The Blaise Pascal Lecture series has been established following a generous bequest by Mrs Marjorie Roberts in 2006. Each year, one to two Pascal Fellows, typically linked to a Durham Symposium, is chosen from a list of nominees, whose research interests are either in Pure Mathematics or Natural Philosophy (Applied Mathematics and Theoretical Physics).
Below you can find information about the Pascal Lectures that have taken place since 2008.
Second order invariants on spacelike surfaces immersed in Minkowski space
Professor Johan Hastad, KTH Royal Institute of Technology
Abstract: Max-Lin is the problem of, given an over-determined system of linear equations modulo two, find the best solution. In other words to satisfy the maximal number of equations. An old result says that, for any $\epsilon > 0$, it is NP-hard to approximate this within a factor of $\frac 12 + \epsilon$. In other words it is hard to do significantly better than picking a random solution. This implies that Gaussian elimination is not very useful in the presence of errors and that there is no finite field variant of the least squares method. We discuss this result and some related results about other problems like Max-3Sat and basic graph problems. If time permits we will mention some more recent result.
_________________________________________________________________
Professor Hastad obtained his PhD from MIT in 1986, winning the ACM doctoral thesis award for his thesis, and he has been at KTH since 1988. He is most known for his work on the theory of computation, in particular, computational complexity theory. He is a Fellow of the Royal Swedish Academy of Sciences, Fellow of the AMS and Fellow of the ACM (Computer Science analogue of the AMS). He twice won the annual Goedel prize for outstanding papers in Theoretical Computer Science. In 2019 he won the Knuth award for his sustained record of outstanding contributions to the foundations of Computer Science. He won the Göran Gustafsson prize (annual national prize for outstanding scientific achievements) prize in Mathematics. He has been an invited speaker at both the International Congress of Mathematicians and the European Congress of Mathematicians. He has been a recipient of the ERC Advanced Investigator grant. He is the recipient of the most recent Milner award by the Royal Society, the premier European award for outstanding achievement in computer science.
Return to the list of Pascal Lectures ↑
Professor François Delarue, Université Côte d’Azur
Abstract: The aim of this presentation is to explore the regularizing effects of an infinite-dimensional common noise on mean-field game or control models. Ideally, it is expected that an infinite-dimensional common noise can enforce the uniqueness of solutions. However, the construction of such a forcing involves the introduction of a diffusion process taking values in the space of probability measures. Here, we study the impact of a Dirichlet-Fergusson type noise on a mean-field control problem and discuss the associated second-order Hamilton-Jacobi-Bellman equation. We also examine the impact, within the framework of one-dimensional MFGs, of the rearrangement of the stochastic heat equation on the uniqueness of equilibria. The presentation is based on several works with Mattia Martini and Giacomo Sodini, as well as William Hammersley and Youssef Ouknine.
François Delarue is a distinguished French mathematician and professor at Université Côte d’Azur, Nice, known for his work in stochastic analysis, probability theory, and partial differential equations. He earned his doctorate in mathematics in 2002 and went on to hold academic positions at Université Paris-Diderot and later at Nice-Sophia Antipolis. Delarue was a junior member of the Institut Universitaire de France (2014-2019), reflecting his significant contributions to mathematical research. He received the Maurice Audin Prize for Mathematics of the SMAI and the jointly awarded Joseph L. Doob Prize of the American Mathematical Society recognising his influential two-volume work "Probabilistic Theory of Mean Field Games with Applications." Furthermore, he was an invited speaker to the 2022 International Congress of Mathematicians and was awarded an ERC Advanced Grant in 2022.
Professor Eveliina Peltola, University of Bonn (IAM)
Abstract: About a hundred years ago, Charles Loewner introduced a recipe to encode planar growth into evolution of holomorphic maps. While his original motivation was purely in geometric function theory, this idea led to a success story also in the relatively modern field of random geometry, started about 75 years later. Namely, 25 years ago Oded Schramm introduced a random version of Loewner's evolution based on perhaps the most ubiquitous random object: standard Brownian motion.
