The KCL/UCL Junior Geometry Seminar is a joint seminar of King's College London and University College London, presenting topics from Algebraic Geometry, Differential Geometry, Geometric Analysis, Geometric Group Theory, Topology, and related areas.
The target audience is young researchers — in particular PhD students — with the goal of being useful to those that attend. Talks can be introductory, or more advanced. All sessions of this seminar are held on Mondays at King's College in room (TBD) on Tuesdays from 16:00 to 17:00 , and snacks will be provided. If you would like to see a particular topic, or give a talk, please email one of the organizers:
- Simon Alonso (s.alonso24@imperial.ac.uk)
- Zhaoyang Liu (Zhaoyang.1.liu.24@kcl.ac.uk)
- Fulin Zhong (fulin.zhong.24@ucl.ac.uk)
The format of this seminar is slightly different from the usual weekly talk one. This year we will have one expert speaker every three weeks (or exceptionally two) and hold two preparatory sessions (or exceptionally only one) on the subject of the expert talk. These sessions will be cooperative and revolve around discussions and questions asked by the expert. The two preliminary sessions will sometimes start with a brief exposition of the questions by the chair of the session but their goal is to encourage discussions and exchange. Whether you already know a lot about the subject or you are simply curious to learn about it, you are very welcome to attend : the diversity of point of views is very precious when learning maths !
This seminar is run in parallel with the Imperial Junior Geometry Seminar , which features one talk every week, and we strongly encourage everyone to attend both.
Other seminars in London which may be of interest:
- Imperial Junior Geometry Seminar
- London Junior Number Theory Seminar
- DOGS (Derived Obsessed Graduate Students)
- UCL Geometry Seminar
- KCL Geometry Seminar
- London Geometry and Topology Seminar
- MAGIC Seminar
Subscription
To receive updates about upcoming talks, you can subscribe to our mailing list by sending an email with subject "Subscribe" to maths-juniorgeom-subscribe@ucl.ac.uk.
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Schedule
Upcoming Talks
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Title:
Speaker: TBD
Tuesday ?th April, 16:00pm–17:00pm, Bush House(S)4.03 KCL
TBD
Past Talks
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Title: Wall crossing of Donaldson-Thomas invariants.
Speaker: Ashesh Bati
Tuesday 31th March, 16:00pm–17:00pm, Bush House(S)4.03 KCL
Modern enumerative geometry is characterised by a framework provided by Behrend-Fantechi. In this talk, I will give an introduction to this through the example of Donaldson-Thomas (DT) invariants: upon introducing the moduli space, and discussing its deformation theory, I will explain this is used to produce a virtual class, which is then used to define DT invariants. Then, I will discuss how the theory of Bridgeland stability conditions play a role in this: in particular, how objects behave when crossing walls in the stability manifold, and sketch how this is used to prove powerful reduction results.
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Title: A brief introduction to enumerative algebraic geometry.
Speaker: Edward Young
Tuesday 24th March, 16:00pm–17:00pm, Bush House(S)4.03 KCL
We will continue our exploration of enumerative algebraic geometry with Edward Young who will be introducing us to Bridgeland stability .
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Title: A brief introduction to enumerative geometry.
Speaker: Patrick Luo
Tuesday 17th March, 16:00pm–17:00pm, Bush House(S)4.03 KCL
This final block will be about enumerative geometry and in particular DT theory (for all our algebraic folks) and will be introduced by Patrick Luo who will talk about the necessary ingredients to reach the definition of virtual classes. .
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Title: The 3-dimensional Geroch conjecture.
Speaker: Natasha Diederen
Tuesday 10th March, 16:00pm–17:00pm, Bush House(S)4.03 KCL
In the first talk of this series we demonstrated using variational methods that the 3-torus does not admit a metric of positive Ricci curvature. The proof relied on the connection between the second variation of a geodesic and Ricci curvature, but was not strong enough to rule out the possibility of a metric of positive scalar curvature. In this last talk, we use the existence and regularity results for minimal surfaces (which can be loosely viewed as co-dimension one analogues to geodesics) presented in the first two talks to prove that the 3-torus does not admit a metric with positive scalar curvature .
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Title: A brief introduction to minimal surfaces and geometric analysis.
