Our goal is to investigate deformation quantization "à la Kontsevich" and closely related topics.

Feel free to reach out to Alyosha or Guillaume if you are interested in participating.

Planning

Room : seminar room of QM

• Friday January 31, 2025, 2pm - Alyosha: Formality of the little n-disks operad, Notes.

• Friday February 7, 2025, 2pm - Guillaume: Proof of formality of the little n-disks operad, Notes.

• Wednesday February 12, 2025, 1pm - Alyosha & Guillaume: The Kontsevich integral + 2 alternative proofs of formality (Tamarkin & Petersen strategies), Notes. Followed by Chandan's talk at 3pm: Grothendieck-Teichmüller group and the (cyclic) ribbon group operad.

• Friday February 21, 2025, 2pm - Alyosha: KZ connection and Drinfeld associators.

• Monday March 10, 2025, 1:30pm - Guillaume: Formality of the little discs implies deformation quantization of Poisson manifolds, Notes.

From here on, our goal will be to study in more details the paper "Higher Operations in Perturbation Theory" by Gaiotto-Kulp-Wu (2024).

• April 2, 2025, 7:30pm (online) - Alyosha: Overview of the results.

• April 17, 2025, 3pm - Guillaume: The Laman graphs operad.

References

• Kontsevich, Deformation quantization of Poisson manifolds, 1997
• Tamarkin, Another proof of M. Kontsevich formality theorem, 1998
• Tamarkin, Formality of chain operad of small squares, 1998
• Kontsevich, Operads and motives in deformation quantization, 1999
• Tamarkin, Formality of chain operad of little discs, 2002
• Doubek-Markl-Zima, Deformation theory (lecture notes), 2007
• Lambrechts-Volic, Formality of the little n-disks operad, 2008
• Severa-Willwacher, Equivalence of formalities of the little discs operad, 2009
• Petersen, Minimal models, GT-action and formality of the little disk operad, 2013
• Willwacher, The homotopy braces formality morphism, 2015
• Fresse, Homotopy of operads and Grothendieck-Teichmüller Groups, Part I, 2017
• Banks-Panzer-Pym, Multiple zeta values in deformation quantization, 2018
• Charles' Notes on Kontsevich formality theorem, 2021

• Cattaneo-Keller-Torossian-Bruguières, Déformation, quantification, théorie de Lie, 2002

Drinfeld associators

• Drinfeld, On quasitriangular quasi-Hopf algebras and a group closely connected with Gal(Q/Q), 1991
• Calaque--Roca-Lucio, Associators from an operadic point of view, 2024
• Etingof-Schiffmann, Lectures on quantum groups, 2010

• Severa, Formality of the chain operad of framed little disks, 2010
• Giansircusa--Salvatore, Formality of the framed little 2-disks operad and semidirect products, 2010
• Campos, BV formality, 2015
• Boavida de Brito-Horel-Robertson, Operads of  genus zero curves and the Grothendieck-Teichmüller group, 2017
• Calaque-Willwacher, Triviality of the higher formality theorem, 2015

• Gaiotto-Kulp-Wu, Higher Operations in Perturbation Theory, 2024.
• Balduf-Gaiotto, Combinatorial proof of a non-renormalization theorem, 2024.