Christian Elsholtz

Employment:

1997/99: Wissenschaftlicher Mitarbeiter, University of Stuttgart

1999/2003 Wissenschaftlicher Assistent, Technical University of Clausthal

2003-2006: Lecturer in Pure Mathematics at Royal Holloway, University of London.

2006-2009: Senior Lecturer in Pure Mathematics at Royal Holloway, University of London.

2009-today: Reader in Mathematics at Royal Holloway, University of London.

Tenure since 2006.

Degrees:

Diploma in Mathematics, 1996, Technical University of Darmstadt.

Ph.D., 1998, Technical University of Darmstadt.
Subject: Sums of k Unit Fractions.
My Ph.D. ancestors

Habilitation/Privatdozent 2002, Technical University of Clausthal.
Title: Combinatorial prime number theory- A study of the gap structure of the set of primes.
Comments:
I am occasionally asked: "what is Habilitation?"
The Habilitation is a formal degree based on postdoctoral work, and is considered to be more significant than a Ph.D. In the German system it is the highest scientific qualification. It consists of a written Thesis, a talk on current research including an oral exam, and a lecture to demonstrate teaching skills. For each of the latter two talks I had to submit three distinct subjects (covering the whole range of mathematics) of which the faculty chose: The crossing number in graph theory and its applications, and Fair division of sandwiches and cakes.

Address:

Department of Mathematics
Royal Holloway, University of London
Egham
Surrey TW20 0EX
UK.
Phone: ++44 1784 414021
Fax: +44 1784 430766
eMail: . AT-symbol ..

Fields of Interest:

Elementary, combinatorial, and analytic number theory, additive and multiplicative problems

Combinatorial group and ring theory

Graph Theory, combinatorics and geometry (in particular extremal graph theory)

my number theoretical interests in detail:

Applications of sieve methods, in particular of the large sieve.
The additive structure of the set of primes.
Additive decomposition of sets, Hilbertcubes.
Prime k tuple conjecture.
Detection of large structures in "unstructured" sets.
Diophantine equations.
Sums of unit fractions.
Sums and products of sets of integers.
Zero sums (Erdos-Ginzburg-Ziv-type theorems).
Sums of two squares.
Computational methods.

my algebraic interests detail:

Zero sums in abelian groups Z_n^d.
Generators of cyclic groups.
How many elements are necessary to ensure the existence of certain substructures?
Combination of additive and multiplicative properties in rings.

my combinatorial interests in detail:

Extremal graph theorey. (Forbidden substructures).
Kovari-Sos-Turan type theorems.
The cube lemma.
Algorithmic approaches to the topics above.
Crossing numbers of graphs.
Lattice point problems, geometric problems.
Regular structures in "unstructured" sets.

Here is a link to a list of my scientific work.

Teaching material.

I used to organise the Pure Maths seminar at Royal Holloway for some years. Current Pure Maths seminars.

I am director of the two Master courses
MSc in Mathematics of Cryptography & Communications and
MSc in Mathematics for Applications

I organise talks for schools, such as Exploring Mathematics

Collection of useful links (books, journals, dictionaries etc).

Number theory day 2003.

Workshop analytische Zahlentheorie (3.-7. April 2000)