
Geometry Tea
Geometry Tea is the junior geometry seminar series in
Cambridge covering all aspects of geometry. It's usually given by PhD
students or postdocs. Talks usually take place on Fridays in MR13 at 3pm at the
faculty of mathematics, and are followed by tea and biscuits in the
Pavilion E common room. If you would like to give a talk or invite a
speaker please contact me at col24 (at) cam.ac.uk. Expenses can be
provided by the department for external speakers, roughly on the level
of travel from London.


Easter Term 2016
Friday 29th April:
Claudius Zibrowius (Cambridge).
On the wrapped Fukaya category of the 4punctured sphere
Abstract: The starting point of this talk will be a nonglueable categorification of certain tangle invariants generalising the Alexander polynomial of knots and links. After discussing their construction and some properties, we will specialise to 2stranded tangles and explore what a glueing formula should look like in this case. As an application, we will see why mutation of a (2,3)pretzel tangle does not change deltagraded knot Floer homology. This is joint work with Jake Rasmussen.
Friday 6th May:
Ben Barrett (Cambridge).
JSJ decompositions of groups
Abstract: The JSJ decomposition of an object in a class of a topological spaces or groups is a maximal canonical way of cutting it up into simpler pieces. These were introduced in the study of 3manifolds and have since been applied in more general situations. In this talk we shall first look at some general definitions and results before specialising to the case of hyperbolic groups and the Bowditch JSJ decomposition.
Friday 13th May:
Zhi Jin (Cambridge).
GromovWitten invariants and point constraints
Abstract: This talk will start with an introduction to the GromovWitten invariants in algebraic geometry. Then the calculation of the invariants with point constraints will be illustrated by an example before we generalize the invariants and the calculation to logarithmic geometry.
Friday 20th May:
Tim Talbot (Cambridge).
Gluing asymptotically cylindrical CalabiYau threefolds: or, how seven dimensions are easier than six
Abstract: Given two asymptotically cylindrical CalabiYau threefolds, with matching asymptotics, we may ask whether they can be glued to give a CalabiYau threefold. I will explain this problem and why it is not as straightforward as we might like, and also how it can be done, using an extra dimension to simplify the problem.
Friday 27th May:
Kim Moore (Cambridge).
Calibrated Geometry
Abstract: The seminal paper of Harvey and Lawson 'Calibrated Geometries' was published in the early 1980s. Motivated by Kähler manifolds (a certain class of complex manifold) they define what it means to be a calibrated submanifold, which has the desirable property of being volume minimising in its homology class. With links to special holonomy and complex geometry and also such physical theories as string theory and Mtheory, the field has received much attention from mathematicians over the years.
In this talk I hope to introduce you to calibrated geometry, with motivating examples. Time permitting, I will go on to discuss some highlights of work in the field, and perhaps talk briefly about my own research.
Friday 3rd June:
Giuseppe Papallo (Cambridge, DAMTP).
Causality in Lovelock theories of gravity
Abstract: In Einstein's theory of General Relativity (GR), gravity is described in terms of curvature of the spacetime, a fourdimensional PseudoRiemannian manifold. The field equations, which relate the curvature of spacetime and its matter content, form a system of quasilinear secondorder PDEs in the metric.
Interestingly, Lovelock showed that GR is the unique geometric theory of gravity that we can write down in four dimensions, such that the field equations are second order and energy is locally conserved.
However, this 'uniqueness' does not persist in higher dimensions. In fact there exist more general theories satisfying these assumptions, the socalled Lovelock theories of gravity.
These theories differ from GR in that their field equations are fully nonlinear and these nonlinearities give rise to several interesting phenomena which don't appear in GR, such as superluminal propagation of signals or formation of shocks.
I will discuss some general properties of Lovelock theories, their causal structure and the (im)possibility of constructing time machines.
Friday 10th June:
Bernadette Stolz (Oxford).
