Geometric Analysis Reading Seminar


OVERVIEW

SCHEDULE

INFO

PAST SEMINARS



Overview

This is an informal reading seminar on topics in geometric analysis organised by geometers at UCL, which is also of interest to analysts, and is attended by researchers at Imperial, King's, Queen Mary and UCL, as well as Cambridge and ULB (Brussels). The topics we cover range from the elementary to the advanced and the seminar is meant to be informal and a chance to learn about the subject, so suggestions for future topics are greatly encouraged. We particularly encourage participation by PhD students.

We keep talks between 1 and 2 hours, and we will often follow a theme for a few weeks. Our current agenda and plans for future topics include:
  • Allen-Cahn equation and min-max theory
  • Einstein metrics
  • Yang-Mills flow


Schedule

The schedule is usually Wednesdays 1-3pm at UCL, with some Thursday afternoon meetings. The room at UCL is Room 707 in the UCL Mathematics Department, 25 Gordon Street. Please check the schedule below for the exact room and directions.


Term 3 2017

Thur 27 April 2017
13:00-15:00
UCL Maths Department Room 707
Desingularizing Einstein metrics
Speaker: Michael Singer (UCL)
Abstract: The goal will be to present Biquard's paper on desingularizing 4-dimensional Einstein orbifolds via gluing, including discussions of the obstructions.
Thurs 11 May 2017
15:30-17:30
UCL Maths Department Room 707
An overview of Yang-Mills flow
Speaker: Casey Kelleher (UC Irvine)
Abstract: The aim is to provide a discussion of the basics of Yang-Mills flow, including the analogy with harmonic map heat flow, the work of Donaldson and Struwe, and potentially singularities and removal of singularities.
Wed 17 May 2017
13:00-15:00
UCL Maths Department Room 707
Uhlenbeck gauge construction
Speaker: Yang Li (Imperial/LSGNT)
Abstract: This talk will focus on the construction of an appropriate gauge in which to study Yang-Mills connection, given by work of Uhlenbeck.
Wed 24 May 2017
13:00-15:00
UCL Maths Department Room 707
Yang-Mills flow in dimension 4: parabolic gauge
Speaker: Huy Nguyen (QMUL)
Abstract: In this first of three talks discussing Waldron's preprint on Yang-Mills flow in dimension 4, the goal will be to discuss the modification of the gauge construction from the previous talk to this parabolic setting.
Thurs 1 June 2017
13:00-15:00
UCL Maths Department Room 707
Yang-Mills flow in dimension 4: energy cascade
Speaker: Reto Buzano (QMUL)
Abstract: In this second of three talks discussing Waldron's preprint on Yang-Mills flow in dimension 4, the goal will be to go through the key energy arguments in the proof.
Tues 13 June 2017
13:00-15:00
UCL Maths Department Room 707
Yang-Mills flow in dimension 4: completing the proof
Speaker: Kim Moore (Cambridge)
Abstract: In this final talk discussing Waldron's preprint on Yang-Mills flow in dimension 4, the key steps from the previous talks will be brought together to summarize the proof.

