Christian Elsholtz
Lecturer in Pure Mathematics at Royal Holloway,
University of London.
Please go to my new web page
The current page will not be updated.
Degrees:
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Diploma in Mathematics, 1996, Technical University of Darmstadt.
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Ph.D., 1998, Technical University of Darmstadt.
Subject: Sums of k Unit Fractions.
My Ph.D. ancestors (Gauss is one of them)
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Habilitation 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:
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Department of Mathematics
Royal Holloway, University of London
Egham
Surrey TW20 0EX
UK.
- Phone: ++44 1784 414021
- Fax: +44 1784 430766
- eMail: elsholtz@math.tu-clausthal.de (TO BE CHANGED
SOON)
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 (in particular the set of primes).
- Prime k tuple conjecture.
- Detection of large structures in "unstructured" sets (like the
primes).
- 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).
- Kövari-Sos-Turan type theorems.
- The cube lemma.
- Algorithmic approaches to the topics above.
- Crossing numbers of graphs.
- Lattice point problems.
- Regular structures in "unstructured" sets.
Here is a link to a list of my scientific work.
Übersicht der Vorlesungen./Teaching material.
Nützliche Links besonders im Bereich
Mathematik/Bibliotheken/Zeitschriften/Bücher