# Kirill Krasnov

## Contact Information

- 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

## Research Interests

I am interested in different formulations of General Relativity. The aspects of most interest to me are how non-renormalisability of perturbative quantum gravity manifests itself in different formulations, and how different formulations suggest different paths towards unification of gravity with other interactions. I am also interested in the relation "Gravity is the square of Yang-Mills theory" that is visible in the scattering amplitudes of both theories, and implications this relation has for the UV divergences in quantum gravity.

I am interested in the geometry of 3-forms in 6 and 7 dimensions, and thus in aspects of geometry of manifolds of exceptional holonomy. These geometrical structures are central to the idea that 4D General Relativity arises as the dimensional reduction of a certain diffeomorphism invariant theory of differential forms in higher dimensions. This idea is what I am currently developing.

A good overview of my current interests can be formed by looking at my most recent papers on the arxiv. See also slides of some of my talks below.

## Some Talks

Deformations of General Relativity Perimeter Institute, May 2010
Renormalized Volume of Hyperbolic 3-Manifolds Teichmüller Theory and its Interactions in Mathematics and Physics, Bellaterra, June 2010
Moduli space of shapes of a tetrahedron and SU(2) intertwiners Moduli spaces in Mathematics and Physics, Strasbourg, September 2010
Gravity as a diffeomorphism invariant Gauge Theory Lorentz geometry in Mathematics and in Physics, Strasbourg, June 2011
Gauge Theory Approach to Gravity EPFL seminar, September 2011
Gauge Theory Approach to Gravity Saclay/Bad Honnef/Utrecht talk, January-March 2012
Gravity as Gauge Theory Brussels/IHES/York/Oxford talk, December 2012-February 2013
Gravity as Gauge Theory Munich talk, July 2013
Diffeomorphism invariant gauge theories Loops 2013 talk, July 2013, Perimeter Institute, Canada
Perturbative Quantum Gravity Luxembourg talk, September 2013
Diffeomorphism invariant gauge theories Oxford Geometry and Analysis seminar, November 2013
One-loop beta-function for an infinite parameter family of gauge theories Probing the Fundamental Nature of Spacetime with the Renormalization Group, Nordita Workshop, March 2015
Gravity vs. Yang-Mills theory XXXV Max Born Symposium, Wroclaw, Poland, 7 - 12 September 2015
Colour/Kinematics Duality and the Drinfeld Double of the Lie algebra of Diffeomorphisms QCD meets gravity workshop, Higgs Center, Edinburgh, April 4-8, 2016
3D/4D Gravity as the Dimensional Reduction of a theory of 3-forms in 6D/7D International Loop Quantum Gravity Seminar, February 21, 2017
Quantising Gravitational Instantons GARYFEST: Gravitation, Solitons and Symmetries, March 22-24, 2017
SO(7,7) structure of the SM fermions Perimeter Institute, February 2019

## Series of lectures on formulations of General Relativity

In February 2019 I gave four lectures on "Formulations of General Relativity" at Perimeter Institute, Canada.

Lecture 1: Motivations, metric and related formulations (Einstein-Hilbert, Palatini, Eddington-Schoedinger), first half of the presentation of tetrad formulations, including discussion of soldering and finishing with Einstein-Cartan action.
Lecture 2: Tetrad related formulations (Einstein-Cartan, Teleparallel, MacDowel-Mansouri, Stelle-West), followed by the presentation of BF-type formulations, including the discussion of the pure spin connection formulation.
Lecture 3: Discussion of the BF-type formulations finished, followed by the presentation of chiral formalisms for GR in four spacetime dimensions. Discussion of the self-dual/anti-self-dual decomposition of the Riemann curvature. Chiral Einstein-Cartan action. Chiral description of the Yang-Mills theory.
Lecture 4: Spinor form of the chiral Einstein-Cartan, chiral pure connection formulation to second order. Encoding the metric into knowledge of which forms are self-dual. Geometry of Plebanski formulation of GR. Chiral pure connection action in closed form. Chiral formulations of BF plus potential for the two-form field type. Summary and conclusions.

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

Introductory slides
Parts I,II
Part III
Part IV