Term 2 2017

Wed 1 February 2017
13:00-15:00
UCL Maths Department Room 707
Convergence of the Allen-Cahn equation to Brakke’s motion by mean curvature
Speaker: Felix Schulze (UCL)
Abstract: I will present the main results of Ilmanen’s paper on convergence of solutions to the Allen-Cahn equation to Brakke’s motion by mean curvature.
Wed 8 February 2017
13:00-15:00
UCL Maths Department Room 707
The min-max construction of Allen--Cahn critical points
Speaker: Fritz Hiesmayr (Cambridge)
Abstract: In my talk I will discuss the paper by Guaraco entitled "Min-max for phase transitions and the existence of embedded minimal hypersurfaces" from 2015. After situating the paper in the broader context of the construction of minimal hypersurfaces, I will present its results in two parts: first, the PDE min-max construction, and then the energy upper and lower bounds. Time permitting, I might make a short comparison between the Allen--Cahn construction and the earlier Almgren--Pitts theory.
Wed 22 February 2017
13:00-15:00
UCL Maths Department Room 707
Stability and absence of classical singularities for the minimal hypersurface obtained as limit of Allen-Cahn stable solutions.
Speaker: Costante Bellettini (UCL)
Abstract: Two weeks ago Fritz described how to construct an index one critical point for the ε-Allen-Cahn functional: a suitable subsequence as ε→0 delivers a minimal hypersurface (integral varifold) in the limit. I will describe the contents of Tonegawa and Tonegawa-Wickramasekera, which show respectively how the stability of Allen-Cahn solutions is inherited by the limit varifold and how to check that the varifold has no classical singularities. These are the properties that enable the use of Wickramasekera's regularity (codimension-7 singular set).
Wed 1 March 2017
13:00-15:00
UCL Maths Department Room 707
Calabi-Yau metrics on Kummer surfaces
Speaker: Eleonora di Nezza (Imperial)
Abstract: After Yau proved the Calabi conjecture, showing the existence of Kähler metrics with Ricci curvature identically zero on compact Kähler manifolds with vanishing first Chern class, there has been a lot of use of "gluing constructions" in order to give an almost-explicit description of these metrics in some special cases. In this talk I will present a paper of Donaldson: the goal is to explain a gluing construction for some Calabi-Yau metrics on K3 surfaces.
Wed 8 March 2017
13:00-15:00
UCL Maths Department Room 707
Collapsing Calabi-Yau metrics on K3 surfaces via gluing
Speaker: Fabian Lehmann (LSGNT)
Abstract: After last week's gluing construction of a Calabi-Yau metric, this week we will look at Foscolo's recent construction of a family of hyperkahler metrics on the K3 which collapse with bounded curvature outside of finitely many points to T3/Z2. The geometry around points where the curvature blows up is modelled on rescaled ALF gravitational instantons.
Wed 15 March 2017
13:00-15:00
UCL Maths Department Room 707
Minimal surfaces in Poincaré-Einstein manifolds
Speaker: Joel Fine (ULB)
Abstract: The talk will be loosely based on the article "Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds" by Alexakis and Mazzeo. A Poincaré-Einstein metric is an Einstein metric on the interior of a manifold with boundary which is asymptotically hyperbolic near the boundary. Such a metric induces a conformal structure on the boundary. They were first systematically studied by Fefferman and Graham as a way to investigate conformal structures. A central problem is to find a Poincaré-Einstein metric filling in a given conformal infinity and even count the number of such solutions. Minimal surfaces give a simpler version of this boundary problem: for a fixed Poincaré-Einstein metric, given a curve on the boundary, how many minimal surfaces can one find in the interior which meet the boundary at right angles in the given curve? Alexakis and Mazzeo show that, when the ambient manifold has dimension 3, the boundary value map for minimal surfaces is proper, Fredholm of index 0 and so one can define its degree, which “counts” the number of solutions to this Dirichlet type problem. I will explain their proof and then discuss why I hope a similar result should hold for certain ambient manifolds of dimension 4. If there is time, I will try and outline why this may be of interest for the original question of finding a Poincaré-Einstein metric with given conformal structure at infinity.
Wed 22 March 2017
13:00-15:00
UCL Maths Department Room 707
Gluing Eguchi-Hanson metrics and a question of Page
Speaker: Jason Lotay (UCL)
Abstract: The goal will be to present a paper by Brendle and Kapouleas which modifies the gluing construction for Ricci-flat metrics on a 4-manifold (the K3 surface) known as the Kummer construction, described in Eleonora's talk on 1 March. The original motivation of the paper was to try to produce the first example of a compact Ricci-flat metric with full holonomy, which in particular would be the first compact non-Kaehler Ricci-flat 4-manifold. However, the end result is not a Ricci-flat metric, but instead an ancient solution to Ricci flow. I will explain the apparent obstructions to the Ricci-flat gluing problem and the modification required to obtain the solution to Ricci flow.