Application of Persistent Homology to Biological Networks
Abstract: Computational topology is a set of algorithmic methods developed to understand topological invariants such as loops and holes in highdimensional data sets. In particular, a method know as persistent homology has been used to understand such shapes and their persistence in point clouds and networks. It has only been applied in biological contexts in recent years.
In network science, most tools focus solely on local properties based on pairwise connections, the topological tools reveal more global features. I apply persistent homology to biological networks to see which properties these tools can uncover, which might be invisible to existing methods. In my talk I will show the use of three different methods from Computational Topology, so called filtrations: a filtration by weights, a weight rank clique filtration and a VietorisRips filtration to analyse networks. The example networks I apply these tools to consist of fMRI data from neuroscientific experiments on human motorlearning and the study of schizophrenia, a mathematical oscillator model (the Kuramoto model), as well as imaging data from tumour blood vessel networks. In all cases I will show how these tools reveal insights into the biology or dynamics of the studied problems.
Past Talks
Lent Term 2016
Friday 15th January:
Nina Friedrich (Cambridge).
Homological Stability of Moduli Spaces of High Dimensional Manifolds
Abstract: We start the talk with a short introduction to homological stability. For the example of moduli spaces of high dimensional manifolds we will see a way to relate this geometric setting to an algebraic one. Using a generalisation on the algebraic site we can then improve the homological stability theorem, which in the version proven by GalatiusRandalWilliams just holds for simplyconnected manifolds, to a much larger class of manifolds.
Friday 22nd January:
Jack Smith (Cambridge).
The AurouxKontsevichSeidel criterion
Abstract: The AurouxKontsevichSeidel criterion is a constraint on the selfFloer cohomology of monotone Lagrangians, which is important both conceptually and in calculations. It follows from the construction of a ring homomorphism, the closedopen string map, from the quantum cohomology of the ambient symplectic manifold into Floer cohomology. In this talk I'll try to give a nontechnical introduction to these ideas.
Friday 29th January:
Dmitry Tonkonog (Cambridge).
Laurent phenomenon and symplectic cohomology
Abstract: The function x+y+1/xy stays Laurent under a sequence of certain birational changes of coordinates called cluster tranformations. We will look at this phenomenon from the point of view of symplectic cohomology, observing along the way several other (classical) applications of the theory.
Friday 5th February:
Charlotte KirchhoffLukat (Cambridge, DAMTP).
Generalised Geometry and Dorfman Brackets
Abstract: I will give an introduction to the generalised geometry introduced by Nigel Hitchin and his collaborators, and outline how it is applied in theoretical physics to describe closed string theory in compact spacetimes.
The second part of the talk introduces extended generalised geometries and some of my own work on Dorfman brackets for extended generalised tangent bundles.
Friday 12th February:
Georgios Dimitroglou Rizell (Cambridge).
An introduction to knot contact homology
Abstract: We give an exposition of the geometric and algebraic setup of knot contact homology. This is a powerful knot invariant due to EkholmEtnyreNgSullivan which is based upon the symplectic geometry of cotangent bundles, and defined using pseudoholomorphic curve counts. It is known that this invariant contains the Apolynomial of a knot and that it distinguishes the unknot inside threespace.
Friday 19th February:
Christian Lund (Cambridge).
Einstein structures on manifolds and orbifolds
Abstract: In this talk we study the moduli space of Einstein structures on compact manifolds. We will see how the deformation theory of Einstein metrics on compact Kähler manifolds allows us to get a better understanding of this moduli space. Time permitting, we will also tough upon the generalization of this to orbifolds.
Friday 26th February:
Anna Barbieri (University of Pavia).
Frobenius manifolds and isomonodromic families of connections
Abstract: A Frobenius structure on a manifold is a structure which makes the tangent bundle into an algebra, with a multiplication related to a flat bilinear pairing (metric). I will give an introduction to complex Frobenius manifolds, and we will see their relation with isomonodromic families of meromorphic connections over the projective line.
Friday 4th March:
Mihajlo Cekic (Cambridge).
