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- Sebastian Steinhaus

In my research on quantum gravity, I mainly focus on spin foam models, which is a discrete path integral approach closely related to loop quantum gravity. A typical spin foam can be imagined to mediate between an initial and final (discrete) 3D geometry, which are encoded in so-called spin network states. Then the spin foam assigns an amplitude to this transition by summing over all 4D geometries compatible with this boundary data.

In any discrete theory, we must address the question whether the dynamics are consistent, that is do not depend on the ambigious choices made in its definition, and how to establish a connection back to well-known continuum physics. Indeed, both issues are crucial for making contact with observations.

Both these issues can be tackled by studying renormalization of spin foams; the idea is the following: consider a coarse and a fine boundary. The fine boundary can naturally store more information, i.e. it comes with a larger Hilbert space, but, given a coarse state, this state can also be represented in the finer, more complex, Hilbert space. Relating and identifying states across Hilbert spaces is crucial, since we can then compare coarser and finer spin foams for the *same* transition. Generically we have to assign different spin foam amplitudes to both discretisations in order to get consistent results; a renormalization group flow of amplitudes.

To implement such a procedure non-perturbatively using numerical methods is indispensable. A class of algorithms perfectly matching this renormalization scheme is tensor network renormalization, which is a strong research focus at Perimeter. Recently I have also studied simplified, restricted 4D spin foam models using Monte Carlo methods and found encouraging results, e.g. indications for a UV-attractive fixed point. In addition to extending on these previous results, I am also looking at extracting effective quantities out of spin foams, e.g. their spectral dimension, and coupling matter to the dynamical geometry encoded in a spin foam.

A list of my research interests include:

- Background independent approaches to quantum gravity, e.g. spin foams or loop quantum gravity

- Renormalization of background independent theories

- Tensor network renormalization

- Monte Carlo techniques for renormalization

- Machine Learning for renormalization

- Observables in general covariant systems

- Matter coupling in quantum gravity

- 2017 - present, Perimeter Institute f. Theoretical Physics, Waterloo, Canada, postdoctoral researcher
- 2014 - 2017, II. Institute f. Theoretical Physics, Hamburg University, Hamburg, Germany, postdoctoral researcher
- 2012 - 2014, Perimeter Institute for Theoretical Physics, Waterloo, Canada, PhD student
- 2010 - 2012, Albert Einstein Institute, Potsdam, Germany, PhD student
- 2009 - 2010, Albert Einstein Institute, Potsdam, Germany, Diploma student

- Emergence of Spacetime in a restricted Spin-foam model, Sebastian Steinhaus and Johannes Thürigen, Phys. Rev. D98 (2018) no.2, 026013, arXiv: 1803.10289
- Hypercuboidal renormalization in spin foam quantum gravity, Benjamin Bahr and Sebastian Steinhaus, Phys.Rev. D95 (2017) no.12, 126006, arXiv: 1701.02311
- Coarse graining flow of spin foam intertwiners, Bianca Dittrich, Erik Schnetter, Cameron J. Seth and Sebastian Steinhaus Phys. Rev. D94 (2016) no.12, 124050, arXiv: 1609.02429
- Numerical evidence for a phase transition in 4d spin foam quantum gravity, Benjamin Bahr and Sebastian Steinhaus, Phys. Rev.Lett. 117 (2016) no.14, 141302, arXiv: 1605.07649
- Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners, Benjamin Bahr and Sebastian Steinhaus, Phys. Rev. D93 (2016) no.10, 104029, arXiv: 1508.07961
- Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models, Sebastian Steinhaus, Phys. Rev. D92 (2015) no.6, 064007, arXiv: 1506.04749
- Decorated tensor network renormalization for lattice gauge theories and spin foam models, Bianca Dittrich, Sebastian Mizera and Sebastian Steinhaus, New J. Phys. 18 (2016) no.5, 053009, arXiv: 1409.2407
- Discretization independence implies non-locality in 4D discrete quantum gravity, Bianca Dittrich, Wojciech KamiÅski and Sebastian Steinhaus, Class.Quant.Grav. 31 (2014) no.24, 245009, arXiv: 1404.5288
- Quantum group spin nets: refinement limit and relation to spin foams, Bianca Dittrich, Mercedes Martin-Benito and Sebastian Steinhaus, Phys.Rev. D90 (2014) 024058, arXiv: 1312.0905
- Time evolution as refining, coarse graining and entangling, Bianca Dittrich and Sebastian Steinhaus, New J.Phys. 16 (2014) 123041, arXiv: 1311.7565
- The Barrett-Crane model: asymptotic measure factor, Wojciech KamiÅski and Sebastian Steinhaus, Class.Quant.Grav. 31 (2014) 075014, arXiv: 1310.2957
- Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions, Wojciech KamiÅski and Sebastian Steinhaus, J.Math.Phys. 54 (2013) 121703, arXiv: 1307.5432
- Path integral measure and triangulation independence in discrete gravity, Bianca Dittrich and Sebastian Steinhaus, Phys.Rev. D85 (2012) 044032, arXiv: 1110.6866
- Perfect discretization of reparametrization invariant path integrals, Benjamin Bahr, Bianca Dittrich and Sebastian Steinhaus, Phys.Rev. D83 (2011) 105026, arXiv: 1101.4775
- Renormalization in symmetry restricted spin foam models with curvature, Benjamin Bahr, Giovanni Rabuffo and Sebastian Steinhaus, arXiv: 1804.00023

- Spin foams and background independent renormalization, Jena, Germany
- Spectral dimension of cuboid spin foams, Nijmegen, Netherlands
- Spectral dimension of cuboid spin foams, 6th Tux workshop on quantum gravity, Tux, Austria
- Renormalizing spin foam models: quantum cuboids and beyond, Plenary talk @ Loops'17 conference, Warsaw, Poland
- Coupled intertwiner dynamics: a toy model for coupling matter to spin foams, Quantum spacetime and renormalization workshop, Leiden, Netherlands
- PIRSA:17060087, Tutorial: Coarse-graining of Spin Foams, 2017-06-22, Making Quantum Gravity Computable
- PIRSA:17060080, Tutorial: Coarse-graining of Spin Foams, 2017-06-21, Making Quantum Gravity Computable
- PIRSA:15090085, Coarse Graining Spin Net Models, 2015-09-30, Renormalization in Background Independent Theories: Foundations and Techniques
- PIRSA:14050124, Phases for (analogue) spin foam models, 2014-05-21, Quantum Gravity Day 2014
- PIRSA:14050037, HPC in Quantum Gravity, 2014-05-07, Compute Ontario Research Day
- PIRSA:13070041, Spin Foams - 1, 2013-07-22, Loops 13

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