Information

The current members of the group include:
  • Costante Bellettini (UCL)
  • Reto Buzano (QMUL)
  • Eleonora Di Nezza (Imperial)
  • Joel Fine (ULB)
  • Karsten Fritzsch (UCL)
  • Udhav Fowdar (UCL)
  • Raul Sanchez Galan (UCL)
  • Fritz Hiesmayr (Cambridge)
  • Fabian Lehmann (LSGNT)
  • Jason Lotay (UCL)
  • Mattia Miglioranza (UCL)
  • Kim Moore (Cambridge)
  • Huy Nguyen (QMUL)
  • Felix Schulze (UCL)
  • Michael Singer (UCL)
  • Giuseppe Tinalgia (KCL)
  • Francesca Tripaldi (KCL)
For more information about the seminar contact Felix Schulze (f dot schulze at ucl dot ac dot uk). You can also subscribe to the seminar mailing list, if you are within the UCL network. If you are not within the UCL network, please send an email to Felix Schulze (f dot schulze at ucl dot ac dot uk) with a request to subscribe you to the mailing list.



Past seminars

Term 1 2015

Wed 9 December 2015
14:00-16:00
UCL Maths Department Room 707
Hölder continuity of tangent cones of limit spaces
Speaker: Reto Buzano (Müller) (QMUL)
Abstract: In this talk, we will focus on Colding and Naber's result that tangent cones of limit spaces of manifolds with lower bounds on the Ricci curvature vary Hölder continuously along geodesics. This will follow from the Hölder continuity of the geometry of small balls with the same radius in smooth manifolds. All results can be found in http://arxiv.org/abs/1102.5003 - the aim is to give a comprehensive overview of the most important parts of this paper.
Wed 2 December 2015
14:00-16:00
UCL Maths Department Room 707
Almost volume cones and almost metric cone and the size of the singular set
Speaker: Felix Schulze (UCL)
Abstract: In this talk we will discuss that almost volume cones are almost metric cones and discuss the structure and the size of the limiting singular set.
Wed 4 November 2015
14:00-16:00
UCL Maths Department Room 707
Almost rigidity: volume convergence
Speaker: Yong Wei (UCL)
Abstract: This talk will focus on the volume convergence part of Cheeger-Colding theory.
Wed 28 October 2015
14:00-16:00
UCL Maths Department Room 707
Almost rigidity: the almost splitting theorem
Speaker: Yang Li (LSGNT)
Abstract: This talk will be mainly about the almost splitting theorem (and depending on time I may or may not talk about the volume convergence).
Wed 21 October 2015
14:00-16:00
UCL Maths Department Room 500
Introduction to Cheeger-Colding theory
Speaker: Panagiotis Gianniotis (UCL) and Jason Lotay (UCL)
Abstract: In this talk we will first discuss the Cheng-Yau gradient estimate, before starting on Cheeger-Colding theory, including quantitative maximum principles, rigidity and almost rigidity, and the structure of limit spaces.
Wed 14 October 2015
14:00-16:00
UCL Maths Department Room 707
Introduction to spaces with lower Ricci curvature bounds
Speaker: Panagiotis Gianniotis (UCL)
Abstract: In this talk I will survey some of the basic results in Riemannian Geometry which will form the building blocks for the study of limits of spaces with Ricci curvature bounded below. In particular, I will discuss the Bochner formula, volume and Laplacian comparision theorems, rigidity, Gromov's compactness theorem, the strong maximum principle and the splitting theorem.

