Professor Russoniello’s field of study is algebraic combinatorics, with a particular focus on using combinatorial tools to investigate the algebraic and geometric structures of certain Lie algebras. His dissertation work centered around combinatorial constructions and classifications of “Lie proset algebras” – Lie algebras arising from pre-ordered sets – that admit contact structures. Recently, in addition to extending the work done in his dissertation, he has been working with an undergraduate from the College of William & Mary on a project involving posets associated with Kohnert polynomials, which have applications in representation theory.

# Nick Russoniello

### Teaching Assistant Professor

Ph.D. Lehigh University, 2022

B.S. University of Scranton, 2017

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### Research Areas

### Additional Interests

- Algebraic combinatorics
- Lie theory

### Research Statement

### Biography

Professor Russoniello received a Bachelor of Science degree from the University of Scranton in Scranton, PA in 2017. He obtained his Ph.D. from Lehigh University and won the Elizabeth V. Stout Dissertation Award in 2022 before joining the faculty as a Visiting Assistant Professor at the College of William & Mary in Williamsburg, VA. He returned to Lehigh as a faculty member in July 2024.

Publications and selected preprints.

*Shellability of Kohnert posets*(with C. Kerr* and N. Mayers), submitted.*Contact Lie poset algebras of types B, C, and D*(with N. Mayers), submitted.*Seaweed algebras and the unimodal spectrum property*(with N. Mayers), submitted.*Classification of contact seaweeds*(with V. Coll), Journal of Algebra,**659**:811-817 (2024).*A matrix theory introduction to seaweed algebras and their index*(with A. Cameron, V. Coll, and N. Mayers), Expositiones Mathematicae,**41**(1): 125509 (2023).*On toral posets and contact Lie algebras*(with N. Mayers), Journal of Geometry and Physics,**190**: 104861 (2023).*Contact seaweeds*(with V. Coll, N. Mayers, and G. Salgado), Pacific Journal of Mathematics,**320**(1): 45-60 (2022).*The breadth of Lie poset algebras*(with A. Cameron, V. Coll, and N. Mayers), Linear and Multilinear Algebra,**71**(16): 2565-2584 (2022).*Contact Lie poset algebras*(with V. Coll and N. Mayers), Electronic Journal of Combinatorics,**28**(3): #P3.35 (2022).*The evolution of the spectrum of a Frobenius Lie algebra under deformation*(with V. Coll and N. Mayers), Communications in Algebra,**50**(3): 998-1009 (2021).*The index and spectrum of Lie poset algebras of types B, C, and D*(with V. Coll and N. Mayers), Electronic Journal of Combinatorics,**28**(3): \#P3.47 (2021).*The index of nilpotent Lie poset algebras*(with V. Coll and N. Mayers), Linear Algebra and its Applications,**605**: 118-129 (2020).

(*) Undergraduate student at the time of writing the article.

### Teaching

__Lehigh__

Fall 2024: Math 231, Probability/Statistics. Math 000, Prep. for Calculus.

__William & Mary__

Spring 2024: Math 112, Calculus II. Math 111, Calculus I.

Fall 2023: Math 311, Elementary Analysis. Math 111, Calculus I.

Spring 2023: Math 211, Linear Algebra. Math 112, Calculus II.

Fall 2022: Math 212, Intro. to Multivariable Calculus. Math 211, Linear Algebra.