Wrinkles and h-principles, old and new
A wrinkle courtesy of Eliashberg-Galatius-Mishachev.
The Workshop will take place 22-26 June 2015 at the Mathematical Institute of the LMU in Munich. The talks will begin on Monday morning and the final talk will be on Friday before lunch. Some
funding is available for young researchers and PhD-students.
Registration is now closed.
The following definition of wrinkles is taken from Merriam-Webster's online dictionary:
wrin⋅kle noun \'riŋ-kəl\
In geometry, wrinkles are useful for proving h-principles. This technique was introduced by N. Mishachev and Y. Eliashberg in a series of three papers.
It provides an efficient construction of families of maps with simple singularities. Such maps play an important role in differential topology (Morse functions, submersions, immersions, etc.).
So far, the most well known applications of wrinkling include proofs of the following results:
- a small line or fold that appears on your skin as you grow older
- a small fold in the surface of clothing, paper, etc.
- a surprising or unexpected occurrence in a story or series of events
The principal aim of this workshop is to provide an introduction to the theory of wrinkling together with some of these applications.
- The Mumford conjecture on the homological stability of mapping class groups. This proof (due to Eliashberg, Galatius and Mishachev) reduces the
calculation of the stable homology groups to Harer stability.
- Thurston's existence theorems for foliations of codimension 2 or higher.
- Igusa's theorem about the homotopy type of the space of framed functions whose singularities are non-degenerate or of birth-death type.
This plays an important role in Lurie's discussion of the cobordism hypothesis.
All talks take place in room 349 on the third floor of Theresienstr. 39 with the exception of the Colloquium talk of Emmy Murphy on Thursday, which will take place in A027.
A detailed programme is available here.
- Eliashberg, Y.; Mishachev, N., Wrinkling of smooth mappings and its applications. I. Invent. Math. 130 (1997), no. 2, 345-369.
- Eliashberg, Y.; Mishachev, N., Wrinkling of smooth mappings. II. Wrinkling of embeddings and K. Igusa's theorem. Topology 39 (2000), no. 4, 711-732.
- Eliashberg, Y.; Mishachev, N., Wrinkling of smooth mappings. III. Foliations of codimension greater than one. Topol. Methods Nonlinear Anal. 11 (1998), no. 2, 321-350.
- Eliashberg, Y; Galatius, S; Mishachev, N, Madsen-Weiss for geometrically minded topologists. Geom. Topol. 15 (2011), no. 1, 411-472.
- Eliashberg, Y.; Mishachev, N, The space of framed functions is contractible. Essays in mathematics and its applications, 81-109, Springer, Heidelberg, 2012.
- Thurston, W, The theory of foliations of codimension greater than one. Comment. Math. Helv. 49 (1974), 214-231.
How to get here
From the airport it is easiest to take the s-Bahn (S1 or S8). Both travel into the city and their direction is unique. There are ticket machines on the platform at the station. To get to the math department change to the 27 Tram at Karlsplatz Stachus going to Petuelring (see this map). Or if the weather is nice you may just want to walk.
From the main train station (Hauptbahnhof) either walk to Karlsplatz Stachus and take the tram, take the 100 Bus to the stop Pinakotheken (see this map) or take a (15-20 Minute) walk.
Please make sure to book a hotel room well in advance as there will be a trade fair during the week of the workshop. Here is a list of possible hotels.
Possibilities for lunch
Here is a map showing some of the restaurants and cafes near the maths department.
In case of questions please contact Jonathan Bowden or Thomas Vogel.