Term 3 2015

Wed 3 June 2015
14:00-16:00
UCL Medical Sciences G46 HO Schild Pharmacology Lecture Theatre
Monopole moduli spaces and metrics (Part 4) - The Atiyah-Hitchin Proposition
Speaker: Karsten Fritzsch
Abstract: In this part of our mini lecture series on magnetic monopoles, I will focus on a proposition by Atiyah and Hitchin concerning a type of asymptotic decomposition of monopoles. This proposition was already stated in the last part of this series and it was explained that it can be regarded as a starting point for a route towards a compactification of the moduli space of magnetic monopoles. In this part, I will go into the details of the proof of this proposition and in particular explain the convergence results of Uhlenbeck leading to this proposition.
Wed 27 May 2015
14:00-16:00
UCL Medical Sciences G46 HO Schild Pharmacology Lecture Theatre
The Kaehler-Ricci flow on Kaehler surfaces and MMP
Speaker: Eleonora di Nezza (Imperial)
Abstract: It was recently proposed by Song and Tian a conjectural picture that relates the Kaehler-Ricci flow (KRF) to MMP (Minimal Model Program) with scaling. Although not so much is known in high dimension, much is understood about the KRF in the case of Kaehler surfaces. We will describe the behavior of the KRF on Kaehler surfaces and how it relates to the MMP. In particular, we will show how the KRF carries out the algebraic procedure of contracting (-1)-curves.
(The results I will talk about are due to Song and Weinkove)
Wed 20 May 2015
14:00-16:00
UCL Medical Sciences G46 HO Schild Pharmacology Lecture Theatre
Monopole moduli spaces and metrics (Part 3)
Speaker: Michael Singer
Wed 13 May 2015
14:00-16:00
UCL Medical Sciences G46 HO Schild Pharmacology Lecture Theatre
Monopole moduli spaces and metrics (Part 2)
Speaker: Michael Singer
Wed 6 May 2015
14:00-16:00
UCL Medical Sciences G46 HO Schild Pharmacology Lecture Theatre
Monopole moduli spaces and metrics (Part 1)
Speaker: Michael Singer
Abstract: We shall start with relevant definitions of monopoles, moduli spaces and the moduli space metrics. The conjectural structure of the asyptotic region of the moduli spaces will be discussed, and new progress on these metrics will be described. I will also aim to mention some important open problems within the first two weeks. After this, we will get technical with the analytic tools we use, including manifolds with corners, the relevant non-compact elliptic theory and so on. In particular I hope to explain why the use of manifolds with corners is natural and sensible for this problem.

Term 2 2015

Wed 10 March 2015
11:00-1:00
UCL Taviton (16) Room 431
An Introduction to the Kaehler--Ricci flow
Speaker: Eleonora di Nezza (Imperial)
Abstract: I will give an exposition of a number of well-known results such as the maximal time of existence of the flow and the convergence on manifolds with negative and zero first Chern class. I will also discuss the regularizing properties of the Kaehler-Ricci flow. Finally, if time permits, I will show that the Kaehler-Ricci flow can be run from an arbitrary positive closed current, and that it is immediately smooth in a Zariski open subset of X. .
Wed 25 February 2015
11:00-1:00
UCL Taviton (16) Room 431
Tangent cones to two-dimensional area-minimizing integral currents are unique
Speaker: Tom Begley (Cambridge)
Abstract: I will give an overview of the paper of Brian White of the same name. In this paper the author first reduces the problem of uniqueness of tangent cones to an 'epiperimetric' inequality. Then, for two-dimensional area-minimizing currents, the inequality is proved by constructing explicit comparison surfaces using multiple-valued harmonic functions. As well as discussing the paper, I will start with a quick recap of the requisite geometric measure theory.
Wed 11 February 2015
11:00-1:00
UCL Taviton (16) Room 431
Heat Kernel and curvature bounds in Ricci flows with bounded scalar curvature (Part II)
Speaker: Yong Wei
Abstract: I will talk about the results in sections 6-7 of the paper "Heat Kernel and curvature bounds in Ricci flows with bounded scalar curvature" by Richard Bamler and Qi Zhang (arXiv:1501.01291). By assuming the scalar curvature is bounded along the Ricci flow, they proved the backward pseudolocality theorem which can be coupled with Perelman's forward pseudolocality theorem to deduce a stronger \epsilon-regularity theorem for Ricci flow. As an application, they derived a uniform L^2-bound for the Riemannian curvature in 4-dimensional Ricci flow with uniformly bounded scalar curvature and show that such flow converges to an orbifold at a singularity.
Wed 4 February 2015
11:00-1:00
UCL Drayton House Room B04
Mean value inequalities and heat kernel bounds for the Ricci flow
Speaker: Panagiotis Gianniotis
Abstract: In their recent paper : "Heat Kernel and curvature bounds in Ricci flows with bounded scalar curvature" Richard Bamler and Qi Zhang analyse Ricci flows in which there is a bound on the scalar curvature. The ultimate goal of this work is to understand the possible singular behaviour of a Ricci flow when the scalar curvature remains bounded, and find situations that this singular behaviour can be excluded.
I will talk about the first part of their paper, focusing on the results on Sections 3-5, in which they prove a distance distortion estimate (answering a question of Hamilton), construct good cut-off functions and prove several mean value inequalities for solutions of the heat and conjugate heat equations. These results finally lead to Gaussian bounds for heat kernels.
Wed 28 January 2015
1:00-3:00
UCL 25 Gordon Street Room 707
Asymptotic Rigidity of Self-shrinkers in Mean Curvature Flow
Speaker: Lu Wang (Imperial)
Abstract: In this talk, we discuss uniqueness of self-shrinkers with prescribed asymptotic behavior at infinity. The main tool is the Carleman type estimates.

