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February 2, 2007

Higher Structure in Geometry and Physics – and in Paris

Posted by Urs Schreiber

Two weeks ago ended the conference in honor of Murray Gerstenhaber’s 80th and Jim Stasheff’s 70th birthdays

Higher Structures in Geometry and Physics.

As Jim Stasheff kindly points out #, slides of many of the talks are now available online.

Paul Baum (Penn State),
Lawrence Breen (Paris 13),
Giovanni Felder (ETH Zurich),
Kenji Fukaya (Kyoto),
Ezra Getzler (Northwestern),
Anthony Giaquinto (Loyola U Chicago),
Simone Gutt (UL Brussels),
Johannes Huebschmann (Lille 1),
Hiroshige Kajiura (Kyoto),
Mikhail Kapranov* (Yale),
Bernhard Keller (Paris 7),
Maxim Kontsevich (IHES),
Yvette Kosmann-Schwarzbach (Polytechnique),
Janko Latschev (Humboldt U Berlin),
Jean-Louis Loday (Strasbourg 1),
Sergei Merkulov (Stockholm),
Pierre Schapira (Paris 6),
Daniel Sternheimer (Dijon),
Dennis Sullivan (CUNY),
Charles Torossian (ENS Paris),
Boris Tsygan (Northwestern),
Alan Weinstein (UC Berkeley).

Posted at February 2, 2007 3:13 PM UTC

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n-Java

I imagine that at some point in the future, people will use special drawing and animation software to write, process and visualize proofs and concepts in higher dimensional algebra.

We had recently seen something along these lines in the context of Guiraud on Higher-Dimensional Rewrite Rules.

Now I see that Berhard Keller provides with the slides for his talk a collection of Java applets that allow hands-on graphical manipulations of quiver mutations.

Posted by: urs on February 2, 2007 3:35 PM | Permalink | Reply to this

Re: n-Java

While reading up on operads, properads and PROPs with Merkulov in Stockholm, just before finishing my MSc, I started toying with a programming project to fascilitate working with finitely presented differential graded PROPs.

My idea was to give generators in terms of the size of the corresponding corolla, and relators, and then have some sort of Gröbner base system (would need to have some theoretical underpinnings to be certain to work though) that would rewrite it for you.

I see similar projects as the obvious way to go in tiny categories, 2-categories, n-categories and possibly even for certain kinds of w-categories. What it would need is a bunch of Gröbner-base style theorems for esoteric contexts.

Posted by: Mikael Johansson on February 2, 2007 9:17 PM | Permalink | Reply to this

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