Dan Ciubotaru
Diana Brown Fellow & Tutor in Pure Maths; Professor of MathematicsMy research is in representation theory, an area of mathematics concerned with the study of symmetries.
I am particularly interested in unitary representations of reductive Lie groups and Hecke algebras in the framework of the local Langlands correspondence.
My research has been recently supported by the EPSRC grants “New Horizons” EP/V046713/1 (1/2021-12/2023) and EP/N033922/1 (09/2016-08/2020).
At Somerville, I teach Prelims and Part A Pure Maths tutorials. In 2017, I was awarded an MPLS Teaching Award. I am currently the Academic Lead for Prelims and Part A in the Maths Institute.
Some unipotent Arthur packets for reductive p-adic groups, with L. Mason-Brown and E. Okada, arXiv:2210.00251v2 (2023), to appear in IMRN.
Symplectic Dirac operators for Lie algebras and graded Hecke algebras, with M. De Martino and P. Meyer, Transformation Groups, online 08/2022, doi.org/10.1007/s00031-022-09762-4
Weyl groups, the Dirac inequality, and isolated unitary unramified representations, Special issue to the memory of T.A. Springer, Indag. Math. 33 (2022), no. 1, 1-23.
The Dunkl-Cherednik deformation of a Howe duality
Ciubotaru, D; De Martino, M
JOURNAL OF ALGEBRA volume 560 page 914-959 (15 October 2020)
Cocenters of p-adic groups, III: elliptic and rigid concenters
Ciubotaru, D; He, X
Peking Mathematical Journal (13 October 2020)
Dirac induction for rational Cherednik algebras
Ciubotaru, D; De Martino, M
International Mathematics Research Notices (5 July 2018)
On the reducibility of induced representations for classical p-adic groups and related affine Hecke algebras
Ciubotaru, D; Heiermann, V
Israel Journal of Mathematics issue 1 volume 231 page 379-417 (7 June 2019)
Karin Erdmann
Emeritus FellowKarin Erdmann is a German mathematician specializing in representation theory (especially modular representation theory) and homological algebra (especially Hochschild cohomology).
She is best known for her work in modular representation theory which has been cited over 1500 times according to the Mathematical Reviews. Her nephew Martin Erdmann is professor for experimental particle physics at the RWTH Aachen University.
The representation dimension of Hecke algebras and symmetric groups
Bergh, P; Erdmann, K
ADVANCES IN MATHEMATICS issue 4 volume 228 page 2503-2521 (10 November 2011)
Radical cube zero selfinjective algebras of finite complexity
Erdmann, K; Solberg, O
JOURNAL OF PURE AND APPLIED ALGEBRA issue 7 volume 215 page 1747-1768 (July 2011)
The non-projective part of the Lie module for the symmetric group
Erdmann, K; Tan, K
ARCHIV DER MATHEMATIK issue 6 volume 96 page 513-518 (June 2011)
Delta-filtered modules and nilpotent orbits of a parabolic subgroup in O-N
Baur, K; Erdmann, K; Parker, A
JOURNAL OF PURE AND APPLIED ALGEBRA issue 5 volume 215 page 885-901 (May 2011)
The stable Auslander-Reiten quiver of a quantum complete intersection
Bergh, P; Erdmann, K
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY volume 43 page 79-90 (February 2011)
Renaud Lambiotte
Fellow & Tutor in Mathematics; Professor of Networks and Nonlinear Systems
Renaud Lambiotte
Fellow & Tutor in Mathematics; Professor of Networks and Nonlinear Systems
Renaud Lambiotte is a Professor of Networks and Nonlinear Systems.
His main research interests are the modelling and analysis of large networks, with a particular focus on clustering and temporal networks, and applications in social and neuronal systems. He is Associate Editor for Science Advances and a Turing Fellow. See more here.
Renaud Lambiotte has a PhD in Physics from the Université Libre de Bruxelles. Following postdocs at ENS Lyon, Université de Liège, UCLouvain and Imperial College London, and a Professorship in Mathematics at the University of Namur, he is currently Professor of Networks and Nonlinear Systems at the Mathematical Institute of Oxford University.
Selected Publications
Cabral, J., Castaldo, F., Vohryzek, J., Litvak, V., Bick, C., Lambiotte, R., … & Deco, G. (2022). Metastable oscillatory modes emerge from synchronization in the brain spacetime connectome. Communications Physics, 5(1), 184.
Devriendt, K., & Lambiotte, R. (2022). Discrete curvature on graphs from the effective resistance. Journal of Physics: Complexity, 3(2), 025008.
