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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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| Mar 19 |
Wed |
Kuba Krawczyk |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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Pontryagin duality for all locally compact groups |
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Hicks Seminar Room J11 |
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Abstract:
Pontryagin duality is famously defined for abelian locally compact groups. In this talk we are going to look for the apropriate caregory to consider duals of also non-abelian groups. This search will serve as a gentle introduction to quantum groups and non-commutative geometry.
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| Mar 28 |
Fri |
Tommaso Faustini (Warwick) |
ShEAF: postgraduate pure maths seminar |
| 12:00 |
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TBA
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Hicks Seminar Room J11 |
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Abstract:
TBA
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| Apr 2 |
Wed |
Jason |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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TBA |
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Hicks Seminar Room J11 |
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Abstract:
TBA
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| Apr 9 |
Wed |
Andrew Neate |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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TBA
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Hicks Seminar Room J11 |
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Abstract:
TBA
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| Apr 16 |
Wed |
Haoran Shi |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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TBA |
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Hicks Seminar Room J11 |
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Abstract:
TBA
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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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| May 14 |
Wed |
Haoran Shi |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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A biased view of Floer theories and Arnol'd conjecture |
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Hicks Seminar Room J11 |
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Abstract:
In this talk, we will give an accessible introduction to classical Floer theories and their applications in symplectic geometry. We begin by motivating symplectic geometry through its origins in Hamiltonian mechanics, assuming no prior background in the subject. The main focus will be Floer's approach to the Hamiltonian Arnol'd conjecture, which leads to the construction of Hamiltonian Floer (co)homology. We will explain the key ideas behind this theory and outline its significance in symplectic topology. Time permitting, We will also provide informal insights into other Floer-type theories and their applications, including symplectic (co)homology and Lagrangian Floer theory.
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| May 21 |
Wed |
Andrew Neate |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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Enriched categories - The correct framework (but not for the faint of heart)
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Hicks Seminar Room J11 |
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Abstract:
A category theorist might describe their job as generalising mathematical structures so that we don't need to worry about which specific category we're using to prove things about it. Unfortunately, the definition of an ordinary category fails at this spectacularly. Linear maps between vector spaces themselves form a vector space, we need additional data to define additive categories, infinity categories, or even just to talk about natural transformations for more than 2 categories at once. These structures (and many more) are all examples of enriched categories.
The aim of this talk is to discuss work in progress where I am using enriched categories to generalise the notions of "restriction and extension" from representation theory. We will talk about some of the difficulties which arise from trying to work with enriched categories and how you should try to think if you want to solve these problems.
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| May 28 |
Wed |
Constantinos Papachristoforou |
ShEAF: postgraduate pure maths seminar |
| 16:00 |
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TBA
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Hicks Seminar Room J11 |
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Abstract:
TBA
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