bulk closed string theory.   As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A model, which enjoys a gauge-string duality.   We define a notion of generalized entropy for closed strings on the resolved conifold using the replica trick.   As in AdS/CFT, we find this is dual to (defect) entanglement entropy in the dual Chern Simons gauge theory.   Our main result is a bulk microstate interpretation of generalized entropy in terms of open strings and their edge modes, which we identify as entanglement branes.   

 

More precisely, we give a self consistent factorization of the closed string Hilbert space which introduces open string edge modes transforming under a q-deformed surface symmetry group. Compatibility with this symmetry requires a q-deformed definition of entanglement entropy. Using the topological vertex formalism, we define the Hartle Hawking state for the resolved conifold and compute its q-deformed entropy directly from the reduced density matrix.   We show that this is the same as the generalized entropy.   Finally, we relate non local aspects of our factorization map to analogous phenomenon recently found in JT gravity.

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • String Theory Journal Club
17 June 2021
16:00
HAOYANG CAO
Abstract

Abstract: In this work, we analyze a class of stochastic inverse optimal control problems with entropy regularization. We first characterize the set of solutions for the inverse control problem. This solution set exemplifies the issue of degeneracy in generic inverse control problems that there exist multiple reward or cost functions that can explain the displayed optimal behavior. Then we establish one resolution for the degeneracy issue by providing one additional optimal policy under a different discount factor. This resolution does not depend on any prior knowledge of the solution set. Through a simple numerical experiment with deterministic transition kernel, we demonstrate the ability of accurately extracting the cost function through our proposed resolution.

 

Joint work with Sam Cohen (Oxford) and Lukasz Szpruch (Edinburgh).

  • Mathematical and Computational Finance Internal Seminar
17 June 2021
14:00
Georg Stadler
Abstract

I will discuss modified Newton methods for solving nonlinear systems of PDEs. These methods introduce additional variables before deriving the Newton linearization. These variables can then often be eliminated analytically before solving the Newton system, such that existing solvers can be adapted easily and the computational cost does not increase compared to a standard Newton method. The resulting algorithms yield favorable convergence properties. After illustrating the ideas on a simple example, I will show its application for the solution of incompressible Stokes flow problems with viscoplastic constitutive relation, where the additionally introduced variable is the stress tensor. These models are commonly used in earth science models. This is joint work with Johann Rudi (Argonne) and Melody Shih (NYU).

 

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A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact trefethen@maths.ox.ac.uk.

  • Computational Mathematics and Applications Seminar
17 June 2021
13:00
Sue Ann Campbell

Further Information: 

Synchronized activity of neurons is important for many aspects of brain function. Synchronization is affected by both network-level parameters, such as connectivity between neurons, and neuron-level parameters, such as firing rate. Many of these parameters are not static but may vary slowly in time. In this talk we focus on neuron-level parameters. Our work centres on the neurotransmitter acetylcholine, which has been shown to modulate the firing properties of several types of neurons through its affect on potassium currents such as the muscarine-sensitive M-current.  In the brain, levels of acetylcholine change with activity.  For example, acetylcholine is higher during waking and REM sleep and lower during slow wave sleep. We will show how the M-current affects the bifurcation structure of a generic conductance-based neural model and how this determines synchronization properties of the model.  We then use phase-model analysis to study the effect of a slowly varying M-current on synchronization.  This is joint work with Victoria Booth, Xueying Wang and Isam Al-Darbasah.

Abstract

Synchronized activity of neurons is important for many aspects of brain function. Synchronization is affected by both network-level parameters, such as connectivity between neurons, and neuron-level parameters, such as firing rate. Many of these parameters are not static but may vary slowly in time. In this talk we focus on neuron-level parameters. Our work centres on the neurotransmitter acetylcholine, which has been shown to modulate the firing properties of several types of neurons through its affect on potassium currents such as the muscarine-sensitive M-current.  In the brain, levels of acetylcholine change with activity.  For example, acetylcholine is higher during waking and REM sleep and lower during slow wave sleep. We will show how the M-current affects the bifurcation structure of a generic conductance-based neural model and how this determines synchronization properties of the model.  We then use phase-model analysis to study the effect of a slowly varying M-current on synchronization.  This is joint work with Victoria Booth, Xueying Wang and Isam Al-Darbasah

The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).

  • Industrial and Applied Mathematics Seminar
17 June 2021
12:00
Alexis Michelat

Further Information: 

A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact Benjamin Fehrman.

Abstract

The integral of mean curvature squared is a conformal invariant that measures the distance from a given immersion to the standard embedding of a round sphere. Following work of Robert Bryant who showed that all Willmore spheres in the 3-sphere are conformally minimal, Robert Kusner proposed in the early 1980s to use the Willmore energy to obtain an “optimal” sphere eversion, called the min-max sphere eversion.

We will present a method due to Tristan Rivière that permits to tackle a wide variety of min-max problems, including ones about the Willmore energy. An important step to solve Kusner’s conjecture is to determine the Morse index of branched Willmore spheres, and we show that the Morse index of conformally minimal branched Willmore spheres is equal to the index of a canonically associated matrix whose dimension is equal to the number of ends of the dual minimal surface.

  • PDE CDT Lunchtime Seminar

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