The random growth process thus obtained --- now termed Schramm-Loewner evolution --- has been a key player in numerous recent breakthrough results (e.g., computation of the fractal dimension of planar Brownian frontier, proof of conformal invariance of critical planar lattice systems, models for random surfaces and quantum gravity via conformal welding). It has also turned out to share very deep and occasionally surprising connections to other areas of mathematics (e.g., Teichmueller theory, real algebraic geometry, and conformal field theory). I will give a glimpse to this classical topic from the perspective of the 21st century.
Dr. Eveliina Peltola is a mathematician working at the intersection of probability theory, mathematical physics, and complex analysis. She is an Associate Professor at Aalto University, Finland, and a Professor (Bonn Junior Fellow) at the University of Bonn, Institute for Applied Mathematics and Hausdorff Centre for Mathematics. She completed her B.Sc., M.Sc., and Ph.D. at the University of Helsinki, where her doctoral research focused on quantum groups and conformally invariant random geometry. After earning her Ph.D. in 2016, Peltola held a postdoctoral position at the University of Geneva with Professor Stanislav Smirnov.
Her work explores connections between Schramm–Loewner Evolution and Conformal Field Theory. Peltola has received multiple honors, including the 2024 Väisälä Prize from the Finnish Academy of Science and Letters. She leads an ECR Starting Grant Project, an Academy of Finland grant, and is a principal researcher for the Finnish Centre of Excellence in Randomness and Structures.
Professor Sir Martin Hairer FRS, Imperial College London
Abstract: The tiny world of particles and atoms and the gigantic world of the entire universe are separated by about forty orders of magnitude. As we move from one to the other, the laws of nature can behave in drastically different ways, sometimes obeying quantum physics, general relativity, or Newton's classical mechanics, not to mention other intermediate theories. Understanding the transformations that take place from one scale to another is one of the great classical questions in mathematics and theoretical physics, one that still hasn't been fully resolved. In this lecture, we will explore how these questions still inform and motivate interesting problems in probability theory and why so-called toy models despite their superficially playful character sometimes lead to certain quantitative predictions.
Martin Hairer studied at the University of Geneva, where he completed his PhD in Physics in 2001. He subsequently held positions at the University of Warwick (UK) and the Courant Institute (US), before moving to Imperial College London, where he currently holds a chair in probability and stochastic analysis. His work is in the general area of probability theory with a main focus on the analysis of stochastic partial differential equations.
Author of a monograph and over 100 research articles, Professor Hairer is a Fellow of the Royal Society as well as many other academies in Europe. His work has been distinguished with a number of prizes and awards, most notably the LMS Whitehead and Philip Leverhulme prizes in 2008, the Fermat prize in 2013, the Fröhlich prize and Fields Medal in 2014, a knighthood in 2016, the Breakthrough prize in Mathematics in 2020, and the King Faisal prize in 2022.
Dr Nira Chamberlain, President of IMA
Abstract: The 2017 film, Hidden Figures, is based on the true story of a group of black female mathematicians that served as the brains behind calculating the momentous launch of the NASA astronaut John Glenn into orbit. However, these mathematicians of colour are not the only ‘Hidden Figures’. Nira Chamberlain will discuss other inspirational men and women who overcame obstacles to prove that ‘mathematics is truly for everybody!’Black History Month, also initially known as the African American History Month, is a month-long tradition of celebrating the achievements of the black community. It began as a way for remembering important people and events in the history of the African diaspora. The event is celebrated every year in October in the UK.
To celebrate the contributions of black role models to the field of mathematical sciences, the Department of Mathematical Sciences, Durham University is pleased to have Dr Nira Chamberlain as guest speaker, who will be delivering the annual Pascal lecture 2020.
Nira Chamberlain is the current president of the Institute of Mathematics and its Applications (IMA). He has more than 25 years of experience of writing mathematical models/simulation algorithms that solve complex industrial problems. He has developed mathematical solutions within many industrial sectors, including spells in France, the Netherlands, Germany and Israel. In 2015 Dr Chamberlain joined the exclusive list of 30 UK mathematicians who are featured in the autobiographical reference book Who’s Who. He has held visiting positions in many prestigious UK universities.
