- office:
School of Mathematical Sciences

The Mathematical Sciences Building, Office C12

University of Nottingham

Nottingham, NG7 2RD, UK

- phone: (+44) 115 951 3866
- fax: (+44) 115 951 4951
- email: kirill.krasnov at nottingham dot ac dot uk

I was born in Kyiv, Ukraine in 1973. For the last 3 years of my school studies I attended a specialist "mathematics class". I had a great teacher in both maths and physics, but physics appealed more to me, and in 1989 I became an undergraduate student in the Faculty of Physics of Kyiv's Taras Schevchenko University. I graduated with distinction with specialisation "Theoretical Physics" in 1994. For the next few years I was a graduate student (called "aspirant" in the Soviet academic system) in the Bogolyubov Institute for Theoretical Physics, Kyiv. My official supervisor was Petro Ivanovich Fomin, and these are his lectures that got me interested in quantum gravity. The other person who was important in my formation was Yuri Shtanov, from whom I learned about loop quantum gravity, and who remains a good friend and collaborator till this day. Another person who had a great influence on me was Petro Ivanovich Holod, who ran a student seminar on the geometry of integrable systems, where I was an active participant.

In 1996 I became a PhD student in the Physics Department of the Pennsylvania State University, USA. My PhD advisor was Abhay Ashtekar. I started working on the topic of black hole entropy in loop quantum gravity while still in Kyiv, and after coming to the USA I co-authored several papers that later became my most cited works. During the same time I became interested in the subject of "Spin Foam Models of Quantum Gravity", which was just crystallizing around that time, and which became the topic of my PhD dissertation. I got my PhD in 1999, and in the same year became a postdoc in the Physics Department of the University of California in Santa Barbara. In 2002 I moved to Germany, to a long-term (5-year) researcher position in the Albert Einstein Institute for Gravitational Physics in Golm. I started on a lecturership in the University of Nottingham, UK in 2004, where I am ever since.

I had an EPSRC Advanced Fellowship during 2004-2010, supporting my research on the geometry of 3-manifolds and the renormalised volume. I held an ERC Consolidator Grant during 2011-2017, supporting my work on the chiral descriptions of GR. I became a full professor in Nottingham in 2012.

Gravity = geometry, but there are many different ways to interpret the "geometry" part of this equation. The standard way uses the Riemannian geometry of metrics, but there are other "geometries" that can be used to describe gravity. Thus, there is Cartan's viewpoint that uses tetrads and the spin connection. Related to this is a series of formalisms specific to four spacetime dimensions that are chiral. There is a beautiful and potentially deep geometry underlying the chiral 4D descriptions, and I have spent more than a decade learning and developing the chiral language for 4D GR.

This story is summarised in a book titled "Formulations of General Relativity: Gravity, spinors and differential forms", published by Cambridge University Press. It collects and describes formulations of GR that can be phrased in the language of differential forms. Particular emphasis is given to the chiral formulations of 4D GR. I also describe aspects of the twistor story, and in particular describe the geometry of the Euclidean signature twistor space, as this relates to the chiral description of the Euclidean 4D gravity.

A taster pdf-file containing the Table of Contents, Preface, Introduction and Concluding Remarks is available here.

Slides for all the lectures are contained below in 4 pdf-files.