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.
To stop receiving updates, send an email with subject "Unsubscribe" to maths-juniorgeom-subscribe@ucl.ac.uk.
Schedule
Upcoming Talks
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Title:
Speaker: Aliaksandra Novik (Imprial)
Tuesday 9th December, 16:00pm–17:00pm, Bush House(S)4.03 KCL
Past Talks
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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: DK Conjecture
Speaker: Edward Young (LSGNT)
Tuesday 25th November, 16:00pm–17:00pm, Bush House(S)4.03 KCL
TBD
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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
TBD
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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: TBD
Speaker: Oliver (LSGNT)
Monday 20th October, 16:00pm–17:00pm, Somewhere KCL
TBD
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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.