Past Seminars › Seminar Series

Algebra Kinderseminar (past)

Wed, 10/03/2010
11:30 		Peter Neumann (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Understanding the Second Mémoire of Évariste Galois: modern counterexamples to ancient writings
The first part of Galois' Second Mémoire, less than three pages of manuscript written in 1830, is devoted to an amazing insight, far ahead of its time. Translated into modern mathematical language (and out of French), it is the theorem that a primitive soluble finite permutation group has prime-power degree. This, and Galois' ideas, and counterexamples to some of them, will be my theme.
Wed, 24/02/2010
11:30 		Jason Semeraro (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Topics in Fusion Systems
Wed, 17/02/2010
11:30 		George Wellen (Bradfield College) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
$ \pi $
Wed, 10/02/2010
11:30 		Algebra Kinderseminar Add to calendar
NO SEMINAR
Wed, 03/02/2010
11:30 		David Craven (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Elliptic Curves and Cryptography
This talk will introduce various aspects of modern cryptography. After introducing RSA and some factoring algorithms, I will move on to how elliptic curves can be used to produce a more complex form of Diffie–Hellman key exchange.
Wed, 27/01/2010
11:30 		Nikolay Nikolov (Imperial College, London) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Linear algebra and geometric combinatorics
Wed, 20/01/2010
11:30 		Peter Neumann (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Synchronizing groups and irreducible modules over the field of size two
Wed, 02/12/2009
11:30 		Matthew Clarke (University of Cambridge) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Generalized Gelfand–Graev representations for finite groups of Lie type
This talk is about the ordinary representation theory of finite groups of Lie type. I will begin by carefully reviewing algebraic groups and finite groups of Lie type and the construction and properties of (ordinary) Gelfand–Graev characters. I will then introduce generalized Gelfand–Graev characters, which are constructed using the Lie algebra of the ambient algebraic group. Towards the end I hope to give an idea of how generalized Gelfand–Graev characters can and have been used to attack Lusztig's conjecture and the role this plays in the determination of the character tables of finite groups of Lie type.
Wed, 25/11/2009
11:30 		Algebra Kinderseminar Add to calendar
NO SEMINAR
Wed, 18/11/2009
11:30 		David Craven (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
The Major Problems in Group Representation Theory
The representation theory of groups is surrounded by deep and difficult conjectures. In this talk we will take a tour of (some of) these problems, including Alperin's weight conjecture, Broué's conjecture, and Puig's finiteness conjecture.
Wed, 11/11/2009
11:30 		Colva Roney-Dougal (St Andrews) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Matrix groups: From geometry to homomorphisms
Wed, 04/11/2009
11:30 		Tobias Barthel (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
The Quest for $ \mathbb{F}_\mathrm{un} $
We will present different ideas leading to and evolving around geometry over the field with one element. After a brief summary of the so-called numbers-functions correspondence we will discuss some aspects of Weil's proof of the Riemann hypothesis for function fields. We will see then how lambda geometry can be thought of as a model for geometry over $ \mathbb{F}_\mathrm{un} $ and what some familiar objects should look like there. If time permits, we will explain a link with stable homotopy theory.
Wed, 28/10/2009
11:30 		Owen Cotton-Barratt (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
When good groups go bad
Much of group theory is concerned with whether one property entails another. When such a question is answered in the negative it is often via a pathological example. We will examine the Rips construction, an important tool for producing such pathologies, and touch upon a recent refinement of the construction and some applications. In the course of this we will introduce and consider the profinite topology on a group, various separability conditions, and decidability questions in groups.
Wed, 21/10/2009
11:30 		Peter Pappas (Vassar College) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
On the Semisimplicity Problem for Group Rings
The semisimplicity problem is the long-standing conjecture that the group algebra $ KG $ of a $ p' $-group $ G $ over a field $ K $ of characteristic $ p\geqslant 0 $ has zero Jacobson radical. We will discuss recent advances in connection with this problem.
Wed, 14/10/2009
11:30 		Algebra Kinderseminar Add to calendar
NO SEMINAR
Wed, 17/06/2009
11:30 		Mikhail Ershov (University of Virginia) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Introduction to Golod-Shafarevich groups
I will describe in detail the first construction of infinite, finitely generated torsion groups due to Golod in early 60s – these groups are special cases of the so-called Golod-Shafarevich groups. If time allows, I will discuss some related constructions and open problems.
Wed, 10/06/2009
11:30 		Tobias Barthel (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Elliptic cohomology theories
Using the theory of formal groups, Landweber´s exactness theorem provides means to construct interesting invariants of topological spaces out of geometric objects. I will illustrate the resulting connection between algebraic geometry and stable homotopy theory in the special case of elliptic curves.
Wed, 03/06/2009
11:30 		Armin Shalile (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
An Introduction to Brauer's Centralizer Algebras
Wed, 27/05/2009
11:30 		Algebra Kinderseminar Add to calendar
NO SEMINAR
Wed, 20/05/2009
11:30 		David Craven (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
The abc conjecture and related topics
We begin by proving the abc theorem for polynomial rings and looking at a couple of its consequences. We then move on to the abc conjecture and its equivalence with the generalized Szpiro conjecture, via Frey polynomials. We look at a couple of consequences of the abc conjecture, and finally consider function fields, where we introduce the abc theorem in that case.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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