# Publications

Most of my publications are about extremal combinatorics in finite geometries which I often solve with help from algebraic combinatorics.

## Accepted/Published

Please note that sometimes there are significant differences between the preprint and the journal version of a paper.- With Mohammad Adm, Ryan Bergen, Ferdinand Ihringer, Sam Jaques, Karen Meagher, Alison Purdy, and 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. Journal of Combinatorial Designs, Accepted. Preprint.
- 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. Discrete Applied Mathematics, Accepted. Preprint.
- With Klaus Metsch and Bernhard Mühlherr: An EKR theorem for finite buildings of type Dl. Journal of Algebraic Combinatorics, Accepted.
- With Karen Meagher: Miklós-Manickam-Singhi Conjectures on Partial Geometries. Designs, Codes and Cryptography, Accepted. Preprint.
- 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, 2018. Preprint.
- With Klaus Metsch: Large {0, 1,...,t}-Cliques in Dual Polar Graphs. Journal of Combinatorial Theory A, 2018. Preprint.
- With Anurag Bishnoi: The non-existence of distance-2 ovoids in H(4)^D. Contributions to Discrete Mathematics, 2017. Preprint.
- A Switching for Strongly Regular Collinearity Graphs From Polar Spaces. Journal of Algebraic Combinatorics, 2017. 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). Preprint.
- With Andries E. Brouwer, Sebastian M. Cioabă, and Matt McGinnis: The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters. Preprint.
- With Andrey Kupavskii: Regular Intersecting Families. Preprint.
- With Yuval Filmus: Boolean degree 1 functions on some classical association schemes. Preprint.
- With Yuval Filmus: Boolean constant degree functions on the slice are juntas. Preprint.

## Coauthors

Karen Meagher (3), Klaus Metsch (3), Ryan Bergen (2), Yuval Filmus (2), Alison Purdy (2), Boting Yang (2), John Bamberg, Anurag Bishnoi, Andries E. Brouwer, Sebastian M. Cioabă, Jan De Beule, Shaun Fallat, Adam Gorr, Sam Jaques, Andrey Kupavskii, Matt McGinnis, Bernhard Mühlherr, Deepak Rajendraprasad, Peter Sin, Thilo Weinert, Qing Xiang, Guanglong Yu.

## 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

- Subsets in Association Schemes, Tel Aviv University, Tel Aviv, Israel, 2018.
- 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

- Strongly Regular Graphs Related to Polar Spaces, Finite Geometries, Fifth Irsee Conference, Irsee, 2017.
- The Largest t-Intersecting Erdős-Ko-Rado Sets of Polar Spaces, MCGTC, Malta, 2017.
- 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.