Professor Peter Sarnak, IAS Princeton
Abstract: A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions. There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems. Joint works with Bourgain/Gamburd and with Ghosh.
________________________________________________________________
Peter Sarnak is a South African-born mathematician who has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, and is also on the permanent faculty at the School of Mathematics of the Institute for Advanced Study. He is known for his work in analytic number theory. Peter is the recipient of many prestigious prizes, such as the George Pólya Prize (1998), the Ostrowski Prize (2001), the Levi L. Conant Prize (2003), the Cole Prize (2005) and the Wolf Prize (2014).
Professor Peter Diggle, Lancaster University
Abstract: A spatiotemporal point process, P, is a stochastic model for generating a countable set of points (x(i), t(i)) ∈ IR2 × IR+, where each x(i) denotes the location, and t(i) the time, of an event of interest. A typical data-set is a partial realisation of P restricted to a specified spatial region A and time-interval [0,T], possibly supplemented by covariate information on location, time or the events themselves. In this talk, I will first give examples of different interpretations of this scenario according to whether only one or both of the sets of locations and times are stochastically generated. I will then discuss in more detail methods for analysing spatiotemporal point process data based on two very different modelling approaches, log-Gaussian Cox process models; and conditional intensity models, and describe applications of each in the context of human and veterinary epidemiology.
Peter Diggle is a Fellow of the Royal Statistical Society and Distinguished University Professor in the Lancaster Medical School, and holds a part-time post at the University of Liverpool, Department of Epidemiology and Population Health. He also has adjunct appointments at the Johns Hopkins University School of Public Health, Columbia University International Research Institute for Climate and Society, and Yale University School of Public Health. He is a trustee for the Biometrika Trust, a member of the Advisory Board for the journal Biostatistics, chair of the Medical Research Council’s Strategic Skills Fellowship Panel and President-Elect of the Royal Statistical Society. His research concerns the development and application of statistical methods relevant to the biomedical and health sciences.
Professor Caroline Series, University of Warwick
Abstract: In 2014, Maryam Mirzakhani of Stanford University became the first women to be awarded the Fields medal. The starting point of her work was a remarkable relationship called McShane’s identity, about the lengths of simple closed curves on certain hyperbolic surfaces. The proof of this identity, including the Birman-Series theorem about simple curves on surfaces, uses only quite basic ideas in hyperbolic geometry which I will try to explain. We will then look briefly at Mirzakhani’s ingenious way of exploiting the identity and where it led.
Caroline Series is Emeritus Professor of Mathematics at the University of Warwick, where she has been since 1978. Following her first degree at Somerville College, Oxford, she won a Kennedy Scholarship to Harvard where she did a Ph.D. under George Mackey. Her early research was in dynamical systems and chaos, for which she won an LMS Junior Whitehead prize in 1987. She held an EPSRC Senior Research Fellowship in 1999 -- 2004. A flavour of her recent work, about the geometry of three dimensional hyperbolic manifolds and the fractal sets associated to their symmetry groups, can be gained from her widely praised book Indra's Pearls, coauthored by D. Mumford and D. Wright, recently republished in paperback (CUP 2015).
Professor Series has served the mathematical community on many committees both national and international, and was a member of both the RAE and REF maths panels. She has given many distinguished public lectures. Throughout her career she has taken a leading role in encouraging women mathematicians. In 2014, she was awarded the first Senior Anne Bennett prize of the London Mathematical Society and she is vice-chair of the newly formed IMU Committee for Women in Mathematics.
Professor Dimitri Petritis, Université de Rennes
Abstract: Starting from a simple example (sharp gambles with a classical dice) we shall describe progressively more involved systems (like unsharp gambles with classical dice and hidden Markov chains). Then a physical experiment showing the insufficiency of classical probability to describe Nature will be explained and the notion of quantum probability and of repeated unsharp quantum measurements will be introduced. We shall conclude with a limit theorem concerning repeated quantum measurements.
