Abstract: Algebraic geometry is a subject with ancient origins, which studies geometric objects that can be described by polynomial equations. I will discuss the motivating questions of the field through sketching its history, starting with the Greeks’ investigation of conic sections and Newton’s of cubic curves, through to modern developments. I will touch on some advanced topics which can play a role in development-focused research in particular.

Abstract: Around 700 BC, Queen Didon arrived in the north of Africa where she found a king who granted her a portion of his land that could only be surrounded by the skin of an ox. Didon cut this skin into a narrow band and used it to delimit the edge of a semi-circular territory centered at a point of the coast.  She thus obtained the vastest possible ground to build a citadel which was then the acropolis of Carthage. In doing so, Didon had found the solution of the “isoperimetric problem in a half plane.” We will discuss some isoperimetric problems, inequalities and their applications to quantum mechanics.

Abstract: In the past three years, the LIGO and Virgo gravitational wave (GW) detectors have announced the discovery of ten binary black hole mergers as well as the the first binary neutron star merger GW170817. The discovery of both gravitational wave and electromagnetic (EM) radiation from this binary neutron star merger, GW170817, has opened up a new era of multi-messenger physics. Although only a single event, the unprecedented EM follow-up and joint GW+EM characterization have offered us a new perspective on the Universe enabling critical insights into diverse fields from gravity, high-energy astrophysics, nuclear physics, to cosmology. In this talk, I will give a brief overview of the GW discovery and EM follow-up of this event, and then discuss how to place compact object mergers in their full cosmological context using joint GW+EM measurements. I will conclude by discussing the lessons that we are learning from this one event and the remarkable opportunities and challenges that have emerged in this new observationally driven and fast paced field as we move from the discovery era to one of precision physics in the next decade.

Abstract: Quantum computers are different. They process information using fundamental principles of quantum mechanics: superposition, entanglement and interference. Making cunning use of these principles, quantum computers can outperform classical computers for specific computational tasks.

Software for quantum computation has a layered structure. Closest to the hardware is the `quantum control’ of physical qubits. One layer up is the compilation of `native’ quantum gates into a universal gate library and quantum circuits of increasing complexity. The top layer is a quantum algorithm for a concrete computational task. Recent experimental progress has allowed the execution of all layers of this software stack on small qubit systems, and the comparison of the performance of different platforms.

My lecture will introduce the subject and reflect on the current status, often characterised as NISQ (Noisy Intermediate Scale Quantum). I will also discuss ideas for quantum control directly at the level of N coupled quits, surpassing the approach based on 1- and 2-qubit gates.

Abstract: The Cosmic Microwave Background (CMB) is the radiation emitted when the universe was about 380,000 years old. The target of the current CMB experiments is the detection of the CMB polarized component, the so called B modes. A B modes detection, in fact, would provide  unique insights into the primordial universe. In particular, it would confirm the inflationary theory, according to which the primordial universe underwent a supernatural expansion.

A CMB telescope has to measure tiny polarized signals (i.e., fractions of micro-Kelvin) in a frequency band centered at 150GHz. Such a challenging scientific target requires large focal planes populated with superconducting  detectors cooled down to 0.3 K. Moreover, microwave detectors demand very dry telescope sites, such as the Atacama desert, the South Pole or the Tibetan plateau. Since many instrumental effects and astrophysical sources can mimic the cosmological signal, an accurate control of the systematic effects and sky observations in a large frequency coverage (e.g. 40-270GHz) are also necessary.

After presenting the main properties of the CMB, I will discuss the working strategy and the technology of a typical CMB telescope.

