Intensive courses.

LTCC intensive courses run over a period of 24 hours (1pm or day one to 1pm on day two) usually at De Morgan House in the summer. Each course is free and open to both students and practitioners.

The courses are taught by experts in their respective fields, all working on new research in hot topics in mathematics and the physical sciences.

The LTCC will be running two intensive courses this summer:

Introduction to the Theory of Dissipative Operators and Applications by Ian Wood and Sergey Naboko of Kent University
1pm - 5pm on Monday 20 May
9am - 1pm on Tuesday 21 May.
This course will take place in room 505, which is on the 5th floor of the Mathematics Department at UCL (25 Gordon Street)
http://www.ucl.ac.uk/find-us

The course will give an introduction to the theory of dissipative operators and consider some applications. It will start with a review of some basic facts about self-adjoint operators, including the Spectral Theorem. Then dissipative operators will be defined and their spectral and resolvent properties investigated. Wood and Naboko will discuss completely non-self-adjoint dissipative operators, maximal dissipative operators. A principal focus of the course will be on self-adjoint dilations of these operators. Connections to Complex Analysis, strongly continuous semigroups and the extension theory of operators will be pointed out. Various examples of dissipative operators from Mathematical Physics will be presented.

The intension is to make the course self-contained as far as possible, but will assume basic familiarity with linear operators on Hilbert space. If you wish to do some preliminary reading before the course, the following publications are recommended:

1. Akhiezer, Glazman: Theory of Linear Operators in Hilbert Space, Dover, 1993.
2. Riesz; Sz.-Nagy: Functional analysis. Dover Publications, 1990, especially the appendix on dilation theory written by Sz.-Nagy.
3. Sz.-Nagy, Foias, Bercovici, Kerchy: Harmonic Analysis of Operators on Hilbert Space, 2nd
edition, Springer, 2010.


Schubert calculus on Grassmannians by Clelia Pech of King's College, University of London
 1pm - 5pm on Monday 10 June
9am - 1pm on Tuesday 11 June.
This course will take place in room 500, 5th Floor, Mathematics, UCL (25 Gordon Street)
http://www.ucl.ac.uk/find-us

Enumerative problems are an important part of Algebraic Geometry. Their aim is often to count the number of objects (lines, curves ...) satisfying certain incidence conditions. For example, what is the number of circles tangent to three given circles in the plane? What is the number of plane conics through 5 points?
These kinds of questions have been extensively studied during the XIX century and form the bases of Schubert Calculus.

This intensive course will focus on Schubert calculus on Grassmannians, which parametrize vector subspaces of a given dimension in an ambient complex vector space. It involves the beautiful combinatorics of Young tableaux, which are also related to interesting problems in representation theory and the theory of symmetric functions.

Outline of the course :
- the Grassmannians and their projective embedding
- Plücker coordinates and Plücker relations
- Schubert classes, Poincaré duality
- Pieri and Giambelli rules
- the Littlewood-Richardson rule
- overview of recent generalizations : Schubert calculus on homogeneous spaces and quantum Schubert calculus.

Both courses are open for registrations. Email office@ltcc.ac.uk for further information and to obtain a registration form.

Past intensive courses: