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| Jan 29 |
Wed |
Heath Pearson (Nottingham) |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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The generalised Mukai conjecture for spherical varieties |
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Hicks Seminar Room J11 |
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Abstract:
The generalised Mukai conjecture (GMC) concerns the characterisation of powers of projective space among Fano varieties. In this talk, we will prove the GMC for spherical varieties. These varieties generalise toric varieties, and their geometry may be interpreted combinatorially via a 'spherical dictionary'. If time permits, we will explain how this result can be extended to prove a purely combinatorial smoothness criterion for spherical varieties.
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| Feb 5 |
Wed |
Robert Rogers (Sheffield) |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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Moduli of Quiver Representations and GIT Quotients |
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Hicks Seminar Room J11 |
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Abstract:
In this talk we will discuss the notion of a quiver and its applications to algebraic geometry. In particular we will construct moduli spaces of quiver representations and stability conditions on quivers. We will show how to construct some simple GIT quotients from this data. Along the way Gabriel's theorem and Mumford's criterion will be covered.
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| Feb 11 |
Tue |
Fraser Sparks (Nottingham) |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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A (very) brief introduction to motives
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Hicks Seminar Room J11 |
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Abstract:
(Co)homology theories are ubiquitous throughout pure mathematics. Can we find some objects which `capture’ the (co)homological behaviour of our spaces of interest? In algebraic geometry, the answer is the theory of motives. They allow one to use topological methods in the context of algebraic geometry, and can be thought of as a `universal cohomology theory’ for varieties. In this talk I will give a brief introduction to the theory, highlighting the analogies with topology, and I’ll also discuss some applications.
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| Feb 19 |
Wed |
Lily Bennett (Sheffield) |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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Pontryagin Duality for Semilattices |
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Hicks Seminar Room J11 |
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Abstract:
In this talk we discuss the duality of the category of discrete semilattices and the category of compact zero-dimensional semilattices, introduced by Hofmann, Mislove and Stralka in the 1970s. We start by taking a brief look at semilattices and compact zero-dimensional semilattices, before moving on to look at diagram categories and the notion of categorical density. Finally, we use this categorical machinery to provide an outline of the argument for duality.
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| Feb 26 |
Wed |
Jingxiang Ma (Sheffield) |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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Counting rational curves in the projective plane |
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Hicks Seminar Room J11 |
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Abstract:
I will talk about a classical problem in enumerative geometry. We start with special cases that can be solved using elementary geometric arguments. We then move to the modern approach which solves the general problem, where the key idea is to understand these curve counts as Gromov-Witten invariants.
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| Mar 5 |
Wed |
Pierre-Louis Guillot (Sheffield) |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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The G-construction : an un-delooped construction for algebraic K-theory |
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Hicks Seminar Room J11 |
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Abstract:
We will introduce constructions for algebraic K-theory that have the property of being un-delooped -- meaning that they provide simplicial objects whose homotopy groups correspond to the K-groups with no shift in degree. We will see how they can be constructed with increasing generality, and applied to categories with increasingly weak "additivity conditions". The goal is to try to engage with ideas contained in models for algebraic K-theory and try to get a feeling for why these " additivity conditions " matter.
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| Apr 24 |
Thu |
TBA |
ShEAF: postgraduate pure maths seminar |
| 10:00 |
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Hicks Seminar Room J11 |
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| Apr 24 |
Thu |
TBA |
ShEAF: postgraduate pure maths seminar |
| 11:00 |
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Hicks Seminar Room J11 |
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| Apr 24 |
Thu |
TBA |
ShEAF: postgraduate pure maths seminar |
| 12:00 |
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Hicks Seminar Room J11 |
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| Apr 24 |
Thu |
TBA |
ShEAF: postgraduate pure maths seminar |
| 13:00 |
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Hicks Seminar Room J11 |
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| Apr 24 |
Thu |
TBA |
ShEAF: postgraduate pure maths seminar |
| 14:00 |
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Hicks Seminar Room J11 |
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| Apr 24 |
Thu |
TBA |
ShEAF: postgraduate pure maths seminar |
| 15:00 |
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Hicks Seminar Room J11 |
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| Apr 24 |
Thu |
TBA |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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Hicks Seminar Room J11 |
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