CIMPA Research School « Singularities and Applications » July 11-22, 2022

Live lectures


Part 1 of this Research School took place online in June-July 2021, via the IT platform . A great amount of material has been prepared and is still available on this site, more precisely :
- 7 courses as pdf files, with exercises. See link here for the beamers of the 2021 lectures.
- recorded videos of about 7 hours for each of 6 courses, for a total of about 40 hours.
There has been an interactive period of two weeks July 12-23, 2021, supported by the same platform. Over 150 participants had signed up to this IT platform.


Part 2, July 11-22 2022 in live mode at Sao Carlos. OFFICIAL PICTURE HERE!


Here is a list of the main courses that will be delivered in the live meeting at Sao Carlos.

                         Download timetable(updated July 18th) school and JTalks




Course 1. Singularities and algebraic methods. Maria Ruas, Juan Nuno Ballesteros, Bruna Oréfice, Roberta Wik Atique, Terry Gaffney, Matthias Zach, Jim Damon. Links to the material: the Beamer handout pdfThom-Mather Theory at 50 Years of Age


1A. Complete intersections with isolated singularities (ICIS). Links to the material:ICIS, Equisingularity and ICIS

1B. Determinantal singularities. Links to the material: Lecture 1 - Part 1, Lecture 1 - Part 2Equisingularity and EIDS, Slides for Lecture 2 (Gaffney)Lie Group Methods and Characteristic Cohomology, Topology of EIDS


Course 2. Algorithmic and computational aspect of singularities. Anne Frühbis-Krüger, Matthias Zach, Sabrina

Links to the material: slides 1, slides 2, slides 3, slides 4Worksheet 1 (to download, right-click here and select 'save as'), Worksheet 2 (to download, right-click here, and select 'save as'),  Worksheet 3 (to download, right-click here, and select 'save as'), Worksheet 4 (to download, right-click here, and select 'save as')


Course 3. Lipschitz geometry of singularities. Alexandre Fernandes, Edson Sampaio, Zbigniew Jelonek, Lev Birbrair. Links to the material: Notes 1, Notes 2



                                                               Followup sessions.
                                                                      based on the online lectures of the CIMPA School 2021


F1. Hypersurfaces: algebraic methods and singularities. Maria Ruas, Raul Sinha, Roberta Wik Atique, Juan Nuno Ballesteros – see the PDF files on “Program 2021”. No followup talks.


F2. Milnor fibrations, nonisolated singularity, and  the polar degree of projective hypersurfaces. Dirk Siersma, Mihai Tibar

Introduction, Monodromy Bouquet Thm, Nonisolated singularities, Polar degree.


F3. Topology of complex projective hypersurfaces and of their complements. Laurentiu Maxim

All lectures


F4. Real Milnor fibrations, and mixed singularities. Nicolas Dutertre, Mihai Tibar / Cezar Joita

Real Milnor fibrations


F5. Bifurcation of affine maps in real and complex settings. Cezar Joita, Renato Dias. Part 1, Part 2Part 3, Part 4