Term 1 2014

Wed 3 December 2014
1:30-3:00
UCL 25 Gordon Street Room 707
Hyperbolic Alexandrov-Fenchel inequality
Speaker: Yong Wei
Abstract: I will present one work in my Phd thesis. For any 2-convex and star-shaped hypersurface in hyperbolic space, we prove a sharp Alexandrov-Fenchel type inequality involving the 2nd mean curvature integral and area of the hypersurface.
I will start the talk with the motivation of the problem, including an introduction of isoperimetric and Alexandrov-Fenchel inequality in Euclidean space with the recent new proof and applications. Then I state our main result, recent progress and some open problems. Finally, I will give an overview of the proof: in the strictly 2-convex case, the proof relies on an application of Gerhardt's convergence result of inverse mean curvature flow for strictly mean-convex hypersurfaces in hyperbolic space, and sharp Sobolev inequalities on sphere; in the general 2-convex case, the proof involves an approximation argument.
Wed 26 November 2014
1:00-3:00
UCL 25 Gordon Street Room 707
Eleven dimensional supergravity equations on edge manifolds
Speaker: Xuwen Zhu (MIT)
Abstract: We consider the eleven dimensional supergravity equations on B^7xS^4 considered as an edge manifold. We compute the indicial roots of the linearized equations using the Hoge decomposition, and construct a real-valued generalized inverse using different behavior of spherical eigenvalues. We prove that all the solutions near the Freund--Rubin solution are prescribed by three pairs of data on the boundary 6-sphere.
Wed 19 November 2014
1:00-3:00
UCL 25 Gordon Street Room 707
Uniqueness of Lawlor necks
Speaker: Jason Lotay
Abstract: I will discuss the paper by Imagi--Joyce--Oliveira dos Santos on uniqueness of special Lagrangians and Lagrangian self-expanders asymptotic to transverse pairs of planes. This will use the material on Fukaya categories discussed by Jonny Evans in the Symplectic Working Group Seminar on 18 Nov.
Wed 12 November 2014
1:00--3:00
UCL 25 Gordon Street Room 707
Short-time existence of Lagrangian Mean Curvature Flow
Speakers: Tom Begley and Kim Moore
Abstract: We will present recent work on the short-time existence of Lagrangian mean curvature flow with non-smooth initial condition. Specifically we are able to show that given a smooth Lagrangian submanifold with a finite number of isolated singularities, each asymptotic to a pair of transversally intersecting Lagrangian planes P_1 and P_2 such that neither P_1 + P_2 or P_1 - P_2 are area minimising, there exists a smooth Lagrangian mean curvature flow existing for a short time, and attaining the initial condition in the sense of varifolds as t goes to 0, and smoothly locally away from singularities.
We will give an overview of the proof, which relies on a dynamic stability result for self-expanders, a monotonicity formula for the self-expander equation and the local regularity theorem of Brian White.
Wed 29 October 2014
12:30--2:00
UCL 25 Gordon Street Room D103
Results on the Ricci flow on manifolds with boundary
Speaker: Panagiotis Gianniotis
Abstract: Despite the great progress in the study of the Ricci flow on complete manifolds, the behaviour of the flow on manifolds with boundary remains a mystery.
In this talk I will begin with an overview of past work on this problem, and describe the main difficulties it poses. Then, I will show that augmenting the Ricci flow with appropriate boundary conditions, one obtains local existence and uniqueness of the flow, starting from an arbitrary Riemannian manifold with boundary.
I will also describe how these boundary conditions allow derivative estimates similar to Shi's to hold up to the boundary, although the maximum principle arguments that are typically used to obtain such estimates don't seem to be applicable. As a consequence we obtain a compactness result for sequences of Ricci flows and a continuation principle.
I will finish the talk with a discussion on some open problems and questions.
Wed 22 October 2014
12:00--2:00
UCL 25 Gordon Street
Room 706 (12-1)
Room 707 (1-2)
Layer Potential Operators for Two Touching Domains in Rn
Speaker: Karsten Fritzsch
Abstract: So far, no special framework for the study of layer potential operators (or similar operators) on manifolds with corners has been developed even though both approaches, the method of layer potentials and the calculus of conormal distributions on manifolds with corners, have been proven to be very successful.
In this talk, I will demonstrate in two important special cases that the geometric viewpoint of singular geometric analysis leads to a feasible approach to the method of layer potentials: I will solve the Dirichlet and Neumann problems for Laplace's equation on the half-space in Rn in spaces of functions having certain (though very general) asymptotics and then move on to study the more singular situation of two touching domains in Rn. Using the Push-Forward Theorem, on the one hand I will show that the relations between the layer potential operators and their boundary counterparts continue to hold in the singular setting, and on the other hand establish mapping properties of the layer potential operators between spaces of functions with asymptotics. We can improve these by using a local splitting of certain fibrations which arise when applying the Push-Forward Theorem.
In the first half of the talk, I will introduce and discuss the background material, including the method of layer potentials, polyhomogeneity and the Push-Forward Theorem, and the b- and φ-calculi of pseudodifferential operators. If time permits, I will end the talk by sketching the connection to the plasmonic eigenvalue problem on touching domains.
Wed 8 October 2014
11:00--1:00
UCL 25 Gordon Street Room 706
Lagrangian mean curvature flow and symplectic topology
Speaker: Jason Lotay
Abstract: I will discuss aspects of Dominic Joyce's recent preprint in which he conjectures modified versions of the Thomas-Yau conjecture, linking a notion of stability arising in symplectic topology with convergence of Lagrangian mean curvature flow. I will focus on the more concrete parts of his theory and its ramifications for the study of the flow. I will start with an introduction and review of Lagrangian mean curvature flow.