Bovet, A., Delvenne, J. C., & Lambiotte, R. (2022). Flow stability for dynamic community detection. Science advances, 8(19), eabj3063.
Devriendt, K., Martin-Gutierrez, S., & Lambiotte, R. (2022). Variance and covariance of distributions on graphs. SIAM Review, 64(2), 343-359.
Oliver, N., Lepri, B., Sterly, H., Lambiotte, R., Deletaille, S., De Nadai, M., … & Vinck, P. (2020). Mobile phone data for informing public health actions across the COVID-19 pandemic life cycle. Science advances, 6(23), eabc0764.
Shiwei Liu
Fulford Junior Research Fellow
Shiwei Liu
Fulford Junior Research Fellow
Dr. Shiwei Liu is Junior Research Fellow (JRF) at Somerville College. He is also a Royal Society Newton International Fellow at the University of Oxford. He was a Postdoctoral Fellow at the University of Texas at Austin. He obtained his Ph.D. with the Cum Laude from the Eindhoven University of Technology in 2022. His research goal is to leverage, understand, and expand the role of low-dimensionality in neural networks, whose impacts span many important topics, such as efficient training/inference/transfer of large-foundation models, robustness and trustworthiness, and generative AI. His current main research interest focuses on improving the efficiency and accessibility of LLMs, making them accessible tooling to everyone. Dr. Liu has received two Rising Star Awards from KAUST and the Conference on Parsimony and Learning (CPAL). His Ph.D. thesis received the 2023 Best Dissertation Award from Informatics Europe. Personal Website: https://shiweiliuiiiiiii.github.io/
Professor Dame Angela McLean
Honorary FellowProfessor Dame Angela McLean DBE FRS is a professor of Mathematical Biology in the Department of Zoology at Oxford University and Director of The Institute for Emerging Infections of Humans.
She was appointed as the Chief Scientific Adviser for the Ministry of Defence and in September 2019 and served as Deputy Chief Scientific Adviser during the Covid-19 pandemic.
Angela’s research interests lie in the use of mathematical models to aid our understanding of the evolution and spread of infectious agents. She is also interested in the use of natural science evidence in formulating public policy and has co-developed the Oxford Martin School Restatements: an activity which restructures and presents the evidence underlying an issue of policy concern or controversy in a short, uncharged, intelligible form for non-technical audiences.
Angela established Mathematical Biology at the Biotechnology and Biological Science Research Council’s Institute for Animal Health in 1994. Before this, Angela was a Royal Society Research Fellow at Oxford University and a Research Fellow at the Institut Pasteur in Paris.
In 2009 Angela was elected as a Fellow of the Royal Society. She has been awarded the Gabor Medal in 2011 and the Weldon Memorial Prize in 2018. She received her damehood in the 2018 Queen’s Birthday Honours List.
Hilary Ockendon
Emeritus FellowMy research interests were initially in fluid dynamics but working in industrial mathematics has led me to problems in a wide variety of fields.
The unifying theme of my work is the use of continuum models and the application of asymptotic methods to physical problems in order to provide useful simplifications and illuminate the model and its predictions.
Among problems on which I have worked in fluid mechanics are nonlinear wave propagation in gases including real gas effects and resonant sloshing in gases and liquids. Many industrially relevant problems involve thin layer models of viscous fluids, and similar mathematics can apply in very varied situations. Examples include injection moulding, concentration polarization in ultra filtration, contact lens modelling and the drying of paint. Following my early work in relaxing gases, I have had a continuing interest in two-phase flows and I have developed several fluid-fibre and fibre-fibre interaction models for problems in the textile industry. This last example has proved a fruitful area of research for over ten years and resulted in one MSc and four PhD theses in collaboration with industry.
Mathematical modelling of elastoplasticity at high stress, P.D.Howell, H.Ockendon, J.R.Ockendon, Proc. Roy. Soc. A, vol 468, p3842-3863, 2012.
Books
Waves and Compressible Flow, H.Ockendon, J.R.Ockendon, Springer 2004.
Viscous Flow, H.Ockendon, J.R.Ockendon, Cambridge 1995.
Mason Porter
Senior Research Fellow; Professor of Mathematics, UCLA
Mason Porter
Senior Research Fellow; Professor of Mathematics, UCLA
I am a Professor in the Department of Mathematics at UCLA. Previously, I was Professor of Nonlinear and Complex Systems in the Mathematical Institute at University of Oxford.
I was also a Tutorial Fellow in Somerville College. Before then, I studied at Caltech and Cornell, before a postdocs at Georgia Tech and and Berkeley.
I am also a die-hard fan of the Los Angeles Dodgers. You can also find me on Facebook and Twitter (@masonporter). I am also involved with the Legends of Caltech movie and co-edited Legends of Caltech III.
