# Jon Xu

**Address:** Department of Mathematics and Statistics,
University of Melbourne,

Parkville, VIC
3010, Australia

**Office:** Peter Hall Building, Room G95

**E-mail:** jyxu[at]student.unimelb.edu.au

## About Me

I am a recently graduated PhD student and casual tutor at the University of Melbourne.

My supervisor is Arun Ram (University of Melbourne)

and my cosupervisor is John Bamberg (University of Western Australia).

My
PhD Thesis
studies flag varieties of Chevalley groups from the point of view of finite geometry.

In particular, it gives a combinatorial method to calculate the number of i-planes incident with a given j-plane inside a Schubert cell.

It also shows how key examples of ovoids arise as flag varieties, and provides a Schubert cell decomposition of the classical ovoid in Hermitian space.

I am also generally interested in representation theory and finite geometry, some keywords are:

-flag varieties and alcove walks (see Parkinson-Ram-Schwer)

-Chevalley groups

-Describing extremal subobjects (spreads, blocking sets, m-ovoids, MDS-codes, EKR-sets) of representation theoretic objects (e.g Schubert cells and Schubert varieties)

-characterising finite geometric objects using point-line incidence axioms (e.g the Veblen-Young theorem, the classification of spherical buildings of rank greater than 2 by Tits,

the classification of ovoids of projective spaces over fields of odd characteristic by Segre-Barlotti-Panella).

-Schubert calculus

-representation theory of quantum groups and Hecke algebras

-representation theory of finite/affine complex Lie algebras.

Preprints/Papers
Teaching
Curriculum Vitae