16:00
Departmental Colloquium
George Lusztig is the Abdun-Nur Professor of Mathematics. He joined the MIT mathematics faculty in 1978 following a professorship appointment at the University of Warwick, 1974-77. He was appointed Norbert Wiener Professor at MIT 1999-2009.
Lusztig graduated from the University of Bucharest in 1968, and received both the M.A. and Ph.D. from Princeton University in 1971 under the direction of Michael Atiyah and William Browder. Professor Lusztig works on geometric representation theory and algebraic groups. He has received numerous research distinctions, including the Berwick Prize of the London Mathematical Society (1977), the AMS Cole Prize in Algebra (1985), and the Brouwer Medal of the Dutch Mathematical Society (1999), and the AMS Leroy P. Steele Prize for Lifetime Achievement (2008), "for entirely reshaping representation theory, and in the process changing much of mathematics."
Professor Lusztig is a Fellow of the Royal Society (1983), Fellow of the American Academy of Arts & Sciences (1991), and Member of the National Academy of Sciences (1992). He was the recipient of the Shaw Prize (2014) and the Wolf Prize (2022).
16:00
North meets South
Abstract
North Wing talk: Dr Thomas Karam
Title: Ranges control degree ranks of multivariate polynomials on finite prime fields.
Abstract: Let $p$ be a prime. It has been known since work of Green and Tao (2007) that if a polynomial $P:\mathbb{F}_p^n \mapsto \mathbb{F}_p$ with degree $2 \le d \le p-1$ is not approximately equidistributed, then it can be expressed as a function of a bounded number of polynomials each with degree at most $d-1$. Since then, this result has been refined in several directions. We will explain how this kind of statement may be used to deduce an analogue where both the assumption and the conclusion are strengthened: if for some $1 \le t < d$ the image $P(\mathbb{F}_p^n)$ does not contain the image of a non-constant one-variable polynomial with degree at most $t$, then we can obtain a decomposition of $P$ in terms of a bounded number of polynomials each with degree at most $\lfloor d/(t+1) \rfloor$. We will also discuss the case where we replace the image $P(\mathbb{F}_p^n)$ by for instance $P(\{0,1\}^n)$ in the assumption.
South Wing talk: Dr Hamid Rahkooy
Title: Toric Varieties in Biochemical Reaction Networks
Abstract: Toric varieties are interesting objects for algebraic geometers as they have many properties. On the other hand, toric varieties appear in many applications. In particular, dynamics of many biochemical reactions lead to toric varieties. In this talk we discuss how to test toricity algorithmically, using computational algebra methods, e.g., Gröbner bases and quantifier elimination. We show experiments on real world models of reaction networks and observe that many biochemical reactions have toric steady states. We discuss complexity bounds and how to improve computations in certain cases.
16:00
OUI: Consultancy 101
Abstract
Come to this session to learn how to get started in consultancy from Dawn Gordon at Oxford University Innovation (OUI). After an introduction to what consultancy is, we'll explore case studies of consultancy work performed by mathematicians and statisticians within the university. This session will also include practical advice on how you can explore consultancy opportunities alongside your research work, from finding potential clients to the support that OUI can offer.
16:00
Looking after our mental health in an academic environment
Abstract
To tie in with mental health awareness week, in this session we'll give a brief overview of the mental health support available through the department and university, followed by a panel discussion on how we can look after our mental health as in an academic setting. We're pleased that several of our department Mental Health First Aiders will be panellists - come along for hints and tips on maintaining good mental health and supporting your colleagues and friends.
16:00
SIAM Student Chapter: 3-minute thesis competition
Abstract
For week 4's @email session we welcome the SIAM-IMA student chapter, running their annual Three Minute Thesis competition.
The Three Minute Thesis competition challenges graduate students to present their research in a clear and engaging manner within a strict time limit of three minutes. Each presenter will be allowed to use only one static slide to support their presentation, and the panel of esteemed judges (details TBC) will evaluate the presentations based on criteria such as clarity, pacing, engagement, enthusiasm, and impact. Each presenter will receive a free mug and there is £250 in cash prizes for the winners. If you're a graduate student, sign up here (https://oxfordsiam.com/3mt) by Friday of week 3 to take part! And if not, come along to support your DPhil friends and colleagues, and to learn about the exciting maths being done by our research students.
16:00
Departmental Colloquium: Liliana Borcea
Liliana Borcea is the Peter Field Collegiate Professor of Mathematics at the University of Michigan. Her research interests are in scientific computing and applied mathematics, including the scattering and transport of electromagnetic waves.
Abstract
Title: When data driven reduced order modelling meets full waveform inversion
Abstract:
This talk is concerned with the following inverse problem for the wave equation: Determine the variable wave speed from data gathered by a collection of sensors, which emit probing signals and measure the generated backscattered waves. Inverse backscattering is an interdisciplinary field driven by applications in geophysical exploration, radar imaging, non-destructive evaluation of materials, etc. There are two types of methods:
(1) Qualitative (imaging) methods, which address the simpler problem of locating reflective structures in a known host medium.
(2) Quantitative methods, also known as velocity estimation.
Typically, velocity estimation is formulated as a PDE constrained optimization, where the data are fit in the least squares sense by the wave computed at the search wave speed. The increase in computing power has lead to growing interest in this approach, but there is a fundamental impediment, which manifests especially for high frequency data: The objective function is not convex and has numerous local minima even in the absence of noise.
The main goal of the talk is to introduce a novel approach to velocity estimation, based on a reduced order model (ROM) of the wave operator. The ROM is called data driven because it is obtained from the measurements made at the sensors. The mapping between these measurements and the ROM is nonlinear, and yet the ROM can be computed efficiently using methods from numerical linear algebra. More importantly, the ROM can be used to define a better objective function for velocity estimation, so that gradient based optimization can succeed even for a poor initial guess.