Research Interests

My research is mostly in the area of finite geometry which, in a very general sense, constitutes the study of incidence structures containing a finite number of points and lines. This includes the study of graphs, combinatorial designs, polar spaces, and other geometric structures. The nature of these objects puts their study at the intersection of geometry, combinatorics, and algebra. In particular, techniques from permutation group theory, matrix theory, and the theory of finite fields have been used to construct and analyze important examples of finite incidence structures. A major focus is on substructures of a projective space having some specified combinatorial structure; often these objects can be used to define error-correcting codes that are "good" in some sense. Finite polar spaces are an area of particular interest for me; these geometries are defined by quadratic or semilinear forms on finite projective spaces, and are naturally associated with the finite classical groups.

In my dissertation, I applied algebraic and computational methods to find new examples of Cameron-Liebler line classes in PG(3,q); under the Klein correspondence, these are equivalent to tight sets in the hyperbolic polar spaces Q+(5,q). You can download a copy here.

Publications

  1. Regular sets of lines in rank 3 polar spaces (with Ferdinand Ihringer). (submitted)
  2. Strong ovoids and Cameron-Liebler sets of generators in polar spaces (with Maarten De Boeck and Jozefien D'haeseleer). (submitted)
  3. Cameron-Liebler line classes with parameter x=(q+1)2/3 (with Tao Feng, Koji Momihara, Qing Xiang, and Hanlin Zou). Advances in Mathematics, Volume 385 (2021).
  4. Cameron-Liebler sets of generators in finite classical polar spaces (with Maarten De Boeck, Leo Storme, and Andrea Svob). Journal of Combinatorial Theory, Series A, Volume 167 (2019), pp 340-388. (pdf)
  5. Classification of 8-dimensional rank two commutative semifields (with Michel Lavrauw). Advances in Geometry, Volume 19, Issue 1 (2019), pp 57-64. (pdf)
  6. Cameron-Liebler k-classes in PG(2k+1,q) (with Leo Storme and Andries Vansweevelt). Combinatorica, Volume 38, Issue 3 (2018), pp 737-757. (pdf)
  7. A new family of tight sets in Q+(5,q) (with Jan De Beule, Jeroen Demeyer, and Klaus Metsch). Designs, Codes and Cryptography, Volume 78, Issue 3 (2016), pp 655-678. (pdf)
  8. Double k-sets in symplectic generalized quadrangles (with Stanley Payne) Designs, Codes and Cryptography, Volume 72, Issue 2 (2014), pp 265-271. (pdf)
  9. Cameron-Liebler line classes, Designs, Codes and Cryptography, Volume 68, Issue 1-3 (2013), pp 33-37. (pdf)

Selected Research Presentations

Department of Mathematics Department of Mathematics
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