# Adam David John Dent

**Email:**mmadjd@leeds.ac.uk**Thesis title:**Highest weight vectors for classical reductive groups

#### Profile

I attended the University of Leicester from October 2010 to June 2014, where I completed an undergraduate MMath degree in mathematics at the Department of Mathematics. During my studies there, I focused on pure mathematics, particularly algebra and number theory (finite group representations, commutative algebra, Galois theory, geometry and topology), and a group project on quandles as knot invariants for a reading module on knot theory in my third year inspired the topic of my master's dissertation the following year, titled *Racks and Lie theory*, which I wrote under the supervision of Dr Teimuraz Pirashvili. During the four years I also served as a course representative, worked as a departmental open day helper, and was elected as House President of the Department of Mathematics' Euler House, a position I held from 2011 to 2014.

In October 2014 I started my PhD at the University of Leeds in the Pure mathematics department of the Scool of Mathematics, under the supervision of Dr Rudolf H. Tange, with Prof William W. Crawley-Boevey as advisor until the latter's secondment to Bielefeld University, after which Prof Robert J. Marsh has acted as advisor. The areas of my research have mainly included representation theory of Lie algebras and of algebraic groups, and algebraic geometry. Apart from research, I have taught classes and marked exams for various undergraduate modules (mostly in the pure mathematics department); participated in the algebra staff seminar and pure mathematics postgraduate seminar (the latter of which I have organised since December 2015,) as well as algebra and algebraic geometry study groups; taken various algebra-related MAGIC courses; attended several conferences, mostly meetings of the ARTIN group; and acted as a PGR representative for pure mathematics. I expect to submit my thesis in 2017 or early 2018, and to complete my PhD in 2018.

In 2016 Dr Tange and I co-authored a paper, *Bases for spaces of highest weight vectors in arbitrary characteristic*, which can be found at arxiv.org/abs/1610.06948. It is currently (as of August 2017) awaiting publication.

#### Research interests

Representation theory;

Noncommutative algebra and representation theory;

Algebraic geometry;

Combinatorics.

#### Qualifications

- MMath mathematics (4 years), University of Leicester