Term 3 2014

Wed 11 June 2014
11:00--1:00
UCL 25 Gordon Street Room 505
Uniqueness of Lagrangian self-expanders (part 2)
Speaker: Jason Lotay
Abstract: I will continue to talk about my joint paper with A. Neves on the uniqueness of Lagrangian self-expanders with two planar ends.
Wed 4 June 2014
1:00--2:30
UCL Drayton House Room B.16
Uniqueness of Lagrangian self-expanders (part 1)
Speaker: Jason Lotay
Abstract: I will talk about my joint paper with A. Neves on the uniqueness of Lagrangian self-expanders with two planar ends and some related results on Lagrangian self-expanders, including results by Neves and Tian, Joyce--Lee--Tsui and Imagi--Joyce--Oliveira dos Santos.
Wed 21 May 2014
1:00--2:30
UCL Drayton House Room B.04
Finite-time singularities of Lagrangian mean curvature flow (part 4)
Speaker: Felix Schulze
Abstract: I will continue to speak on the paper of A. Neves: Finite-time singularities of Lagrangian mean curvature flow.
Wed 14 May 2014
1:00--2:30
UCL 25 Gordon Street Room 500
Finite-time singularities of Lagrangian mean curvature flow (part 3)
Speaker: Felix Schulze
Abstract: I will continue to speak on the paper of A. Neves: Finite-time singularities of Lagrangian mean curvature flow.
Wed 30 Apr 2014
1:00--2:30
UCL 25 Gordon Street Room 500
Finite-time singularities of Lagrangian mean curvature flow (part 2)
Speaker: Felix Schulze
Abstract: I will speak on the paper of A. Neves: Finite-time singularities of Lagrangian mean curvature flow.

