KTH

SE-100 4 Stockholm, Sweden

Email: solus@kth.se

My general research interests include combinatorics and combinatorial convex geometry. I particularly like to focus on problems in these fields arising in the context of commutative algebra and algebraic statistics. In the context of commutative algebra, I am currently investigating real-rootedness, log-concavity, and unimodality of Ehrhart h*-polynomials of lattice polytopes using both univariate and multivariate techniques. In the context of algebraic statistics, I am now working on problems arising from the combinatorics of causality and some others relating to the geometry of hyperbolic exponential families.

I am currently an NSF Mathematical Sciences Postdoctoral Research Fellow at KTH.

NSF Postdoctoral Mentor: Dr. Petter Brändén.

In 2016 I was a postdoctoral researcher working at IST Austria and MIT.

Postdoctoral Mentor: Dr. Caroline Uhler.

In December 2015 I completed my PhD in mathematics at University of Kentucky.

Doctoral Advisor: Dr. Ben Braun.

In April 2014 I completed my masters in mathematics at University of Kentucky.

Masters Advisor: Dr. Ben Braun.

In May 2011 I completed my bachelors in mathematics at Oberlin College.

Honors Advisor: Dr. Kevin Woods.

Academic Advisor: Dr. Jim Walsh.

- L. Solus.

Simplices for numeral systems.

To appear in Transactions of the American Mathematical Society (2017).

arXiv version available here. - Y. Wang, L. Solus, K. Dai Yang, and C. Uhler.

Permutation-based causal inference algorithms with interventions.

Advances in Neural Information Processing Systems (2017).

arXiv version available here. - L. Solus, Y. Wang, L. Matejovicova, and C. Uhler.

Consistency guarantees for greedy permutation-based causal inference algorithms.

Preprint available here (2017). - A. Radhakrishnan, L. Solus, and C. Uhler.

Counting Markov equivalence classes for DAG models on trees.

Preprint available here (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 and The Proceedings of the 2017 UAI Special Workshop on Causality (2017).

arXiv version available here. - V. Karwa, D. Pati, S. Petrovic, L. Solus, N. Alexeev, M. Raic, D. Wilburne, R. Williams, and B. Yan.

Exact tests for stochastic block models.

Preprint available here. - B. Braun, R. Davis, and L. Solus.

Detecting the integer decomposition property and Ehrhart unimodality in reflexive simplices.

Preprint available here (2016). - L. Solus, C. Uhler, and R. Yoshida.

Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K_5 Minors.

Linear Algebra and its Applications (2016). DOI 10.1016/j.laa.2016.07.026

arXiv version available here. - T. Hibi and L. Solus.

The facets of the r-stable (n,k)-hypersimplex.

Annals of Combinatorics (2016). DOI 10.1007/s00026-016-0325-x

arXiv version available here. - B. Braun and L. Solus.

r-stable hypersimplices.

Preprint available here (2016). - 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),

arXiv version available here. - L. Solus.

A topological generalization of partition regularity.

Involve: A Journal of Mathematics 3-4 (2010), 421-433. DOI 10.2140/involve.2010.3.421.

Available here. - L. Solus.

Normal and $\Delta$-Normal Configurations in Toric Algebra.

Oberlin College Honors Theses, Bachelor of Arts, 2011. Available here.

This semester I am not teaching any courses. However, in the previous semesters I had the privilege of teaching the following:

Primary Instructor:

Teaching Assistant:

In my free time I enjoy rock climbing and hiking. I love to boulder, but I do sport climb as well. I also like to make computer music and play my violin.

Postdoctoral Researcher in Mathematics

KTH Royal Institute of Technology

Last updated on 20 December, 2017