This School aims to bring together graduate students and young researchers from all regions in Brazil and countries of the South America as audience, and confirmed researchers from all over the world representing different approaches to singularities in Mathematics as speakers.

The school will offer a solid introduction to this rich topic by presenting the fundamentals of the topology and geometry of singularities of spaces and maps, and of the geometric bifurcation theory, together with the necessary algebraic and analytic tools, aiming to a bunch of current research lines.

It will be presented ongoing research topics such as determinantal varieties, bifurcation of families, fibrations structures and new classes of singularities, Lipschitz geometry of singularities, vision and other applications. All courses will be planned to provide the students with practical tools via the open source computer algebra system ‘Singular’.

How to register and ask for supports?

  • Applicants from abroad (any country) and from Brazil but outside São Paulo state, are invited to apply for support in the CIMPA-UNESCO link until March 29th, 2021
  • All candidates to the Research School should also register in the local link until April 30th, 2021.
  • One may apply for support on the CIMPA link and on the local link.


CIMPA Research School “Singularities and Applications”

Updated program 2021 and 2022


Due to the covid pandemic, we have decided to split our program in two parts:

Part 1, July 2021: online lectures followed by an exchange with students on questions and exercises via an IT platform
(for its address, please write an email to one of the organisers). The majority of the lectures will be uploaded before July as video and pdf files. There will be an interactive period supported by the platform during the period July 12-23.

Part 2, July 11-22  2022:  at Sao Carlos.


In Part 1 we will offer the lectures listed below.

Part 2 will complement this list up to the initial program, and possibly go beyond it if time allows.


----------- List of the online lectures, 2021 -----------


Maria Ruas, Juan Nuno Ballesteros, Raul Sinha, and Roberta Wik Atique

Hypersurfaces: algebraic methods and singularities.

1. Basics on classification of singularities.

2. Singularities of germs of functions.


Mihai Tibar and Dirk Siersma
1. Milnor fibrations and their topology. Bouquet theorems.

2. Nonisolated singularity and their topology. 

3. Polar degree of projective hypersurfaces.


Laurentiu Maxim

Topology of complex projective hypersurfaces and of their complements
4 lectures.

Ying Chen, Raimundo Araújo dos Santos, and Mihai Tibar

1. Real Milnor fibrations.

2. Newton polyhedra and mixed singularities.

Renato Dias, Cezar Joita, and Mihai Tibar

1. Bifurcation of polynomial maps in real and complex settings.

2. Topology of polynomial maps.


Jim Damon

Medical Imaging, Skeletal structures and singularities.

3 lectures.


Each lecture is 1h30, for a total of 16 lectures.

Details will appear soon.

Applicants should register for the online part 2021 as explained above, without asking for support.

There will be another registration for the 2022 part.



USP-ICMC, Brazil
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.This email address is being protected from spambots. You need JavaScript enabled to view it.

Mihai-Marius TIBĂR

Université de Lille, France
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

1. Topology of singularities

1a. Milnor fibrations 
1b. Topological invariants 

Singularities and algebraic methods
2a. Hypersurfaces and complete intersections 
2b. Determinantal singularities 

Computing and applications 
3a. Computing with ‘Singular’ 
3b. Applications including vision 

4. Bifurcation theory and Lipschitz geometry 
4a. Bifurcation of affine maps 
4b. Lipschitz geometry of singularities


List of Lecturers

J. Damon, U. North Carolina at Chapel Hill, USA

T. Gaffney, Northeastern Univ., Boston, USA

O. Saeki, Kyushu University, Japan *

Z. Jelonek, Polish Academy, Poland

D. Siersma, Utrecht Univ., The Netherlands

L. Paunescu, U Sydney, Australia *

Maria Ruas, USP, Brasil

R. Araújo dos Santos, USP, Brasil

D. Dreibelbis, U North Florida, USA

L. Maxim, Madison, USA

Anne Frühbis-Krüger, Univ. Oldenburg, Germany

Magdaleen Marais, U Pretoria, South Africa * 

M. Tibar, U Lille, France

N. Dutertre, U Angers, France

C. Joita, Romanian Academy, Romania

J. J. Nuno Ballesteros, Univ Valencia, Spain * 

R. O. Sinha, Univ Valencia, Spain

M. Zach, Univ. Mainz, Germany

Roberta Wik Atique, USP, Brasil

A. Fernandes, Univ, Federal of Ceara, Brasil

L. Birbrair, Univ. Federal of Ceara, Brasil

E. Sampaio, Univ. Federal of Ceara, Brasil

L. Camara, Univ. Federal do Espirito Santo, Brasil

M. Ribeiro, Univ. Federal do Espirito Santo, Brasil

Taciana O Souza, Univ. Federal Uberlandia, Brasil

Thais Dalbelo, UFSCar, Brasil

Bruna O Okamoto, UFSCar, Brasil

R. Dias, Univ. Federal Uberlandia, Brasil

Nguyen Thuy, Unesp, Brasil

Y. Chen, Huazhong Univ.,  China


Universidade do Ceará, Brazil


University of Oldenburg, Germany

Laurentiu PAUNESCU

University of Sydney, Australia

Maria Aparecida RUAS

ICMC, Universidade de São Paulo, Brazil

Thaís Maria DALBELO

Universidade Federal de São Carlos (UFSCar), Brazil

Luis Renato Gonçalves DIAS

Universidade Federal de Uberlandia (UFU), Brazil

Alexandre César Gurgel FERNANDES

Universidade Federal do Ceará, Brazil

Miriam Garcia MANOEL

ICMC, Universidade de São Paulo, Brazil

 Ana Claudia NABARRO

ICMC, Universidade de São Paulo, Brazil

Marcelo SAIA

ICMC, Universidade de São Paulo, Brazil