Abstract: The MeerKAT radio telescope has been constructed in the Karoo region of South Africa, and in the process of being commissioned. It is the most sensitive radio telescope in the world over the frequency bands in which it operates, and is the largest single scientific instrument in Africa. The core telescope was funded by the South African government, and the majority of the design and construction work was done in South Africa. Additional instrumentation that extends the capabilities of the core telescope have been provided by partner institutions in The UK, Germany, Australia and the USA.  MeerKAT is a precursor for the larger, internationally funded Square Kilometre Array (SKA) telescope that is planned for construction within the next decade.  As a precursor, MeerKAT is a pathfinder for technologies to be used for the SKA, and will conduct preparatory science observations for the SKA. This talk provides a technical overview of the MeerKAT telescope, including how engineering design decisions were made to maximize the science capabilities of the telescope.  The science objectives of the telescope will be introduced, and early scientific results that have been obtained will be presented.

Abstract: Observations of redshifted 21-cm emission of neutral hydrogen over a wide range of radio frequencies allow us to access redshifts that encompass a vast comoving volume, including the  era of dark energy. In this talk I will present the Hydrogen Intensity Mapping and Real time Analysis eXperiment (HIRAX) project, which is a proposed 21cm intensity mapping experiment operating at 400-800 MHz that will measure the evolution of dark energy over the redshift range z=0.8-2.5 by using the characteristic baryonic acoustic oscillation scale as a standard ruler. The HIRAX radio telescope array will be sited in the radio-quiet Karoo astronomy reserve in South Africa and will ultimately comprise 1024 dishes, each six metres in diameter, placed in a compact configuration. I will discuss the design and project status of HIRAX and its scientific prospects. This includes dark energy forecasts as well as prospects for interesting cosmological constraints from cross-correlations of HIRAX data  with other large-area, southern-sky cosmological surveys. *** HIRAX will also discover a large number of pulsars and transients including fast radio bursts (FRBs). I will describe our programme to localise these FRBs using HIRAX outriggers in African partner countries.

Abstract: Wojtak, Hansen and Hjorth and others have measured the long-predicted gravitational redshift of light escaping from galaxy clusters. The result seemed to agree with the prediction of Einstein’s general relativity and to conflict with some alternative gravity theories. Here I shall discuss a number of puzzling and surprising aspects of the gravitational redshift and to what extent it may be a useful test of cosmology and gravity in the future.

Abstract: Models with incomplete data are often used to describe phenomenon arising in the real world including environmental problems. The talk is devoted to some mathematical methods that might help to control such models.

Abstract: In the view of the speaker, many young students who are working for a Ph.D., or later doing research, focus far too much on finding a direct path to their anticipated results. In this talk I will try to show the benefits of taking a much broader view of the subject under discussion, and of searching for unlikely connections with other subjects, and I will illustrate this with examples taken over 55 years of experience in research and writing. I shall also discuss how this broader view impacts on speaking about, and writing on, mathematics. Of course, others will have different views, but my objective here is to stimulate discussion on this important topic.

Abstract: I will describe an approach to the mathematical study of biology that begins with formulating empirically informed hypotheses about biological phenomena followed by assessment of the deductive validity of these with the help of models. The models thus constructed provide a foundation for discovering new insights about the phenomena of interest, thus serving as a bridge between the known and the knowable unknown. I’ll use recent examples from my group’s work for illustration.

Abstract: This talk will discuss the applicability of the formalism of quantum mechanics to everyday life. Lie algebra theory will be argued to be a very useful tool in guiding the construction of quantum descriptions of situations in which coming to a conclusion about one thing might affect thinking about another.  It will be suggested that the recognition and incorporation of such mathematical structure into machine learning and artificial intelligence might lead to significant efficiency and generality gains in addition to ensuring probabilistic reasoning at a fundamental level.

Abstract: Feynman’s path integral provides an elegant formulation of quantum physics, particularly suited to theories with continuous symmetries, like gauge theories and general relativity. However, it has proven difficult to rigorously define path integrals without first performing a Wick rotation to Euclidean time, significantly compromising the study of nonperturbative quantum dynamics. We have been developing a new approach to real time path integrals, allowing us to calculate spacetime amplitudes for quantum fields and particles and gravity without a Wick rotation. Surprising applications include quantum cosmology (for example, Hartle and Hawking’s famous no boundary proposal) and strong interference effects in radio astronomy.

