Previous Study Groups
| London Number Theory Study Group Previous Study Groups |
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This term the study groups were on p-adic integration, organized by Jack Lamplugh and Joe Kramer-Miller, and p-adic Hodge theory over Lubin-Tate extensions (organised by Joaquin Rodrigues-Jacinto and Sarah Zerbes). They were at UCL.
This term the study groups were on "my favourite paper" (organised by Kevin Buzzard), an analytic study group, and log geometry (organised by Johannes Nicaise). They were at Imperial.
This term the study groups were on Classification of mod p representations of p-adic groups (organised by Julien Hauseux), an analytic study group, and Scholze's Lubin-Tate tower paper (organised by Wansu Kim). They were at Kings.
This term the study groups were on the Iwasawa theory of elliptic curves (organised by Guhan Harikumar) and "Pretentiousness and beyond" (organised by A. Granville). They were at UCL.
This term the study groups were on the p-adic Langlands programme for GL(2,Q_p) (organised by Toby Gee and James Newton), and the yoga of weights (organised by Wansu Kim and Toby Gee). They were at Imperial College.
This term the study group was on the Arithmetic of Euler Systems. It was organised by Sarah Zerbes and was at Kings College.
This term there were two study groups. The first was on p-adic modular forms and eigenvarieties, organised by James Newton and Sarah Zerbes; the second was on Deligne's proof of the Weil conjectures, organised by Olivier Taibi. The study groups were at UCL.
This term the study group was on Vincent Lafforgue's work on global Langlands conjectures; our main reference was this ArXiv paper of Lafforgue's. It was at Imperial College and was organised by Toby Gee.
This term the study group was on Jared Weinstein's paper "Semistable models for modular curves of arbitrary level"; it was at Kings College and was organised by Toby Gee.
This term there were two study groups: one on Bhargava's work on average ranks of elliptic curves (organized by Toby Gee), and one on perfectoid spaces (organized by Sarah Zerbes).
This term there was a study group on K3 surfaces, in particular
on the Tate conjecture for K3 surfaces and recent
work of Keerthi Madapusi Pera. It was organized by Toby Gee and
Alexei Skorobogatov.
This term there was a study group
on the new approach to proving Langlands
functoriality proposed by Langlands, Frenkel and Ngo using ideas
from the geometric Langlands program. It was organized by Alex Paulin.
This term there were two study groups, hosted at UCL. From 1300-1415 we had Modularity Lifting Theorems (run by Judith Ludwig and following Toby Gee's Arizona Winter School notes) and 1415-1530 we had Fargues--Fontaine (run by Fred Diamond and following the two Fargues--Fontaine papers).
This term there were two London Number Theory Study Groups, hosted by Imperial. From 1200 to 1330 there was a study group run by Christian Johansson, Tristan Kalloniatis, Judith Ludwig and Jack Shotton, on deformation theory. From 1400 to 1530 there was a study group on Arthur's Conjectures, run by Toby Gee.
This term there were two London Number Theory Study Groups, hosted by Kings. From 1200 to 1330 there was a study group run by Fred Diamond on Breuil-Kisin modules and applications. From 1400 to 1530 there was a study group run on Shimura varieties, Hida Theory and Galois representations for unitary groups, run by Mahesh Kakde.
This term there were two London Number Theory Study Groups, hosted by UCL. From 1300 to 1400 there was a study group run by Kevin Buzzard on Iwasawa theory and Wiles' proof of the Main Conjecture. From 1430 to 1530 there was a study group run by Ioannis Petridis on subconvexity in the theory of L-functions.
This term there were two Study Groups, held at Imperial. One was run by Kevin Buzzard and was on the Darmon-Dasgupta-Pollack paper, and the other was run by Fred Diamond and was an introduction to p-adic Hodge Theory.
This term the study group was held at Kings, and was on Scholze's proof of the local Langlands conjectures for GL(n). It was organised by Fred Diamond and met 1400-1530.
This term there were two Study Groups, held at UCL. "The Bernstein Centre" met 1200-1330, organised by Kevin Buzzard, and "Vanishing Cycles" met 1400-1530, organised by Wansu Kim.
This term there were two Study Groups, held at Imperial College. "L-functions of Shimura varieties" met 1200-1330, organised by Kevin Buzzard, and "Etale Homotopy" met 1400-1530, organised by Ambrus Pal.
