KCL/UCL Junior Geometry Seminar

Information

The KCL/UCL Junior Geometry Seminar is a joint seminar of King's College London and University College London. Speakers present 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 — from all London universities. The atmosphere is friendly and informal, most talks are accessible to a wide audience.

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. For inquiries please contact Myles Workman (myles.workman.16@ucl.ac.uk) or Wei Zhou (wei.zhou.20@ucl.ac.uk).

If you want to stop receiving updates, send an email with subject "Unsubscribe" to maths-juniorgeom-subscribe@ucl.ac.uk.



Term 1

27 September 2021 - 17 December 2021


21 October 2021


Quaternion-Kähler manifolds

Ivan Solonenko (King's College London - LSGNT)
King's College, Strand Building, Room S-3.20 • 17:00 - 18:00

Abstract: A quaternion-Kähler manifold is a 4n-dimensional Riemannian manifold whose holonomy group is contained in Sp(n)Sp(1), one of the 7 groups appearing in Berger’s list of Riemannian holonomy groups. They are ...

7 October 2021


Geometric Applications of the Allen-Cahn Equation and Min-Max Techniques

Myles Workman (University College London - LSGNT)
King's College, Strand Building, Room S-3.20 • 17:00 - 18:00

Abstract: The Allen-Cahn equation is a reaction-diffusion equation that originally comes from mathematical-physics, but in recent decades has found a new home in the field of geometric analysis. The equation ...

Term 3

6 May 2021 - 27 June 2021


6 May 2021


Moduli spaces of stable sheaves on K3 surfaces via wall-crossing

Alessio Bottini (Tor Vergata University of Rome/Paris-Sud University)
Zoom • 17:00 - 18:00

Abstract: Moduli spaces of stable sheaves (and stable complexes) on K3 surfaces are a well-studied family of high-dimensional ...

13 May 2021


Convolutions on manifolds and applications to geometric deep learning

Daniel Platt (Imperial College London - LSGNT)
Zoom • 17:00 - 18:00

Abstract: Convolution is a natural operation combining two integrable functions on Euclidean space. This operation motivates ...

20 May 2021


Stability in differential and algebraic geometry

John McCarthy (Imperial College London - LSGNT)
Zoom • 17:00 - 18:00

Abstract: Research at the intersection of differential and algebraic geometry has been dominated by the principle that extremal objects ...

27 May 2021


From Feix-Kaledin metric on T*X to algebraic geometry

Anna Abasheva (Columbia University)
Zoom • 17:00 - 18:00

Abstract: Let X be a Kähler manifold and let’s consider the total space T*X of the cotangent bundle of X. In many nice cases there exists ...

03 June 2021


K3 Surfaces & a Modular Form

Qaasim Shafi (Imperial College London - LSGNT)
Zoom • 17:00 - 18:00

Abstract: A quadric surface in P^3 can be covered completely by lines. A cubic surface famously contains 27 lines. A quartic surface is an example of a K3 surface ...

10 June 2021


Maximum principle and geometric applications

Kostas Leskas (University College London - LSGNT)
Zoom • 17:00 - 18:00

Abstract: One of the main features that distinguishes linear, uniformly elliptic, 2nd order differential operators is the maximum principle ...

17 June 2021


Constant scalar curvature Kähler metrics

Alessio Di Lorenzo (University College London - LSGNT)
Zoom • 17:00 - 18:00

Abstract: Eugenio Calabi had a dream: that one could find on each Kähler manifold a metric that could be called "canonical" ...

24 June 2021


An L-infinity lifting of the first component of the semiregularity map

Emma Lepri (Sapienza Università di Roma)
Zoom • 17:00 - 18:00

Abstract: The subject of the talk is the construction of a lifting of the first component of the (modified) Buchweitz-Flenner semiregularity ...

Term 2

21 January 2021 - 1 April 2021


21 January 2021


Barrier methods for minimal submanifolds and
the Gibbons-Hawking ansatz

Federico Trinca (University of Oxford)
Zoom • 17:00 - 18:00

Abstract: A submanifold of a Riemannian manifold is minimal if it is critical points of the volume functional. Using the maximum principle ...

28 January 2021


A Physics approach to the Atiyah-Singer Index theorem

Andries Salm (University College London)
Zoom • 17:00 - 18:00

Abstract: Do you think your supervisor is too rigorous? Do you silently believe that the world is smooth and finite at the same time? Do ...

4 February 2021


Geometric approaches to Nielsen equivalence

David Sheard (University College London)
Zoom • 17:00 - 18:00

Abstract: In the world of finitely generated groups, presentations are a blessing and a curse. They are versatile and compact, but in general tell you very little about the group. Tietze transformations offer ...

11 February 2021


Mabuchi Geometry of the Space of Kähler/Sasaki Potentials

Thomas Franzinetti (Sorbonne Université)
Zoom • 17:30 - 18:30

Abstract: Given a compact Kähler (resp. Sasakian) manifold, one can endow the space of Kähler (resp. Sasakian) potentials with a so called Mabuchi metric. We show that its metric completion is negatively curved in the sense of Alexandrov.

18 February 2021


From Riemann to Russia: Alexandrov Geometry

Tom Sharpe (LSGNT - King's College London)
Zoom • 17:00 - 18:00

Abstract: Do you long for a coordinate-free approach to Riemannian geometry? Are you filled with dread whenever your metrics develop singularities? Or can you not imagine why anyone would want to leave the world of smoothly varying tensors? Either way, ...