Abstract: The theory of elliptic curves is an elegant and vast subject in mathematics that can be traced back to ancient Greece and beyond. Elliptic fibrations play a central role in many questions of string geometry and in the classification of certain superconformal field theories. I will review the history of elliptic curves and recent developments in the theory of elliptic fibrations with a special interest for their applications in birational geometry and string geometry.

Abstract:This talk has two parts. In the first, we illustrate how scientific computing can be used to guess some results and then provide a formal proof. In fact, we revisit the well-known result stating that the Hermite interpolation polynomials of a function $f$ continuous on $[-1,1]$, with the zeros of the Chebyshev polynomials of the first kind as nodes, converge uniformly to $f$ on $[-1,1]$. Then we extend this result to obtain the uniform convergence of the Hermite interpolation polynomials, with the nodes taken as the zeros of the Chebyshev polynomials of the second, third and fourth kind, not on the interval $[-1,1]$ but rather on its sub-intervals.
In the second part, we will speak about the Cooperative Education Master Program launched in the AIMS Network and at AIMS Cameroon and illustrate with two success stories of our students its great potential to bridge university and industry in Africa and change the mindset by using mathematical sciences to address some of the relevant challenges faced by industry.

Abstract: The Kitaev quantum double models were originally proposed to exploit topological phases of matter for fault-tolerant quantum computation. In this talk, I show that they can be generalised to a framework based on a quantum group K acting on another quantum group A. I describe how the Kitaev model which is based on the Drinfeld quantum double D(H) of a Hopf algebra H acting on H and the recently proposed model for Majid’s mirror bicrossproduct quantum group M(H) acting on H∗ are particular examples of this general construction.

Public Lecture:

17. Neil Turok (Perimeter Institute), “Universe”, 10AM Tuesday 8 July 2019 at University of Rwanda

Abstract: The world is governed by laws we can learn from observation, experiment and logical reasoning. Recently, the pace of discovery has accelerated. We can map the radiation left over from the big bang. We can directly observe black holes and the gravitational waves they emit. We can watch the creation of gold, platinum and uranium when neutron stars collide. The universe is a giant laboratory where the laws of physics are tested to extremes. What we have learned is amazing: the universe is astonishingly simple, yet deeply paradoxical. Everything emerged from a brilliant point of light around fourteen billion years ago. It is all heading towards a vast, empty future. The challenge for twenty first century physics is to make sense of these puzzles, and use that knowledge to improve the world. Doing so will require brilliant young scientists. Africa has the world’s youngest population, with strong motivations to enter and pursue science. Africa is the natural place to look for the next Einstein, and encourage her or him to open new doors to humankind’s future.

Brief biography:
Neil Turok (PhD Imperial College London, 1983) is Emeritus Director and Niels Bohr Chair at the the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. He was previously Professor of Physics at Princeton and Chair of Mathematical Physics at Cambridge. Turok’s research focuses on developing and testing theories of the origins and evolution of the universe. His predictions for the correlations of the polarization and temperature of the cosmic background radiation (CBR) and of the galaxy-CBR correlations induced by dark energy were observationally confirmed. He has pioneered the investigation of many theories of cosmogenesis. He is Director of the Centre for the Universe at Perimeter Institute.

Born in South Africa, Turok founded the African Institute for Mathematical Sciences (AIMS) with centres in South Africa, Senegal, Ghana, Cameroon, Tanzania, and Rwanda. For this work and for his research, Turok was awarded a TED Prize in 2008. In 2012, he delivered the CBC Massey Lectures, broadcast across Canada and published as The Universe Within, a prizewinning bestseller. In 2014 he was elected to the Royal Society of Canada. In 2016 he was made an Honorary Fellowship of the UK Institute of Physics and awarded the John Torrence Tate Medal of the American Institute of Physics for International Leadership in Physics. In 2018 he was named an Officer of the Order of Canada.  In 2019, the magazine Jeune Afrique named him the 60th most influential person in Africa – with one of AIMS’ young Professors at number 54. He currently serves as co-Chair of the National Council for Science and Technology for the Government of Rwanda.