Liam Solus

I am an associate professor of mathematics with specialization in combinatorics and probability in artificial intelligence at KTH Royal Institute of Technology. I am an affliated faculty of the Wallenberg AI, Autonomous Systems and Software Program (WASP) and a faculty member of the Center for Digital Futures at KTH.  Previously, I was a United States National Science Foundation Postdoctoral Fellow at KTH, and a postdoctoral fellow at Institute of Science and Technology Austria.  I completed my PhD in mathematics under the supervision of Benjamin Braun at the University of Kentucky in November 2015.

 

Research Interests

• statistics
• causality
• algebraic statistics
• applied algebra
• algebraic/geometric/enumerative combinatorics
• discrete geometry

Upcoming and Recent Activities (updated 13 January 2025)

• I will be speaking at Effective Methods in Algebraic Geometry (MEGA) 2026 taking place 6-10 July 2026 at Durham University, United Kingdom.

• I will be participating in the workshop on Metric Algebraic Geometry taking place 22-26 June 2026 at Institut Mittag-Leffler.

• I will be speaking at the North British Probability Seminar at the University of Edinburgh on 26 May 2026.

• I will be speaking at the workshop Rigid Structures in Algebraic Combinatorics and Algebraic Statistics taking place 18-22 May 2026 at ICMS, Bayes Center, Edinburgh

• I will be speaking at the Combinatorial Coworkspace - A Session on Algebraic and Geometric Combinatorics taking place 20-28 March 2026 at Haus Bergkranz, Hirschegg, Kleinwalsertal, Austria.

• I will be speaking at the conference Statistics and Algebraic Geometry at University of Lille in France 12-13 March.

• I was appointed a Mercator Fellow of the Combinatorial Synergies DFG Priority Program. To kick this off, I will be visiting University of Osnabrück 16 Feb - 10 March 2026.

 

Publications

T. Boege, K. Kubjas, P. Misra and L. Solus.
Colored Gaussian DAG models.
Journal of the Royal Statistical Society Series B: Statistical Methodology (2025): qkaf068.

E. Duarte and L. Solus.
Representation of context-specific causal models with observational and interventional data.
Journal of the Royal Statistical Society Series B: Statistical Methodology (2025): qkaf059.

D. Deligeorgaki, B. Han and L. Solus.
Colored multiset Eulerian polynomials.
To appear in Combinatorial Theory (2025).
Article Sumary published in the Proceedings of FPSAC 2025, Seminaire Lotharingien de Combinatoire.

M. Juhnke, L. Solus and L. Venturello.
Triangulations of cosmological polytopes.
Algebraic Combinatorics 8.4 (2025): 1141-1168.

Y. Wu, A. Markham, L. Wang, L. Solus and Z. Ma.
Data-driven causal behaviour modelling from trajectory data: A case for fare incentives in public transport.
Journal of Public Transportation, 27, 100114 (2025).

E. Duarte and L. Solus.
Algebraic geometry of discrete interventional models.
Varieties, Polyhedra, Computation. European Mathematical Society-EMS-Publishing House GmbH, 2025. 413-454.

S. Linusson, P. Restadh, L. Solus.
On the edges of characteristic imset polytopes.
International Journal of Approximate Reasoning 191, 2026, 109606.

D. Deligeorgaki, A. Markham, P. Misra, and L. Solus.
Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networks.
Algebraic Statistics 14.2 (2024): 233-286.

B. Hollering, J. Johnson, I. Portakal, and L. Solus.
Toric ideals of characteristic imsets via quasi-independence gluing.
Algebraic Statistics 14.2 (2024): 109-131.

B. Braun, R. Davis, D. Hanely, M. Lane, and L. Solus.
The Integer Decomposition Property and Weighted Projective Space Simplices.
Integers, 24 (2024), Article A60.

V. Karwa, D. Pati, S. Petrovic, L. Solus, N. Alexeev, M. Raič, D. Wilburne, R. Williams, and B. Yan.
Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels.
Journal of the Royal Statistical Society Series B: Statistical Methodology 86.1 (2024): 90–121.S. 

Linusson, P. Restadh and L. Solus.
Greedy causal discovery is geometric.
SIAM Journal on Discrete Mathematics 37.1 (2023): 233-252.

E. Duarte and L. Solus.
A new characterization of discrete decomposable models.
Proceedings of the American Mathematical Society 151.3 (2023): 1325-1338.

A. Markham, D. Deligeorgaki, P. Misra, and L. Solus.
A tranformational characterization of unconditionally equivalent Bayesian networks.
The Proceedings of the 11-th International Conference on Probabilistic Graphical Models (PGM22) (2022).

M. Hlavacek and L. Solus.
Subdivisions of shellable complexes.
Journal of Combinatorial Theory, Series A 186 (2022): 105553.
Article Sumary published in the Proceedings of FPSAC 2021, Seminaire Lotharingien de Combinatoire.