This term the Study Group was held at Kings College and was organised by Shu Sasaki. The subject was "Deformations of Galois representations over imaginary quadratic fields".
The study group schedule for Spring 2010
| 12 May | Introduction (Shu Sasaki) | |
| 19 May | Families of p-adic automorphic forms for GL_1 and GL_2 over imaginary quadratic fields (David Loeffler) | |
| 26 May | The Strong Leopoldt conjecture (Edward Sanders) | |
| 2 June |
The London-Paris Number Theory Seminar speakers: F. Brown, M. Hindry, M. Kakde |
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| 9 June | Proof of the main theorem of Calegari-Mazur (Christian Johannson) | |
| 16 June | Families of ordinary modular forms over imaginary quadratic fields (James Newton) |
This term the Study Group was held at University College and was organised by Mahesh Kakde. The subject was "Motivic L-functions".
The study group schedule for Spring 2010
| 13 January | Overview (Minhyong Kim) | |
| 20 January | Deligne's conjectures (Kevin Buzzard) | |
| 27 January | Beilinson conjectures 1 (Andreas Holmstrom) | |
| 10 February | Beilinson conjectures 2 (Andreas Holmstrom) | |
| 17 February | Bloch Kato 1 (Cecilia Busuioc) | |
| 24 February | Bloch Kato 2 (Wansu Kim) | |
| 3 March | Bloch Kato 3 (Mahesh Kakde) | |
| 10 March | Main conjecture (a la Kato) (Minhyong Kim) | |
| 17 March | Noncommutative main conjecture (Mahesh Kakde) |
This term the Study Group was held at Imperial College and was organised by Kevin Buzzard and Shu Sasaki. The subject was Ramakrishna's lifting theorems.
The study group schedule for Autumn 2009
| 7 October | Introduction (Kevin Buzzard) | |
| 14 October | Group cohomology etc. (Christian Johannson) | |
| 21 October | local Tate duality etc. (Edward Sanders) | |
| 28 October | Deformations of Galois representations: intro (Owen Jones) | |
| 4 November | Deformations of Galois representations (Fred Diamond) | |
| 11 November | Ramakrishna's theorem I (Shu Sasaki) | |
| 18 November | Ramakrishna's theorem II (James Newton) | |
| 25 November | Ramakrishna's theorem III (minimal lift) (Wansu Kim) | |
| 2 December | Ramakrishna's theorem III (minimal lift) (continued) (Wansu Kim) | |
| 9 December | Section 2 of Taylor's "On icosahedral Artin representations II" (Kevin Buzzard) |
This term the Study Group was held at King's College and was organised by Behrang Noohi. The subject was "Locally symmetric spaces and arithmetic groups".
The study group schedule for Summer 2009
| 29 April |
Introduction (Behrang Noohi) Algebraic groups, part 1 (Owen Jones) | |
| 6 May | Algebraic groups, part 2 (Kevin McGerty) | |
| 20 May | Symmetric spaces (Behrang Noohi) | |
| 27 May 11:30am-1:00pm |
Compactifications of locally symmetric spaces (Payman Kassaei) | |
| 3 June - 4 June |
The London-Paris Number Theory Seminar at King's College London, room 2B08 theme: p-adic modular forms speakers: Buzzard, Fargues, Loeffler, Colmez, Mokrane, Dimitrov, Panchishkin |
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| 10 June | Buildings (Kevin Buzzard) |
This term the Study Group was held at University College and was organised by Ambrus Pal. The subject was Ngo's recent proof of the fundamental lemma.
The study group schedule for Spring 2009
| 14 January | Statement of the fundamental lemma (Kevin Buzzard) | |
| 21 January | Passage to the equicharacteristic case (Ambrus Pal) | |
| 28 January | Stacks and equivariant cohomology (Behrang Noohi) | |
| 4 February | Neron models (Andrei Yafaev) | |
| 11 February | Compactified Jacobians (Nick Shepherd-Barron) | |
| 18 February | The Hitchin fibration (Tamas Hausel) | |
| 25 February 12:00-13:30 |
Perverse sheaves (Kevin McGerty) |
| Monday 9 March at 3:00 pm room 706 |
Lecture 1: Fundamental lemma and Hitchin fibration | |
| Monday 9 March at 4:30 pm room 706 |
Lecture 2: Symmetry of Hitchin fibration and endoscopy | |
| Friday 13 March at 4:00 pm room 500 |
Lecture 3: Decomposition theorem in the case of the Hitchin fibration |
This term the Study Group was held in Imperial College and was organised by Ambrus Pal. The subject was the work of Ciperiani-Wiles on solvable points.