Speaker: Yuze Jiang (UCL)
Tuesday 3th March, 16:00pm–17:00pm, Bush House(S)4.03 KCL
We will continue our exploration of the theory of minimal surfaces and geometric analysis. Last week we were introduced to the motivation behind the study of minimal (hyper)surfaces and we briefly explained an existence result. This week, Yuze Jiang will guide us through some of the properties of those minimal surfaces, in particular their regularity..
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Title: A brief introduction to minimal surfaces.
Speaker: James Tissot
Tuesday 24th Fenbuary, 16:00pm–17:00pm, Bush House(S)4.03 KCL
For the first preliminary talk, we will have James Tissot speaking about the existence of area minimising hypersurfaces. In the hope of being accessible to anyone, this session will focus on ideas rather than technical details. .
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Title: On McMullen’s expander graph conjecture for SL(2,Z)-orbits.
Speaker: Luke Jeffery (Bristol)
Tuesday 17th Fenbuary, 16:00pm–17:00pm, Bush House(S)4.03 KCL
Square-tiled surfaces (aptly named) are surfaces obtained by gluing together a collection of unit squares along their sides (the square torus being the simplest example). These surfaces are special cases of translation surfaces, whose moduli space carries a natural action of the group SL(2,R). The famous works of Eskin–Mirzakhani and Eskin–Mirzakhani–Mohammadi were concerned with understanding the orbits of this action. This SL(2,R)-action restricts to an action of SL(2,Z) on square-tiled surfaces, and the orbits under this restricted action can be transformed into finite regular graphs. It is a long-standing conjecture of McMullen that a specific family of these orbit graphs in genus two forms a family of expander graphs. I will discuss the history of this conjecture and recent progress towards it obtained in joint work with Carlos Matheus. .
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Title: A brief introduction to McMullen’s expander conjecture..
Speaker: Fulin Zhong
Tuesday 10th Fenbuary, 16:00pm–17:00pm, Bush House(S)4.03 KCL
This week we start a new thematic block that will be two weeks long and culminate with a talk (next week) given by Luke Jeffrey about SL(2,Z)-orbits and McMullen’s expander conjecture. .
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Title: An introduction to quantum ergodicity
Speaker: Léo Thiébaud (Aix-Marseille University)
Tuesday 3th Fenbuary, 16:00pm–17:00pm, Bush House(S)4.03 KCL
We will use the quantization processes defined last week in order to define the analog of some dynamical properties of classical systems in the quantum world, namely quantum ergodicity and the invariance of semi-classical measures. I will also describe as precisely as possible the example of the catmap, which allows a better visual understanding of what happens. I will also give more details about the construction of the quantum torus as another example of quantization.
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Title: A brief introduction to geodesic flow, quantisation and the Weyl asymptotics.
Speaker: Giovanni Bracchi
Monday 26th January, 16:00pm–17:00pm, Bush House(S)4.03 KCL
This week we will have the pleasure to have Giovanni Bracchi who will continue guiding us through the notions of geodesic flow, quantisation and the Weyl asymptotics. This will be the final preliminary talk before the expert's presentation the net week..
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Title: Topics of geodesic flow, Hamiltonian dynamics.
Speaker: Oliver Seaman
Tuesday 20th January, 16:00pm–17:00pm, Bush House(S)4.03 KCL
This first session will be lead by Oliver Seaman who will introduce the topics of geodesic flow, Hamiltonian dynamics and hopefully reach the concept of quantum ergodicity.
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Title: Interactions Between Derived Categories and Birational Geometry.
Speaker: Sasha Novik
Tuesday 9th December, 16:00pm–17:00pm, Bush House(S)4.03 KCL
The DK conjecture establishes a link between birational geometry and derived categories, stating that if two varieties are K-equivalent then their derived categories should be equivalent. It arises from a surprising parallelism between the minimal model program and semi-orthogonal decompositions of derived categories. Although the general case remains wide open, in this talk we will discuss the motivation behind it and outline the strategy for proving the derived equivalence in the case of three-dimensional flops.
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Title: A brief introduction to birational geometry and the minimal model program.
Speaker: Zhengyang Cui (KCL)
Tuesday 2th December, 16:00pm–17:00pm, Bush House(S)4.03 KCL
This talk is preparation for Sasha’s talk on the DK conjecture, introducing basic concepts and invariants in birational geometry, and giving an informal overview of the minimal model program for surfaces and 3-folds.