L. Solus, Y. Wang, and C. Uhler.
Consistency guarantees for greedy permutation-based causal inference algorithms.
Biometrika 108.4 (2021): 795-814.

P. Brändén and L. Solus.
Symmetric decompositions and real-rootedness.
International Mathematics Research Notices 2021.10 (2021): 7764-7798.

N. Gustafsson and L. Solus.
Derangements, Ehrhart theory, and local h-polynomials.
Advances in Mathematics 369 (2020): 107169.

P. Brändén and L. Solus.
Some algebraic properties of lecture hall polytopes.
Séminaire Lotharingien de Combinatoire (FPSAC 2020), 84B.25 (2020), 12 pp.

L. Solus.
Simplices for numeral systems.
Transactions of the American Mathematical Society 371.3 (2019): 2089-2107.

E. Perrone, L. Solus, and C. Uhler.
The Geometry of Discrete Copulas.
Journal of Multivariate Analysis 172 (2019): 162-179.

F. Liu and L. Solus.
On the relationship between Ehrhart unimodality and Ehrhart positivity.
Annals of Combinatorics 23.2 (2019): 347-365.

L. Solus.
Local h^*-polynomials of some weighted projective spaces.
The Proceedings of the 2018 Summer Workshop on Lattice Polytopes at Osaka University (2018).

B. Braun, R. Davis, and L. Solus.
Detecting the integer decomposition property and Ehrhart unimodality in reflexive simplices.
Advances in Applied Mathematics 100 (2018): 122-142.

B. Braun and L. Solus.
r-Stable Hypersimplices.
Journal of Combinatorial Theory, Series A 157 (2018) 349-388.

A. Radhakrishnan, L. Solus, and C. Uhler.
Counting Markov equivalence classes for DAG models on trees.
Discrete Applied Mathematics 244 (2018): 170-185.

Y. Wang, L. Solus, K. Dai Yang, and C. Uhler.
Permutation-based causal inference algorithms with interventions.
Advances in Neural Information Processing Systems (NeurIPS) (2017).

A. Radhakrishnan, L. Solus, and C. Uhler.
Counting Markov equivalence classes by number of immoralities.
The Proceedings of the 2017 Conference on Uncertainty in Artificial Intelligence (UAI 2017) (2017).

L. Solus, C. Uhler, and R. Yoshida.
Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K5 minors.
Linear Algebra and its Applications 509 (2016): 247-275.

T. Hibi and L. Solus.
The facets of the r-stable (n, k)-hypersimplex.
Annals of Combinatorics 20.4 (2016): 815-829.

J. Calcut, J. Metcalf-Burton, T. Richard, L. Solus.
Borromean rays and hyperplanes.
The Journal of Knot Theory and Its Ramifications Vol. 23, No. 4 (2014).

L. Solus.
A topological generalization of partition regularity.
Involve: A Journal of Mathematics 3.4 (2011): 421-433.

 

Preprints

T. Boege and L. Solus.
Real birational implicitization of statistical models.
Submitted (2025).

F. L. Rios, A. Markham and L. Solus.
Scalable structure learning of sparse context-specific systems.
Submitted (2025).

J Bruckamp, L. Goltermann, M. Juhnke, E. Landin and L. Solus.
Ehrhart theory of cosmological polytopes.
Submitted (2025).

A. Markham, J. A. Chang, I. Hirsch, L. Solus and B. Aragam.
Intervening to learn and compose disentangled representations.
Submitted (2025).

J. Johnson, B. Hollering and L. Solus.
Hyperplane representations of interventional characteristic imset polytopes.
Submitted (2025).

A. Markham, M. Liu, B. Agaram and L. Solus.
Neuro-causal factor analysis.
Submitted (2025).

 

Supervision and Mentorship

Current PhD Students:

• Fedrico Lazzeri

Previous PhD Students:

• Danai Deligeorgaki
• Petter Restadh (co-supervisor)

Current Postdocs: 

• Benjamin Cottreau

Previous Postdocs:

• Marina Garrote-López
• Joseph Johnson
• Tobias Boege
• Alex Markham
• Felix Leopoldo Rios
• Pratik Misra
• Bin Han

Open Positions in my Group

• No openings at this time

 

About WASP

Wallenberg AI, Autonomous Systems, and Software Program (WASP) is Sweden’s largest individual research program ever, a major national initiative for strategically motivated basic research, education, and faculty recruitment. The program addresses research on artificial intelligence and autonomous systems acting in collaboration with humans, adapting to their environment through sensors, information and knowledge, and forming intelligent systems-of-systems. The vision of WASP is excellent research and competence in artificial intelligence, autonomous systems and software for the benefit of Swedish industry.

Read more about WASP here.

The graduate school within WASP is dedicated to providing the skills needed to analyze, develop, and contribute to the interdisciplinary area of artificial intelligence, autonomous systems and software. Through an ambitious program with research visits, partner universities, and visiting lecturers, the graduate school actively supports forming a strong multi-disciplinary and international professional network between PhD-students, researchers and industry.

Read more about the WASP graduate school here.