Comparing community structure to characteristics in online collegiate social networks
Traud, A; Kelsic, E; Mucha, P; Porter, M
SIAM Review issue 3 volume 53 page 526-543 (1 December 2011)
A mathematical model for the dynamics and synchronization of cows
Sun, J; Bollt, E; Porter, M; Dawkins, M
Physica D: Nonlinear Phenomena issue 19 volume 240 page 1497-1509 (15 September 2011)
Dynamic reconfiguration of human brain networks during learning.
Bassett, D; Wymbs, N; Porter, M; Mucha, P; Carlson, J; Grafton, S
Proc Natl Acad Sci U S A issue 18 volume 108 page 7641-7646 (3 May 2011)
Discrete breathers in one-dimensional diatomic granular crystals.
Boechler, N; Theocharis, G; Job, S; Kevrekidis, P; Porter, M; Daraio, C
Phys Rev Lett issue 24 volume 104 page 244302- (18 June 2010)
Community structure in time-dependent, multiscale, and multiplex networks
Mucha, P; Richardson, T; Macon, K; Porter, M; Onnela, J
Science issue 5980 volume 328 page 876-878 (14 May 2010)
Rhiannon Savage
Retaining Fee Lecturer in Pure MathematicsRhiannon is a DPhil Student in Mathematics, specialising in Derived Algebraic Geometry. She previously completed a MMath Master of Mathematics at Oxford (2020). Visit her website here.
Savage, R (2023) Koszul Monoids in Quasi-abelian Categories, Journal of Applied Categorical Structures, 31(50)
Caroline Series CBE
Honorary FellowCaroline Series (1969, Mathematics) is a distinguished mathematician working in hyperbolic geometry, Kleinian groups and Dynamical systems.
After studying at Somerville in 1969, Professor Series held posts in Berkeley and Newnham College, Cambridge before arriving at the University of Warwick in 1978. In 1987 she became Reader in Mathematics at Warwick and, in 1992, Professor. In 2017, she became the third woman in its history to serve as president of the London Mathematical Society. In 2023, she was awarded a CBE in the King’s first list of Birthday Honours.
Recent Publications
- Convergence of spherical averages for actions of Fuchsian Groups, Comment. Math. Helv. 98 2023
- An ergodic theorem for the action of a Fuchsian group (Russian), Uspekhi Math. Nauk Vol 78, 2023
- A symmetric Markov coding & the ergodic theorem for actions of Fuchsian Groups, 2020
- Primitive stability and the Bowditch conditions revisited, ArXiv June 2020
- The diagonal slice of Schottky space, Algebraic & Geometric Topology, Vol.17, 2017
- Limits of limit sets II: Geometrically Infinite Groups, Geometry & Topology V. 21, 2017
Justin Sirignano
Research Fellow; Professor of Mathematics
Justin Sirignano
Research Fellow; Professor of Mathematics
Justin is a Professor of Mathematics at the University of Oxford and Director of the Oxford Masters program in Mathematical & Computational Finance.
Justin’s research lies at the intersection of applied mathematics, machine learning, and high-performance computing and is focused on theory and applications of Deep Learning. Justin develops deep learning models for large financial datasets such as: high-frequency data from limit order books, loans, and options. He is also developing deep learning methods for constructing partial differential equation models from data, which has a variety of applications in science, engineering, and finance.
Justin received his PhD from Stanford University and holds a Bachelors degree from Princeton University. He was a Chapman Fellow at the Department of Mathematics at Imperial College. He was awarded the 2014 SIAM Financial Mathematics and Engineering Conference Paper Prize.
“Mean Field Analysis of Neural Networks: A Law of Large Numbers” (with K. Spiliopoulos). SIAM Journal on Applied Mathematics, 2020.
“Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem” (with K. Spiliopoulos). Stochastic Systems, to appear 2020.
“Inference for large financial systems” (with G. Schwenkler and K. Giesecke). Mathematical Finance, 2020.
“Mean Field Analysis of Deep Neural Networks” (with K. Spiliopoulos). Mathematics of Operations Research, 2021. arXiv: 1903.04440, 2020.
“Universal features of price formation in financial markets: perspectives from Deep Learning” (with Rama Cont). Quantitative Finance, 2019.
“Mean Field Analysis of Neural Networks: A Central Limit Theorem” (with K. Spiliopoulos). Stochastic Processes and their Applications, 2019.
“PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence” (with J. MacArt and K. Spiliopoulos). arXiv:2105.08633, 2021.
Roxanne Zhang
Retaining Fee Lecturer
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