Calderon problem for connections
Abstract: We consider the problem of determining the connection on a vector bundle from the knowledge of the associated DirichlettoNeumann map. This problem admits a natural gauge symmetry, namely automorphisms fixing the boundary. In this talk we will discuss the approach based on Limiting Carleman Weights, that allow us to construct the Complex Geometric Optics solutions (CGO). We will shortly describe how to construct the CGOs from the Gaussian Beams, which are approximate eigenfunctions of the Laplacian that concentrate along geodesics. A reconstruction procedure will be discussed in the case of line bundles and also the interaction between the unique continuation principle and the holonomy with the Cauchy data.
Friday 11th March:
Alexander Betts (Oxford).
Introduction to anabelian geometry
Abstract: The etale fundamental group of a scheme is a profinite group which simultaneously generalises the notion of the fundamental group of a topological space and the Galois group of a field. As a result, the etale fundamental group sees much of the Diophantine geometry of a scheme, in a sense made precise by Grothendieck's anabelian conjectures. We will introduce the notion of the etale fundamental group, and its relationship to the Diophantine geometry of curves over number fields. Time permitting, we may also introduce a suitable linearised variant, the de Rham fundamental group, as well as describing how one relativises the definition to Sschemes.
Michaelmas Term 2015
Friday 9th October (3pm, MR14):
Matthias Ohst (Cambridge).
Deformations of asymptotically cylindrical Cayley submanifolds
Abstract: Cayley submanifolds of R
^{8} were introduced by Harvey and Lawson as an instance of calibrated submanifolds, extending the volumeminimising properties of complex submanifolds in Kähler manifolds. More generally, Cayley submanifolds are 4dimensional submanifolds which may be defined in an 8manifold M equipped with a certain differential 4form invariant at each point under the spin representation of Spin(7). If this 4form is closed, then the holonomy of M is contained in Spin(7) and Cayley submanifolds are calibrated minimal submanifolds. In this talk I will present an extension of McLean's deformation theory of closed Cayley submanifolds to the setting of asymptotically cylindrical Cayley submanifolds.
Friday 16th October (3pm, MR13):
Thomas Prince (Imperial College).
Hodge theory for curves
Abstract: Hodge structures enrich the cohomology of a variety with a filtration dependent on the complex structure, providing a very rich geometric invariant and an essential tool in many areas of modern algebraic geometry. By studying hyperelliptic curves we can introduce a number of important tools and techniques very geometrically and very explicitly. We will cover topics from a subset of: Period domains and the Siegel upper half space, PicardFuchs equations, Torelli theorems and the AbelJacobi map, degenerations of Hodge structures and mixed Hodge structures from log poles. In particular I hope this will be accessible for beginning graduate students but also of general interest.
Friday 23rd October (3pm, MR13):
Giulio Codogni (University of Pavia and University Roma Tre).
Periods in the classical and super setting
Abstract: This talk will be mainly an introduction to the theory of periods in classical complex geometry. I will discuss both the global and local period map; the main examples will be the period of a curve and the period of a K3 surface. If time permits, and you are interested in, I will say a few words about supergeometry and the generalization of periods in this new set up.
Friday 30th October (3pm, MR13):
Nicolau Sarquis (Imperial College).
Geodesic networks in the Sphere
Abstract: We will discuss how to find closed geodesic networks in the sphere that are critical points (of a mass functional) with higher index. We explain what is the width of a manifold and try to compute it for the round sphere. Furthermore, we give a counterexample to a conjecture regarding the index and nullity of closed geodesic networks in ellipsoids.
Friday 6th November (3pm, MR13):
Pierre Haas (Cambridge, DAMTP).
"O Volvox, how dost thou turn thyself inside out?"
