# Publications

Most of my publications are about extremal combinatorics in finite geometries which I often solve with help from algebraic combinatorics.
Among other things I am interested in ovoids, spreads, tight sets, EKR sets, MMS sets, some Ramsey numbers, distance-regular graphs, network codes and generalized polygons.
I try to have descriptive titles which might be more helpful than my random list of keywords.

## Accepted/Published

Please note that sometimes there are significant differences between the preprint and the journal version of a paper.- With Klaus Metsch and Bernhard Mühlherr: An EKR theorem for finite buildings of type Dl. Journal of Algebraic Combinatorics, Accepted.
- With Peter Sin and Qing Xiang: New Bounds for Partial Spreads of H(2d-1, q^2) and Partial Ovoids of the Ree-Tits Octagon. Journal of Combinatorial Theory A, Accepted. Preprint.
- With Karen Meagher: Miklós-Manickam-Singhi Conjectures on Partial Geometries. Designs, Codes and Cryptography, Accepted. Preprint.
- With Klaus Metsch: Large {0, 1,...,t}-Cliques in Dual Polar Graphs. Journal of Combinatorial Theory A, Accepted. Preprint.
- A Switching for Strongly Regular Collinearity Graphs From Polar Spaces. Journal of Algebraic Combinatorics, Accepted. Preprint.
- With Anurag Bishnoi: The non-existence of distance-2 ovoids in H(4)^D. Contributions to Discrete Mathematics, Accepted. Preprint.
- With John Bamberg and Jan De Beule: New non-existence proofs for ovoids of Hermitian polar spaces and hyperbolic quadrics, Annals of Combinatorics, 2017. Preprint.
- A Note on the Manickam-Miklós-Singhi Conjecture for Vector Spaces, European Journal of Combinatorics, 2016. Preprint.
- Cross-intersecting Erdős-Ko-Rado Sets in Dual Polar Graphs, Electronic Journal of Combinatorics, 2015.
- A new upper bound for constant distance codes of generators on hermitian polar spaces of type H(2d − 1, q^2), Journal of Geometry, 2014. Preprint.
- A Characterisation of the Natural Embedding of the Split Cayley Hexagon in PG(6,q) by Intersection Numbers in Finite Projective Spaces of Arbitrary Dimension. Discrete Mathematics, 2014. Preprint.
- With Klaus Metsch: On the Maximum Size of Erdős-Ko-Rado Sets in H(2d+1, q^2), Designs, Codes and Cryptography, 2014. Preprint.

## Submitted/Preprint

- With Deepak Rajendraprasad and Thilo Weinert: New bounds on the Ramsey number r(I_m, L_n)
- With Ryan Bergen, Shaun Fallat, Adam Gorr, Karen Meagher, Alison Purdy, Boting Yang, Guanglong Yu (University of Regina Discrete Mathematics Research Group): Infection in Hypergraphs. Preprint.
- With Mohammad Adm, Ryan Bergen, Ferdinand Ihringer, Sam Jaques, Karen Meagher, Alison Purdy, Boting Yang (University of Regina Discrete Mathematics Research Group): Ovoids of Generalized Quadrangles of Order (q,q^2−q) and Delsarte Cocliques in Related Strongly Regular Graphs. Preprint.

## Work In Progress (titles will usually change, incomplete)

- Erdős-Ko-Rado Sets and Hermitian Polar Spaces
- A Collection of Eigenvalue Bounds for M-Cliques in Polar Spaces
- With Sebastian M. Cioaba and Matt McGinnis: The Smallest Eigenvalue of the Hamming Scheme

## Colloquium/Conference Talks

(Please ask for slides of any of my talks if you want them. I stopped uploading most of them.)- Prairie Discrete Math Workshop 2017, Cospectral Strongly Regular Graphs in Geometrical Settings, Lumsden, Saskatchewan, Canada, 2017.
- Polymath 10: Inequalities Related to the Sunflower Conjecture, IntersectionFest 2016, VCU, Richmond, Virginia, 2016.
- Erdős-Ko-Rado Sets in Finite Geometries, Colloquium to the memory of Thomas Ihringer. TU Darmstadt, 2015.
- On the Maximum Size of M-Cliques of Generators on Hermitian Polar Spaces. Colloquium on Galois geometry. To the memory of Frédéric Vanhove. Ghent, 2014.
- Erdős-Ko-Rado Mengen in endlichen Polarräumen (German), 100. Baerkolloquium, Gießen, 2013.

## Seminar/Invited Session Talks

- The Largest t-Intersecting Erd\H{o}s-Ko-Rado Sets of Polar Spaces, MCGTC, Malta, 2017.
- Ovoids in Generalized Quadrangles, University of Wyoming, Laramie, Wyoming, USA, 2017.
- Large Erdős-Ko-Rado Sets in Polar Spaces, Colorado State University, Fort Collins, Colorado, USA, 2017.
- Ovoids in Generalized Quadrangles, University of Delaware, Newark, Delaware, USA, 2017.
- Intriguing Sets in Generalized Quadrangles, Hexagons, and OCtagons, Kutztown University, Pennsylvania, USA, 2017.
- Erdős-Ko-Rado Sets in Finite Geometries, Rutgers University, New Jersey, USA, 2017.
- Erdős-Ko-Rado Sets in Finite Geometries, University of Regina, Regina, Saskatchewan, 2016.
- Intriguing Sets in Generalized Quadrangles and Hexagons, University of Waterloo, Waterloo, Ontario, 2016.
- The Manickam-Miklós-Singhi Conjecture for Partial Linear Spaces, BLS 2016, Logroño, 2016.
- Intriguing Sets in Generalized Quadrangles and Hexagons, University of Regina, Regina, Saskatchewan, 2016.
- Erdős-Ko-Rado Sets in Finite Spherical Buildings, University of Delaware, Newark, Delaware, 2016.
- Erdős-Ko-Rado Sets in Finite Classical Polar Spaces, University of Western Australia, Perth, 2013.

## Contributed Talks

- A Switching for the Collinearity Graphs of Polar Spaces, Western Sectional Meeting of the AMS, Denver, Colorado, 2016.
- New Bounds on the Ramsey Numbers r(In, L3), Combinatorics 2016, Maratea, 2016.
- The Manickam-Miklós-Singhi Conjecture for Vector Spaces, System of Lines: Applications of Algebraic Combinatorics, Worcester Polytechnic Institute, Worcester, MA, 2015.
- Erdős-Ko-Rado Sets and Semidefinite Programming in Hermitian Polar Spaces, Workshop on Algebraic Combinatorics, Tilburg, 2015.
- Erdős-Ko-Rado Sets and Semidefinite Programming in Hermitian Polar Spaces, CanaDAM, 2015.
- The Manickam-Miklós-Singhi Conjecture for Vector Spaces. Finite Geometries, Fourth Irsee Conference, 2014.
- Erdős-Ko-Rado Sets in Finite Classical Polar Spaces, Fq11, Magdeburg, 2013.
- Erdős-Ko-Rado Sets in Hermitian Polar Spaces, Combinatorics 2012, Perugia, 2012.

## Theses

- PhD Thesis (English), Algebraic Combinatorics Intersecting Finite Geometry, 2015.
- Master Thesis (German), Intriguing Sets in Polar Spaces, 2011.
- Bachelor Thesis (German), $1 \equiv p$ Results in Finite Projective Spaces, 2009.