The study group schedule for Autumn 2008
| 8 October | Introduction (Ambrus Pal) | |
| 15 October | The modular curve X_0(N) (Kevin Buzzard) | |
| 22 October | Complex multiplication (James Newton) | |
| 29 October | Ramified over unramified principle (Alexei Skorobogatov) | |
| 5 November | Kolyvagin classes (Minhyong Kim) | |
| 12 November | The Andre-Oort conjecture (Andrei Yafaev) | |
| 19 November | The Gross-Zagier formula, I (Fred Diamond) | |
| 26 November | Solvable points on geometrically rational surfaces (Ambrus Pal) | |
| 3 December | The Gross-Zagier formula, II (Richard Hill) | |
| 10 December | The ex-Ax conjecture (Ambrus Pal) | |
| 17 December | Brauer diagonalisation and solving in solvable extensions (Trevor Wooley) |
This term the Study Group was held in King's College and organised by Kevin Buzzard. The subject was the seminal Coleman-Mazur paper "The eigencurve".
The study group schedule for Summer 2008
| 23 April | Introduction (Kevin Buzzard) | |
| 30 April | Modular forms (James) | |
| 7 May - 8 May |
The London-Paris Number Theory Seminar | |
| 14 May | p-adic L-functions (Malcolm) | |
| 21 May | p-adic modular forms, weight k (Payman) | |
| 28 May | p-adic modular forms, weight kappa (Kevin) | |
| 4 June | Compact operators on p-adic Banach spaces/modules (Owen) | |
| 11 June | Eigencurve via Hecke algebras (David L) | |
| 18 June | Eigencurve via deformation theory (Kevin/Fred) |
This term the Study Group was held in University College and organised by Ambrus Pal and Alexei Skorobogatov. The subject was arithmetic fundamental groups.
The study group schedule for Spring 2008
| 9 January | Introduction | |
| 16 January | Belyi's theorem (Owen Jones) | |
| 23 January | Chabauty's theorem (Richard Thursby) | |
| 30 January | Tannakian formalism (Alex Paulin) | |
| 6 February | Deligne's paper on the fundamental group of the projective line without 3 points (Kevin Buzzard) | |
| 13 February | Bloch-Kato and the definition of H^1_f of a Galois representation (David Loeffler) | |
| 20 February | F-crystals (Sarah Zerbes) | |
| 27 February | Crystalline fundamental group (Ambrus Pal) | |
| 5 March | Global and local Selmer varieties (Minhyong Kim) | |
| 12 March | Bloch-Kato/Fontaine-Mazur imply Mordell (Minhyong Kim) |
This term the Study Group was held in Imperial College and organised by Sarah Zerbes. The subject was "Fontaine's theory of p-adic representations".
The study group schedule for Autumn 2007
| 3 October | The l-adic case (Kevin) | |
| 10 October | Overview of Fontaine's work (Sarah) | |
| 17 October | Local fields (Owen) | |
| 24 October | Witt vectors (James) | |
| 31 October | General equivalence of categories (Richard) | |
| 7 November | Fields of norms (Kevin) | |
| 14 November | (phi,Gamma)-modules (Payman) | |
| 21 November | B_dR + properties (Fred) | |
| 28 November | B_cris/B_max + properties (Alex) | |
| 5 December | B_st, example of the representation associated to an elliptic curve (tba) | |
| 12 December | Relation to (phi,Gamma)-modules (outline) (David) |
This term the Study Group was held in University College and organised by Kevin Buzzard. The subject was Emerton's work on eigenvarieties.