Abstract: Deformations of cell sheets pervade early animal development, but they arise from an intricate interplay of cell shape changes, cell
migration, cell intercalation, and cell division. We explore this interplay of geometry and elasticity in what is perhaps the simplest instance of cell sheet folding: the "inversion" process in the green alga Volvox, whose embryos, in a process hypothesised to be driven by cell shape changes alone, must turn themselves inside out to complete their development. An elastic model, in which cell shape changes correspond to local variations of intrinsic curvature and stretches of an elastic shell, reproduces the dynamics and sheds light on the underlying mechanics of inversion.
Friday 13th November (3pm, MR13):
Alejandro Betancourt (Oxford).
An introduction to Ricci solitons
Abstract: Ricci solitons are generalizations of Einstein metrics. They were introduced by R. Hamilton in the late 80's to study the behaviour of the Ricci flow. In this talk I will discuss some of the basic notions around Ricci solitons and see how they are used to understand the Ricci flow. In particular we will analyse the long time behaviour of the flow and study its singularities via blowup methods.
Friday 20th November (3pm, MR13):
Marco Marengon (Imperial).
Cobordism maps in link Floer homology and reduced Khovanov homology
Abstract: Link Floer homology (HFL) and Khovanov homology (Kh) are two link invariants that have been extensively studied during the last 15 years, during which several interactions between the Khovanov theory and the Floer theory were proved or conjectured. In this talk we prove that a reduced version of Khovanov homology can be computed in terms of HFL groups and cobordism maps, adding this result to the list of somewhat mysterious connections between the two theories.
Friday 27th November (3pm, MR13):
Dominic Wallis (Bath University).
In quest for a nonformal G_2 manifold
Abstract: Does a manifold with special holonomy have to be formal? Answering the question to the affirmative has so far eluded mathematicians (to the author's knowledge). Thus the quest is on to find a counter example. Basics of formality and holonomy will be covered briefly. We examine the results that give us clues for where (mainly not) to look, such as Delign et al that Kähler manifolds, which are precisely those with holonomy U(n), are formal. We introduce the technology available to us to conduct a meaningful search. That is, our constructor of manifolds with holonomy G_2, the twisted connected sum; and our formality detector, the BianchiMassey product. We conclude with our results to date.
Friday 4th December (3pm, MR13):
Ruadhai Dervan (Cambridge).
Symplectic reduction and stability of points
Abstract: Somewhat surprisingly, there is a close link between the process of taking quotients in symplectic and algebraic geometry. This talk will discuss the KempfNess Theorem, which relates the two constructions. I will not assume any previous knowledge of symplectic or algebraic geometry.
Easter Term 2015
1st May  Ben Barrett (Cambridge). Boundaries of hyperbolic groups.
8th May  Jack Smith (Cambridge). Axial discs on homogeneous
Lagrangians.
15th May  Tom Brown (Cambridge). An introduction to Floer simple
manifolds, taut foliations and a possible connection between them.
22rd May  Anton Isopoussu (Cambridge). Cones and fibrations in the
theory of Kstability.
29th May  Diletta Martinelli (Imperial). Around the Cone
Conjecture.
5th June  Nina Friedrich (Cambridge). Introduction to homological
stability.
12th June  Zhi Jin (Cambridge). Logarithmic geometry.
Lent Term 2015
16st January  Joe Waldron (Cambridge). The LMMP for threefolds in
positive characteristic.
23rd January  Carmelo di Natale (Cambridge). Grassmannians and
period mappings in derived algebraic geometry.
30th January  Lawrence Barrott (Cambridge). GromovWitten
invariants in algebraic geometry.
6th February  Paul Wedrich (Cambridge). Deformations of link
homologies.
13th February  Ruadhai Dervan (Cambridge). Stability of twisted
constant scalar curvature Kähler metrics.
20th February  Christian Lund (Cambridge). The moduli space of
Ricci flat Kähler metrics.
27th February  Alexandru Cioba (UCL). Topological methods in
contact dynamics.
6th March  Jonathan Grant (Durham). The Alexander polynomial as a
ReshetikhinTuraev invariant.
13th March  Mihajlo Cekic (Cambridge). Limiting Carleman weights
and related inverse problems.
