Objective The thermodynamic behavior of black holes is a precious clue in unravelling the microscopic structure of quantum gravity.High precision computations of quantum black hole entropy provide a new window into the fundamental microscopic theoryof gravity and its deviations from classical general relativity. Traditional methods of quantum field theory have proved to benot well-suited to perform these computations. Two breakthroughs in my recent work establish new ground for progress.On one front, a new method to sum up all perturbative quantum contributions to the entropy of a large class of black holeshas been developed. This gives rise to the first exactly solvable model of a quantum black hole. On a second front, a longstanding theoretical obstacle called the wall-crossing problem has been cleared in my recent work on the microscopicdescription of black holes in string theory. The newly-developed field of mock modular forms is shown to be the correctframework to address questions of exact black hole entropy. This makes a large class of microscopic models amenable toanalytic control, many of which were previously beyond reach.These developments open up a new line of research that I propose to pursue along two intersecting avenues. First, I aim toextend the computations of exact quantum black hole entropy towards models of realistic black holes. Second, I aim toadvance the theoretical understanding of quantum black holes by investigating the deeper origins of mock modularsymmetry. As a concrete application, I aim to establish that newfound group-theoretical structures called “moonshine”symmetries are physically realized in quantum black holes, thus opening up connections between two exciting fields ofresearch previously thought to be distinct. Together, the broad goal is to explain black hole microstructure throughsystematic computations of exact quantum entropy, and to investigate its consequences on the fundamental microscopictheory of gravity. Fields of science natural sciencesphysical sciencesrelativistic mechanicsnatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesphysical sciencesastronomyastrophysicsblack holesnatural sciencesphysical sciencestheoretical physicsstring theory Keywords Black hole entropy String theory Supersymmetric localization Automorphic forms Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-CoG-2015 - ERC Consolidator Grant Call for proposal ERC-2015-CoG See other projects for this call Funding Scheme ERC-COG - Consolidator Grant Host institution KING'S COLLEGE LONDON Net EU contribution € 1 759 064,00 Address STRAND WC2R 2LS London United Kingdom See on map Region London Inner London — West Westminster Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 759 064,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all KING'S COLLEGE LONDON United Kingdom Net EU contribution € 1 759 064,00 Address STRAND WC2R 2LS London See on map Region London Inner London — West Westminster Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 759 064,00
