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. Matejovicova, L. Solus, and C. Uhler.

Restricted permutation search for causal inference with background knowledge.

Preprint available soon on ArXiv, 2016. - A. Radhakrishnan, L. Solus, and C. Uhler.

A combinatorial perspective of Markov equivalence classes for DAG models.

Preprint available soon on ArXiv, 2016. - B. Braun, R. Davis, and L. Solus.

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

Submitted to Discrete and Computational Geometry, 2016.

Preprint available at http://arxiv.org/abs/1608.01614. - 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

Preprint available at http://arxiv.org/abs/1506.06702. - 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

Preprint available at http://arxiv.org/abs/1408.5932. - B. Braun and L. Solus.

Shellability, Ehrhart theory, and r-stable hypersimplices.

Submitted to Journal of Combinatorial Thoery Series A, 2015.

Preprint available at http://arxiv.org/abs/1408.4713. - 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),

Preprint available at http://arxiv.org/abs/1211.6465. - 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 at http://msp.org/involve/2010/3-4/p06.xhtml. - L. Solus.

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

Oberlin College Honors Theses, Bachelor of Arts, 2011. http://etd.ohiolink.edu/view.cgi?acc_num=oberlin1308243895.

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 29 October, 2016