Tue, 02 Dec 2025
16:00
C3

The simplex of traces of groups and C*-algebras

Itamar Vigdorovich
(UCSD)
Abstract

The simplex of traces of a unital C*-algebra has long been regarded as a central invariant in the theory. Likewise, from the group-theoretic perspective, the simplex of traces of a discrete group (namely, the simplex of traces of its maximal C*-algebra) is a fundamental object in harmonic analysis, and the study of this simplex led to many applications in recent years.

Itamar Vigdorovich , UCSD, will discuss several results describing the simplex of traces in concrete and significant cases. These include Property (T) groups and especially higher rank lattices, for which the simplex of traces is as tame as possible. In contrast, for free products, the simplex is typically as wild as possible, yet still admits a canonical and universal structure—the Poulsen simplex. In ongoing work, an analogous result is obtained for the space of traces on the fundamental group of a closed surface of genus g2.

Itamar presents these results, outlines the main ideas behind the proofs, and gives an overview of the central concepts. The talk is based on joint works with Gao, Ioana, Levit, Orovitz, Slutsky, and Spaas.

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Thu, 05 Feb 2026

12:00 - 13:00
L3

OCIAM TBC

Marcelo Dias
(University of Edinburgh)

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Further Information

Dr Marcelo A. Dias is a Reader in Structural Engineering at the University of Edinburgh. His research spans theoretical structural mechanics, soft condensed matter, and materials modelling. He focuses on understanding how the mechanical behaviour of elastic bodies emerges from the interplay between material composition and carefully designed internal geometry. His work has applications across shape formation in nature, biomechanics, materials and structural mechanics, and the controlled design and functionality of thin plates and shells. You can find some wonderful examples of this research on his research site: https://mazdias.wordpress.com/research/ 

Thu, 19 Feb 2026

12:00 - 13:00
L3

OCIAM TBC

Edwina Yeo
(University College London)

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Further Information

Dr Edwina Yeo is an applied mathematician working at the interface of continuum mechanics and mathematical biology. She specialises in developing mathematical models for biological and biomedical fluid-mechanics processes, with research spanning regenerative medicine, nanotechnology, microbiology and geology. Her recent work includes models of bacterial adhesion in fluid flow, Von Willebrand Factor dynamics in arterial flows, and microscale contaminant behaviour extracted from imaging data.

Her publications appear in journals such as Biomechanics and Modelling in Mechanobiology, Advanced Materials, and Royal Society Interface, alongside recent collaborative preprints. She is currently an EPSRC National Fellow in Fluid Dynamics at UCL and a visiting research fellow in OCIAM.

Thu, 12 Mar 2026

12:00 - 13:00
L3

OCIAM TBC

Tobias Grafke
(University of Warwick)

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Further Information

Tobias Grafke's research focuses on developing numerical methods and mathematical tools to analyse stochastic systems. His work spans applications in fluid dynamics and turbulence, atmosphere–ocean dynamics, and biological and chemical systems. He studies the pathways and occurrence rates of rare and extreme events in complex realistic systems, develops numerical techniques for their simulation, and quantifies how random perturbations influence long-term system behaviour.

Thu, 05 Mar 2026

12:00 - 13:00
L3

OCIAM TBC

Stuart Thomson
(University of Bristol)

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Further Information

Dr Stuart J. Thomson is an applied mathematician whose research sits at the intersection of mathematics, physics, and engineering. He works closely with table-top experiments to uncover how complex fluid and soft-matter systems give rise to novel emergent phenomena through nonlinear dynamics, many-body interactions, and geometric confinement. His interests include interfacial hydrodynamics, self-assembly, active and driven matter, interfacial robotics, transport phenomena, and fluid–structure interaction.

He is currently leading the project “The statistical physics of hydrodynamic random walkers: experiments and theory”, which combines experimental and theoretical approaches to understand how fluid-mediated interactions shape the behaviour of randomly moving microscopic walkers. Dr Thomson is based in the School of Engineering, Mathematics and Technology at the University of Bristol.

Thu, 26 Feb 2026

12:00 - 13:00
L3

OCIAM TBC

Robert Van Gorder
(University of Otago)

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Further Information

Dr Rob Van Gorder’s research focuses on how physical phenomena can be described, predicted, and controlled using applied mathematics. He works across mathematical modelling, analytical and asymptotic methods, and numerical simulation, applying this combination to a wide range of physical systems.

His interests in fluid dynamics centre on fundamental flow structures—such as vortices, bubbles, waves, and boundary layers—and how they evolve, persist, or break apart. He also studies spatial instabilities and pattern formation, investigating how mechanisms such as Turing and Benjamin–Feir instabilities extend to heterogeneous or non-autonomous systems arising in chemistry, physics, biology, and epidemiology.

In theoretical physics, Dr Van Gorder works on quantum mechanics, quantum fluids, and nonlinear waves, including the dynamics of Bose–Einstein condensates, quantised vortices in superfluid helium, and confined quantum systems. Across these areas, he aims to understand how nonlinear and quantum systems behave under realistic constraints and external forcing.

His recent publications include work on pattern formation and diffusive instabilities in Proceedings of the Royal Society A.

Thu, 19 Feb 2026

12:00 - 13:00
L3

OCIAM Post-doc Talks

Dr Fiyanshu Kaka & Carmela Moschella
((Mathematical Institute University of Oxford))

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Further Information

Dr Finyashu Kaka is a materials scientist specialising in sustainable energy technologies, advanced functional materials, and computational modelling. His work spans organic photovoltaics, solid-state and metal-ion batteries, MXene-based materials, and next-generation thermal barrier coatings. He combines physics-based modelling with machine-learning methods to understand and optimise process–structure–property relationships in energy devices. His research appears in leading journals, and he holds several patents in flexible electronics and energy-efficient thermal systems. He is currently working with Professor Jon Chapman as a postdoctoral researcher in OCIAM.

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