______________________________________________________________
Dimitri Petritis is based at the Université de Rennes. He joined the Institut de Recherche Mathématique de Rennes there in 1989, and since 2008 has held the position of `Professor of exceptional class'. Dimitri's research is broadly concerned with uncertainty and randomness in physical systems, in the context of probability theory, ergodic theory, mathematical physics, and information theory. Dimitri received his Ph.D. from École Polytechnique on `Zero Mass Effects in Quantum Field Theory' (1984). His subsequent research has focused on statistical mechanics and stochastic processes, with recent work concerning queueing systems and processes in disordered media. Other interests include classical and quantum information, and mathematical biology. Dimitri has held a number of visiting professor positions around the world, and has supervised a number of doctoral students.
Professor Gary Gibbons FRS, University of Cambridge
Abstract: I will begin by providing a short history of the soliton concept, as intended to eliminate the distinction between particles on the one hand and fields on the other. I will then discuss how the idea has fared in General Relativity and bring the story up to date with some remarks about extreme black holes, p-branes and fuzz-balls. If time permits, I will also mention some recent work on how solitons in the absence of gravity can give rise to interesting "emergent" spacetimes.
Gary Gibbons is Professor of Theoretical Physics in DAMTP, Cambridge University, where he has spent most of his career. He was elected a Fellow of the Royal Society in 1999, and to a Professorial Fellowship at Trinity College Cambridge in 2002.
Professor Antti Niemi, University of Uppsala
Abstract: The biological function of a protein depends critically on its three dimensional geometry. But at the moment we do not know how the shape of a protein could be deduced from the DNA sequence alone. As a consequence the protein folding problem endures as one of the most important unresolved problems in science, it addresses the origin of life itself. In this talk we shall argue, that the shape of a protein can actually be determined from very general principles, that are also utilized in the context of string theory and integrable models. We shall argue, that there is a universal energy function which relates to the discrete nonlinear Schrodinger equation, the paradigm integrable lattice model, that describes all known folded protein structures. We show how to derive this energy function from fundamental geometrical concepts. We show that it supports soliton solutions, that describe folded proteins with a precision where the root-mean-square distance between an experimental crystallographic structure in Protein Data Bank and its theoretical description is less than the radius of a carbon atom. We present a number of examples of numerical simulations that show how a protein folds. The simulations are performed with laptop computer, and the simulation proceeds practically as fast as the folding does in vivo.
The Pascal Fellow 2013 is Antti Niemi, CNRS Professor of Theoretical Physics at the University of Tours in France and also at Uppsala University in Sweden. He has worked on a variety of areas in theoretical physics from quantum field theory to classical solitons, and his current research interests involve various aspects of biophysics and mathematical biology. Professor Niemi is a member of the Royal Swedish Academy of Sciences. In 1994, he was awarded the Goran Gustafsson Prize by the Royal Society of Sciences of Sweden.
Professor Jose Seade, Universidad Nacional Autónoma de México
Abstract: Classical Kleinian groups are discrete groups of automorphisms of the Riemann sphere, which can be regarded as being the complex projective line CP1. The study of these type of groups has played for decades a major a role in various areas of mathematics. In this talk we shall discuss how this theory generalizes to discrete groups of automorphisms of the complex projective space CP2, and more generally of CPn. This includes the particularly interesting class of discrete groups of holomorphic isometries of complex hyperbolic spaces.
The Pascal Fellow 2012 is Jose Seade, Professor in the Mathematics Institute of the National Autonomous University of Mexico (UNAM). Professor Seade has been a member of the Mexican Academy of Sciences since 1983 and President of the Mexican Mathematical Society in 1986-87. He has also been President of the Third World Academy of Sciences since 2003. In 2012, Professor Seade was awarded the Ferran Sunyer i Balaguer Prize together with Dr Angel Cano and Dr Juan Pablo Navarrete for a monograph entitled `Complex Kleinian Groups'.
To see other seminars and events that are being held in the Department of Mathematical Sciences please click here.
/prod01/prodbucket01/media/durham-university/departments-/mathematical-sciences/Maths-2-3-2-4029X1177.jpg)