Besides our research seminars, we also organise a reading seminar. Here postdocs and PhD students present papers they have read, in an informal atmosphere. The goal is to broaden everyone’s expertise, and to make it easier to stay on top of recent developments in a range of subjects.
The schedule for this term is below; when a title is a link clicking it will take you to an abstract. The list of previous reading seminars is also available.
Microlocal theory of sheaves and symplectic topology
The topic of this term’s reading seminar is the Microlocal theory of sheaves and symplectic topology. The principal organiser is Roman Golovko. Here are a few introductory words about the topic.
Microlocal theory of sheaves was introduced and systematically developed in 1980’s by Kashiwara and Schapira. Recently, it was used by Guillermou, Kashiwara, Nadler, Schapira, Shende, Tamarkin, Treumann, Tsygan, Williams, Zaslow and many others to study questions in contact and symplectic geometry and topology. For example, it was used to study Arnold nondisplaceability conjecture/theorem in symplectic geometry and topology, nonsqueezing in contact geometry and topology, GromovEliashberg theorem saying that the group of symplectomorphisms of a symplectic manifold is C^0closed in the group of diffeomorphisms, and so on. One of the most recent results was proven by Shende, and says that conormal torus is a complete knot invariant. More precisely, Shende proved that knots can only have Legendrian isotopic conormal tori if they themselves are isotopic or mirror images.
The main goal of this reading seminar is to learn about microlocal sheaf theory approach to problems in symplectic and contact geometry and topology, its advantages and limitations.
References
 S.F. Chiu, Nonsqueezing property of contact balls, arxiv:1405.1178
 S. Guillermou, Quantization of conic Lagrangian submanifolds of cotangent bundles, arxiv:1212.5818.
 S. Guillermou, M. Kashiwara and P. Schapira, Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems, Duke Math. Journal, (2012). arXiv:1005.1517
 S. Guillermou and P. Schapira, Microlocal theory of sheaves and Tamarkin’s nondisplaceability theorem, arxiv:1106.1576, LNM Springer (2014)
 M. Kashiwara and P. Schapira, Sheaves on Manifolds, Grundlehren der Math. Wiss. 292 SpringerVerlag (1990).
 P. Schapira, A short review on microlocal sheaf theory.
 V. Shende, The conormal torus is a complete knot invariant, arXiv:1604.03520
 D. Tamarkin, Microlocal conditions for nondisplaceability, arxiv:0809.1584
 D. Tamarkin, Microlocal Category, arxiv:1511.08961
 B. Tsygan, A microlocal category associated to a symplectic manifold, arXiv:1512.02747
 C. Viterbo, An Introduction to Symplectic Topology through Sheaf theory.
 Notes from the conference on Symplectic topology, sheaves and mirror symmetry, Paris, June 27 – July 8, 2016, IMJPRG.
December 2016

29/11/16 9h3010h45, Salle de Profs, 9th floor building NO.
Roman Golovko
An introduction to sheaves, part 2.
November 2016

29/11/16 9h3010h45, Salle de Profs, 9th floor building NO.
Roman Golovko
An introduction to sheaves. 
15/11/16 9h3010h45, Room to be determined.
Misha Verbitsky
Derived categories
October 2016

04/10/16 14h16h, Salle de Profs, 9th floor NO
Patrick Weber
From complex to hypercomplex cohomologies
September 2016
 30/09/16, 10h12h, Geometry Seminar Room, 7th flor NO
Roman Golovko
A gentle introduction to Legendrian submanifolds towards Arnoldtype estimates, part 2.  20/09/16, 10h12h, Salle de Profs, 9th floor NO
Roman Golovko
A gentle introduction to Legendrian submanifolds towards Arnoldtype estimates  13/09/16, 11h13h, Salle de Profs, 9th floor NO
Joel Fine
An introduction to twistor spaces
Latest news for the reading seminar
 Microlocal sheaf theory and symplectic topology IV, 6th December  The next talk in the reading seminar on microlocal sheaf theory and symplectic geometry will take place on 6th December at 9h30, in the Salle de Profs. The speaker will be Roman, who will continue his introduction to sheaves.
 Microlocal sheaves and symplecitc topology 3  The next reading seminar in our series on Microlocal sheaves and symplectic topology will take place on Tuesday November 29th, from 9h30 to around 10h30. The talk will take place in the Salle de Profs, on the 9th floor of building NO. The speaker is Roman Golovko, who will talk on “An introduction to sheaves”. […]
 Next talk in the sheaves and symplectic topology reading seminar  Next Tuesday (November 15) there will be a Reading seminar at 9:30 (from 9:30 to 10:30 or 10:45). The topic of the seminar is Microlocal theory of sheaves and symplectic topology. You can find out more about the over all theme of the reading seminar as well as several references on the main reading seminar […]
 Reading group on microlocal sheaves in symplectic geometry – first talk Tuesday 25 October  We begin a new reading group this term, on microlocal sheaves in symplectic geometry. The first talk will be given on Tuesday 25 October at 9:30 am. The room is not yet fixed, but we will meet in the differential geometry corridor shortly before. The speaker is Misha Verbitsky. His title is “Derived categories” and […]
 Patrick Weber informal seminar on complex and hypercomplex cohomologies, 4th October  The next informal seminar will be given by our own Patrick Weber. His title is “From complex to hypercomplex cohomologies”. The talk will take place at 2pm in the Salle de Profs (9th floor of building NO). The abstract is below.
 Roman Golovko – an introduction to Legendrians 20th September  The next informal seminar will be given by Roman Golovko, with the title “A gentle introduction to Legendrian submanifolds towards Arnoldtype estimates”. The talk will take place on Tuesday 20th September 1012, in the Salle de Profs, (mathematics department, on the 9th floor of building NO, Campus de la Plaine). Roman’s abstract is below.
 Introduction to twistor spaces, on September 13  The reading seminar will kick off this term with a series of informal talks in which people will introduce the background of the various areas they are working on. The first talk will be give by me (Joel) at 11am on Tuesday 13th September, in the Salle de Profs, 9th floor of building NO. The […]
 Lower Ricci working group, talk 6  On 30th March, 10:3011:30, in the Salle de Profs, Bruno will give the 6th talk in our working group on manifolds with lower bounds on Ricci curvature. He will describe some of the following topics, from Chapter 9 of Cheeger’s notes: almost volume cones and almost metric cones, Reifenberg’s method, tangent cones at infinity.
 Lower Ricci working group, talk 5, 9th March  On 9th March, at the earlier time than normal of 10h12h, but in the usual location, the Salle de Profs, Michael Khanevsky will give the fifth talk in our working group on manifolds with lower bounds on Ricci curvature. Michael will discuss the almost splitting theorem.
 Lower Ricci working group talk 4, held on 2 March  On 2nd March, 10h3012h30, Salle des Profs, Ben Sibley gave the fourth talk in the working group on manifolds with lower Ricci bounds. He discussed the ChengYau gradient estimate, quantitative maximum principles and the existence of special cutoff functions, all necessary technical ingredients for the almost splitting theorem which will be the topic of a […]