Term 2 2014

Tues 1 Apr 2014
11:00--1:00
UCL 25 Gordon Street Room 706
Finite-time singularities of Lagrangian mean curvature flow (part 1)
Speaker: Felix Schulze
Abstract: I will discuss some further details from the paper on the zero-Maslov class case for singularities in Lagrangian MCF by A. Neves.
Wed 12 Mar 2014
11:30--1:30
KCL Strand Building Room S4.29
Singularities of Lagrangian mean curvature flow: zero-Maslov class case
Speaker: Kim Moore
Abstract: I will talk about the paper of the same name by A. Neves.
Wed 5 Mar 2014
12:00--14:00
KCL Strand Building Room S4.36
Introduction to Lagrangian mean curvature flow (part 2)
Speaker: Jason Lotay
Abstract: I will continue to describe some of the basics of Lagrangian mean curvature flow. In particular I will prove that it exists, discuss some examples and describe some more of the known results in the area. Much of what I say is found in my paper with Pacini, a paper by Thomas and Yau, the work of Schoen and Wolfson and in the survey by Neves.
Wed 26 Feb 2014
12:00--14:00
KCL Strand Building Room S4.36
Introduction to Lagrangian mean curvature flow (part 1)
Speaker: Jason Lotay
Abstract: I will describe some of the basics of Lagrangian mean curvature flow. In particular I will describe what it is, the relevant parts of symplectic topology required and what the goal of the flow is. I will also try to survey some of the known results in the area. Much of what I say is found in my paper with Pacini, a paper by Thomas and Yau, the work of Schoen and Wolfson and in the survey by Neves.
Wed 5 Feb 2014
12:00--14:00
KCL Strand Building Room S4.36
A local regularity theorem for mean curvature flow (part 2)
Speaker: Tom Begley
Abstract: I will continue to discuss the paper by Brian White of the same name.
Wed 29 Jan 2014
12:00--13:30
KCL Strand Building Room S4.36
A local regularity theorem for mean curvature flow (part 1)
Speaker: Tom Begley
Abstract: I will discuss the paper by Brian White of the same name.
Wed 22 Jan 2014
13:00--15:00
Birkbeck Torrington Square Room 254
Introduction to mean curvature flow (part 2)
Speaker: Felix Schulze
Wed 15 Jan 2014
13:00--15:00
Birkbeck Torrington Square Room 254
Introduction to mean curvature flow (part 1)
Speaker: Felix Schulze

Term 1 2013

Wed 11 Dec 2013
14:30--16:00
KCL Strand Building Room S4.36
Colding--Minicozzi's curvature estimate (part 2)
Speaker: Giuseppe Tinaglia
Abstract: I will be finishing the proof of the Colding--Minicozzi curvature estimate. We are going to assume the Choi--Schoen curvature estimate from last time and go from there.
Wed 27 Nov 2013
14:30--16:00
UCL Drayton House Room B.06
Colding--Minicozzi's curvature estimate (part 1)
Speaker: Giuseppe Tinaglia
Abstract: Colding--Minicozzi's curvature estimate says that for an embedded minimal disk, the L2 norm of the second fundamental form bounds its L norm. In this part, I will prove a curvature estimate of Choi--Schoen.
Wed 20 Nov 2013
14:30--16:00
KCL Strand Building Room S4.36
Minimal surfaces and the Bernstein theorem
Speaker: Francesca Tripaldi
Abstract: I will discuss the basic theory of minimal surfaces and the proof of Bernstein's theorem.