25 February 2021


Geodesic orbit spaces

Jordan Hofmann (LSGNT - King's College London)
Zoom • 17:00 - 18:00

Abstract: Homogeneous spaces are at the heart of Riemannian geometry, providing a vast "playground" of examples, however this class of spaces is vast and a complete classification is probably out of reach. For this reason many subclasses have been studied ...

4 March 2021


Symplectic embeddings: the Hofer conjecture

Roman Krutowski (University of California, Los Angeles)
Zoom • 17:00 - 18:00

Abstract: The study of symplectic embeddings has a long history starting with the celebrated Gromov's non-squeezing theorem. One of the long-standing conundrums in the field was the ellipsoid embedding problem. The answer to it is now known under ...

11 March 2021


Weinstein handlebodies for toric manifolds

Angela Wu (Imperial College London)
Zoom • 17:00 - 18:00

Abstract: This talk is about two important classes of symplectic manifolds: toric manifolds, which are equipped with an effective Hamiltonian action of the torus, and Weinstein manifolds, which ...

18 March 2021


The Witten genus as the "volume" of the double loop space

Eugenio Landi (Università degli Studi Roma Tre)
Zoom • 17:00 - 18:00

Abstract: Witten introduced his genus in 1986 as a suitable index of a Dirac operator on the loop space of a manifold. In this talk I will recover the Witten genus using the localization theorem in ...

25 March 2021


Hamiltonian Floer Cohomology

Kai Hugtenburg (University of Edinburgh)
Zoom • 17:00 - 18:00

Abstract: Every day the Earth completes a rotation around its axis. In this case there are infinitely many 24-hour periodic orbits, there are even 2 fixed points! This is a slight approximation though ...

1 April 2021


K3-fibred G2 manifolds and their adiabatic limits

Corvin Paul (University College London - LSGNT)
Zoom • 17:00 - 18:00

Abstract: One of the most interesting open conjectures in geometry is the SYZ conjecture. It roughly states that (complex) 3D Calabi Yau manifold should admit a fibration over a (real) 3D base such that ...

Term 1

28 September 2020 - 18 December 2020


1 October 2020


Gauge Theory and Invariants

Jakob Stein (University College London)
MS Teams • 17:00 - 18:00

Abstract: The uses of "gauge theory", that is — connections on principal/vector bundles — to obtain invariants of smooth manifolds, has been a topic of mathematical research since ...

8 October 2020


Intrinsically Harmonic Forms

Ivan Solonenko (King's College London)
MS Teams • 17:00 - 18:00

Abstract: Given a closed differential form on an oriented smooth manifold M, does there exist a Riemannian metric on M with respect to which the form becomes harmonic? Do forms allowing such metrics ...

15 October 2020


The Conway Knot is not Slice

Laura Wakelin (Imperial College London)
MS Teams • 17:00 - 18:00

Abstract: A knot is said to be slice if it bounds a smoothly embedded disc in B^4. For a long time, the question of sliceness had been answered for all knots with up to 12 crossings – except ...

22 October 2020


Introduction to Geometric Flows

Joshua Daniels-Holgate (University of Warwick)
Zoom • 17:00 - 18:00

Abstract: When first introduced to topology, you were probably shown an animation depicting the family of smooth deformations that turn a coffee cup into a donut. One might hope for a way of doing this ...

29 October 2020


Hyper-Kähler Geometry

Jaime Mendizabal Roche (University College London)
Zoom • 17:00 - 18:00

Abstract: Hyper-Kähler manifolds are, in a sense, the quaternionic analogues of Kähler manifolds. As such, many points of view can be taken when studying them. They have a Riemannian metric which ...

5 November 2020


Lefschetz Hyperplane Theorem and the Topology of Algebraic Varieties

Riccardo Carini (Imperial College London)
Zoom • 17:00 - 18:00

Abstract: When dealing with nonsingular varieties over the complex numbers, an extremely powerful method is to regard them as ...

12 November 2020


Singularities in Algebraic Geometry

Federico Bongiorno (Imperial College London)
Zoom • 17:00 - 18:00

Abstract: During the course of a PhD, it is generally very difficult to avoid encountering singular varieties. They arise naturally as limits of smooth varieties but dealing with them requires ...

19 November 2020


Hochschild (co)homology

Federico Barbacovi (University College London)
Zoom • 17:00 - 18:00

Abstract: When studying geometric problems, it is often useful to produce some algebraic invariant that controls the geometry what we are interested in. Sometimes, these algebraic tools are ...

26 November 2020


The Grothendieck Ring of Varieties, and some new Euler Characteristics

Jesse Pajwani (Imperial College London)
Zoom • 17:00 - 18:00

Abstract: The Grothendieck ring of varieties is, depending on your point of view, either a very natural and obvious object to ...

3 December 2020


Equivariant Cohomology of GKM Manifolds

Teresa Lüdenbach (King's College London)
Zoom • 17:00 - 18:00

Abstract: Torus actions and the manifolds which admit them have been vastly studied, in particular by Goresky, Kottwitz and MacPherson ...

10 December 2020


A brief introduction to Mirror Symmetry

Soham Karwa (Imperial College London)
Zoom • 17:00 - 18:00

Abstract: Mirror Symmetry is a striking conjecture/philosophy concerning a certain equivalence of spaces that has revolutionised geometry and ...