Michaelmas Term 2014
10th October  Ruadhai Dervan (Cambridge). An introduction to
Kstability.
17th October  Senja Barthel (Imperial). An introduction to spatial
graph theory.
24th October  Peter Overholser (KU Leuven). Tropical invariants
through mirror symmetry.
31st October  Yoshinori Hashimoto (UCL). GromovHausdorff limits
of smooth projective varieties.
7th November  Joint with Junior Algebra seminar. Mandy Cheung
(Cambridge). Mirror symmetry and cluster algebra.
Ruadhai Dervan (Cambridge). Canonical filtrations of coordinate rings
of varieties with nonreductive automorphism group
14th November  Renato Vianna (Cambridge). Distinguishing Clifford
and Chekanov Lagrangian tori in $\C^2$ and $\CP^2$ via count of
Jholomorphic discs.
21st November  Marco Marengon (Imperial). An introduction to
sutured Floer homology.
28th November  Anton Isopoussu (Cambridge). Analytic and algebraic
aspects of moduli problems.
5th December  Lars Sektnan (Imperial). The nonexistence of a
KählerEinstein metric on CP^2 # ( CP^2) via toric geometry.
13th December  Claudius Zibrowius (Cambridge). Alexander
polynomials for tangles.
Easter Term 2014
27th June  Claudius Zibrowius (Cambridge). Introduction to
Bordered Floer Homology.
13th June  Tom Lovering (Harvard University). A Hitchhiker's guide
to Shimura Varieties.
30th May  Diletta Martinelli (Imperial College). What is a flip?
23rd May  Joe Keir (DAMTP, Cambridge). Geometric Analysis in
General Relativity.
16th May  Michael Kasa (UCSD). Log Geometry and Stable Maps.
9th May  Julien Meyer (Universite Libre de Bruxelles).
CscKMetrics and projective embeddings.
2nd May  Thomas Prince (Imperial College). From Lagrangian tori to
Helices via string theory on Gorenstein toric singularities
Lent Term 2014
14th March  Jakob Blaavand (University of Oxford). What a Higgs
bundle is  and why you should care.
7th March  Christian Lund (Cambridge). Growth properties of
manifolds with curvature.
21st February  Anton Isopoussu (Cambridge). Constant scalar
curvature metrics on projective bundles.
14th February  Dmitry Tonkonog (Cambridge). Affine varieties
versus cotangent bundles from a symplectic viewpoint.
7th February  Ruadhai Dervan (Cambridge). Peaked sections and
algebraic approximations of Kaehler metrics.
31st January  Paul Wedrich (Cambridge). Computing categorified
colored sl(N) quantum invariants of rational tangles.
24th January  David WittNystrom (Cambridge). Okounkov bodies and
the moment map problem.
17th January  Julian Holstein (Cambridge). Morita Cohomology.
Michaelmas Term 2013
13th December  Giulio Codogni (Cambridge). Surface singularities,
representation theory and QFT.
6th December  John Rizkallah (Cambridge). Affine Group Schemes
(special joint junior geometryalgebra seminar).
29th November  Joe Waldron (Cambridge). The cone theorem and base
point freeness.
22nd November  Carmelo di Natale (Cambridge). DGLAs in Deformation
Theory.
15th November  Yoshi Hashimoto (University College London).
Approximating constant scalar curvature Kaehler metrics and Chow
stability.
8th November  Robert Pirisi (Scuola Normale Superiore).
Arithmethic StiefelWhitney classes in algebraic geometry.
1st November  Gabriele Benedetti (Cambridge). The dynamics of
magnetic fields on S^2.
25th October  Andrea Fennelli (Imperial College). The fibres of
Mori fibre spaces.
18th October  John Ottem. Hassett's work on cubic fourfolds.
11th October  Anton Isopoussu. Stability of flag varieties.
4th October  Ruadhai Dervan. Multiplier ideal sheaves and
KählerEinstein metrics.
Last modified: 19th May 2016