Thu, 13 May 2010

12:00 - 13:00
SR1

Moduli of sheaves and quiver sheaves

Vicky Hoskins
(Oxford)
Abstract

A moduli problem in algebraic geometry is essentially a classification problem, I will introduce this notion and define what it means for a scheme to be a fine (or coarse) moduli space. Then as an example I will discuss the classification of coherent sheaves on a complex projective scheme up to isomorphism using a method due to Alvarez-Consul and King. The key idea is to 'embed' the moduli problem of sheaves into the moduli problem of quiver representations in the category of vector spaces and then use King's moduli spaces for quiver representations. Finally if time permits I will discuss recent work of Alvarez-Consul on moduli of quiver sheaves; that is, representations of quivers in the category of coherent sheaves.

Mon, 17 May 2010

12:00 - 13:00
L3

Aspects of heterotic Calabi-Yau compactifications

James Gray
(Oxford)
Abstract
I will discuss various aspects of Calabi-Yau compactifications appropriate for use in models of string phenomenology. Topics covered will include transitions between and deformations of bundles as well as consequences of stability walls for phenomenology.
Mon, 26 Apr 2010

12:00 - 13:00
L3

On Fields over Fields

Yang-Hui He
(Oxford)
Abstract
We investigate certain arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic. Parallel to the Plethystic Programme of counting the spectrum of operators from the complex geometry, we investigate the Hasse-Weil zeta functions and the associated Dirichlet expansions. We find curious dualities wherein the geometrical properties and asymptotic behaviour of one gauge theory is governed by the number theoretic nature of another.
Wed, 26 May 2010
17:00
L2

Editing the manuscripts of Évariste Galois (1811–1832)

Peter Neumann
(Oxford)
Abstract

What do historians of mathematics do? What sort of questions do they ask? What kinds of sources do they use? This series of four informal lectures will demonstrate some of the research on history of mathematics currently being done in Oxford. The subjects range from the late Renaissance mathematician Thomas Harriot (who studied at Oriel in 1577) to the varied and rapidly developing mathematics of the seventeenth century (as seen through the eyes of Savilian Professor John Wallis, and others) to the emergence of a new kind of algebra in Paris around 1830 in the work of the twenty-year old Évariste Galois.

Each lecture will last about 40 minutes, leaving time for questions and discussion. No previous knowledge is required: the lectures are open to anyone from the department or elsewhere, from undergraduates upwards.

Wed, 05 May 2010
17:00
L2

The life, work, and reputation of Thomas Harriot (1560–1621)

Jackie Stedall
(Oxford)
Abstract

What do historians of mathematics do? What sort of questions do they ask? What kinds of sources do they use? This series of four informal lectures will demonstrate some of the research on history of mathematics currently being done in Oxford. The subjects range from the late Renaissance mathematician Thomas Harriot (who studied at Oriel in 1577) to the varied and rapidly developing mathematics of the seventeenth century (as seen through the eyes of Savilian Professor John Wallis, and others) to the emergence of a new kind of algebra in Paris around 1830 in the work of the twenty-year old Évariste Galois.

Each lecture will last about 40 minutes, leaving time for questions and discussion. No previous knowledge is required: the lectures are open to anyone from the department or elsewhere, from undergraduates upwards.

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