The study group schedule for Summer 2007
| 25 April |
Constructing representations (Owen Jones, Imperial) Travaux d'Emerton (Kevin Buzzard, Imperial) | |
| 2 May |
The London-Paris Number Theory Seminar
11 am - 4:30 pm, Imperial College London |
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| 9 May |
p-adic Banach spaces (Shu Sasaki, Imperial) Shimura manifolds (Alex Paulin, Imperial) | |
| 16 May |
Emerton's spectral sequence (David Loeffler, Imperial; Richard Hill, UCL) | |
| 23 May |
Classical modular forms and locally algebraic representations (Payman Kassaei, KCL) The case G(R) compact (Kevin Buzzard, Imperial) | |
| 30 May |
Jacquet functors and eigenvarieties (Kevin Buzzard, Imperial; Toby Gee, Imperial) |
This term the Study Group was held in King's College and organised by Payman Kassaei. The subject was "Representations of p-adic groups and the Local Langlands Conjecture".
The study group schedule for Spring 2007
| 17 January | Introduction (Payman Kassaei, King's) | |
| 24 January | Admissible representations of l-groups (Owen Jones, Imperial) | |
| 31 January | The Jacquet functor and supercuspidal representations (Rebecca Torrey, King's) | |
| 7 February | The classification theorem I (Shu Sasaki, Imperial) | |
| 14 February | The classification theorem II (Brian Tyler, UCL) | |
| 21 February | Whittaker and Kirillov models and strong multiplicity one (Payman Kassaei, King's) | |
| 28 February | Supercuspidal representations of GL_n (David Loeffler, Imperial) | |
| 7 March | The Satake isomorphism (Richard Hill, UCL) | |
| 14 March | Local-global compatibility (Alex Paulin, Imperial) | |
| 21 March | Henniart's approach to Local Langlands (Toby Gee, Imperial) |
This term the Study Group was held in Imperial College and was organised by Richard Hill. The subject was "(g,K)-cohomology".
The study group schedule for Autumn 2006
| 4 October | Introduction (Richard Hill, UCL) | |
| 11 October | Structure of semisimple and reductive groups over R (Owen Jones, IC) | |
| 18 October | Highest weight representations (David Loeffler, IC) | |
| 1 November | Harish-Chandra isomorphism (Imma Galvez-Carrillo, London Metropolitan University) | |
| 8 November | Classification of (g,K)-modules (Alex Paulin, IC) | |
| 15 November | (g,k) and (g,K) and g cohomology and a vanishing theorem (Brian Tyler, UCL) | |
| 22 November | Laplacian and Casimir elements and calculation of (g,k)-cohomology (Kevin Buzzard, IC) | |
| 29 November | (g,k)-cohomology of principal series (Shu Sasaki, IC) | |
| 6 December | (g,k)-cohomology of discrete series (Payman Kassaei, KCL) | |
| 13 December | tba (Richard Hill, UCL) |
This term the Study Group was held in King's College and was organised by Manuel Breuning. The subject was quadratic forms.
The study group schedule for Summer 2006
| 3 May | Introduction (Manuel Breuning) |
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| 10 May | Witt's cancellation and decomposition theorems (James Barrett) |
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| 17 May | Quadratic forms over completions of Q (Malcolm Bovey) |
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| 24 May | Hasse-Minkowski (principle) (Andrew Parker) |
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| 31 May | Witt rings (James Barrett) |
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| 7 June | Clifford algebras (Andrew Parker) |
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| 14 June | Pfister forms and function fields (Manuel Breuning) |
This term the Study Group was held in King's College and was organised by Manuel Breuning and Andrew Parker. The subject was "Classical K-theory of number fields".
The study group schedule for Spring 2006
| 18 January | Overview (Andrew Parker and Manuel Breuning) |
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| 25 January | Definitions and properties of K_0(R) and examples (Malcolm Bovey) |
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| 1 February | Definitions and properties of K_1(R) and examples (Brian Tyler) |
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| 8 February | Definitions and properties of K_2(R) and examples (David Mireles Morales) |
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| 15 February | Long exact sequence of K-groups for Dedekind domains (James Barrett) |
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| 22 February | K_2(Q) / Galois cohomology and Brauer Groups (David Mireles Morales / Andrew Parker) |
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| 1 March | Merkurjev-Suslin Theorem (Andrew Parker) |
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| 8 March | K_1 of the ring of integers of a number field and the congruence subgroup problem (Toby Gee) |
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| 15 March | K_2 of the ring of integers of a number field (Manuel Breuning) |
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| 22 March | Lichtenbaum Conjectures (David Burns) |