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Title: Introduction to DK Conjecture
Speaker: Edward Young (LSGNT)
Tuesday 25th November, 16:00pm–17:00pm, Bush House(S)4.03 KCL
The discussion will be centered around the derived categories side of the DK conjecture and will be led by Edward Young.
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Title: Siegel–Veech Measures of Convex Flat Cone Spheres
Speaker: Kai Fu (MPI Leipzig)
Tuesday 18th November, 16:00pm–17:00pm, Bush House(S)4.03 KCL
A classical theorem of Siegel gives the average number of lattice points in bounded subsets of R^n. Motivated by this result, Veech introduced an analogue for translation surfaces, now known as the Siegel–Veech formula. However, no such formula is known for flat surfaces with irrational cone angles. A convex flat cone sphere is a Riemann sphere equipped with a conformal flat metric with conical singularities, all of whose cone angles are less than 2pi. In this talk, I will introduce recent work extending the Siegel–Veech theory to this setting and present the strategy of the proof.
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Title: Introduction to Volume of Moduli Space of Translation surface
Speaker: Fulin Zhong
Tuesday 11th November, 16:00pm–17:00pm, Bush House(S)2.02 KCL
The moduli spaces of translation surfaces carry natural SL(2,R)-invariant Masur–Veech measures whose volumes encode fundamental geometric and dynamical properties of flat surfaces. Understanding these volumes is essential not only for Teichmüller dynamics and counting problems, but also for broader generalizations of Siegel–Veech theory. This talk provides a concise overview of the computation and asymptotic behavior of Masur–Veech volumes, serving as background and motivation for the upcoming talk on Siegel–Veech Measures of Convex Flat Cone Spheres.
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Title: Introduction to Moduli space of Translation surface
Speaker: Silvia (LSGNT)
Tuesday 4th November, 16:00pm–17:00pm, Bush House(S)2.02 KCL
The first session will be lead by Siliva Gangeri who will guide us through the first definitions of the field and introduce us to the moduli space of translation surfaces, which will be crucial for the expert's talk.
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Title: An Application of Gauge Theory to Four-Dimensional Topology
Speaker: Yichen Zhang (LSGNT)
Tuesday 28th October, 16:00pm–17:00pm, Bush House(S)2.02 KCL
In this talk, I will outline the key ingredients in the proof of Donaldson’s celebrated diagonalisation theorem — a beautiful story intertwining topology, differential geometry, and non-linear analysis, which has opened up a profound area of research. We shall focus on the construction of the moduli space of anti-self-dual (ASD) instantons, emphasising two subtle points: the gauge-fixing issue (how to quotient by an infinite-dimensional group action) and the bubbling phenomenon (how to recover compactness).
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Title: Introduction to gauge theory and differential topology
Speaker: Oliver Sokvari (LSGNT)
Monday 20th October, 16:00pm–17:00pm, Somewhere KCL
Oliver Sokvari very kindly agreed to prepare a gentle introduction to the themes that Yichen will be presenting on the 28th of October. Themes will revolve around gauge theory and differential topology of four-folds.
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Title: Grassmannians as Homogeneous Varieties: From Algebraic Groups to Lie Theory
Speaker: Zhaoyang Liu (LSGNT)
Tuesday 14th October, 16:00pm–17:00pm, Bush House(S)4.03 KCL
In this talk, we will view the Grassmannian not merely as a parameter space of linear subspaces, but as a homogeneous variety under the action of an algebraic group. We will start with a brief overview of algebraic groups and their basic properties, and then introduce the notion of homogeneous spaces. The motivation for this perspective will be discussed, highlighting how it connects the geometry of varieties with the structure theory of Lie groups and Lie algebras. Time permitting, we will also touch on some classical examples illustrating the interplay between algebraic and differential viewpoints.
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Title: Introduction to Grassmannians
Speaker: Simon Alonso (LSGNT)
Tuesday 7th October, 16:00pm–17:00pm, BH(SE) 1.02 KCL
The aim of this session is to prepare for Zhaoyang's talk about Grassmannians next week. We are therefore going to go on a walk through different ways to think about Grassmannians and a collective reflexion on why do we care about them. Informally, the goal is to decide on Zhaoyang's title and abstract so dont hesitate to come and share your point of view.