International School on Fundamental Crystallography: Seventh MathCryst School in Latin America - PERU 2024

International School on Fundamental Crystallography: Seventh MathCryst School in Latin America - PERU 2024

presencial Faculty of Physical Sciences - UNMSM - Lima - Provincia de Lima - Peru | Perú - Piruw

About the school

The International School on Fundamental Crystallography, a series of educational schools in Latin America, commenced seventeen years ago at the University of Havana, Cuba, and has been hosted biannually in various countries across the region, including Havana, Cuba, Montevideo, Uruguay, Uberlândia, Brazil, La Plata, Argentina, and Bogota, Colombia. The school has served as an important space for the training of Latin American graduate students in the field of crystallography.

The VII edition of the school, set to take place in Lima, Peru, in 2020, was postponed due to the global COVID-19 pandemic. Consequently, at the request of the Peruvian academic community, the Commission on "Mathematical and Theoretical Crystallography" of the International Union of Crystallography (IUCr) granted the Faculty of Physical Sciences at the Universidad Nacional Mayor de San Marcos in Lima, Peru, the opportunity to organize the International School on Fundamental Crystallography: Seventh MaThCryst School in Latin America, from August 12 to 16, 2024.

The school, designed for students from the region, aims to bring together crystallographers from various countries and promote graduate studies in this scientific field. Since its first edition, the school has experienced steady growth in the number of participating Latin American professors and students, thanks to financial support from important institutions such as the IUCr, CLAF, and other regional universities. It is noteworthy that this event has already been recognized as an official school of the IUCr.


The official languages of the school are English and Spanish. Some classes will be taught in English, however the presence of Spanish-speaking tutors familiar with the classes beforehand will provide assistance to those who need it by translating or answering questions on the subject.

Scientific program

Morning session (3:30 hours):
Afternoon session (4:00 hours):
Lectures 8:30 - 10:00
Lectures 14:00 16:00
Coffee break: 10:00 10:30
Coffee break: 16:00 16:30
Lectures 10:30 - 12:30
Lectures 16:30 - 18:30
Lunch: 12:30 - 14:00


1st Day, Monday, morning session:

8:30 - 8:40 Opening of the School


8:40-9:30 Opening lecture: María Cristina Nonato

X-ray crystallography : from material science to drug discovery

10:30-12:30 Lecturer: Massimo Nespolo

Symmetry groups and types of symmetry in direct space. Bravais lattices, conventional and non-conventional unit cells. Symmetry of lattices and symmetry directions. Hermann-Mauguin symbols for point groups. Symmetry of crystallographic patterns: holohedries and merohedries. Crystal families, lattice systems and crystal systems.


1st Day: afternoon session

Lecturers: Massimo Nespolo, Mois Aroyo

  • Miller indices. Morphological symmetry, forms and zone. Stereographic projection and its use for the derivation of crystallographic point groups.
  • Basic properties of groups (group axioms, order, multiplication tables, etc.).
  • Subgroups, index, coset decompositions, Lagrange theorem. Concept of isomorphism and homomorphism. Matrix-column presentation of symmetry operations. Symmetry elements: geometric elements and element sets. Geometric interpretation of the matrix-column presentation of the symmetry operations. Transformations of the coordinate systems: change of origin and orientation.


2nd Day, Tuesday, morning session:

Lecturer: Mois Aroyo.

  • Group-subgroup relations (general considerations): index, coset decomposition and normal subgroups. Conjugation and normalizers; conjugate elements and conjugate subgroups; factor groups and homomorphism.
  • Wyckoff positions for point group. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of point groups.


2nd Day: Tuesday, afternoon session

Lecturer: Massimo Nespolo

  • Space groups - general introduction: periodic structure of the crystalline matter. Screw axes and glide planes.
  • Orthogonal projections of space groups. Exercises on space-group diagrams from Volume A of the International Tables for Crystallography. General and special positions, site-symmetry groups.


3rd Day, Wednesday, morning session:

Lecturer: Mois I. Aroyo

  • Space groups and their description in International Tables for Crystallography, Vol. A. Algebraic determination of Wyckoff positions and site-symmetry groups.
  • Computer databases and access tools to crystallographic symmetry data for space groups (International Tables for Crystallography, Volume A: Space-group symmetry): symmetry operations and their matrix-column presentation; geometric interpretation; general and special Wyckoff positions, site symmetry.


3rd Day, Wednesday, afternoon session:

Lecturer: Mois I. Aroyo.

  • Conventional and non-conventional descriptions of space groups; ITA settings.
  • Group-subgroup relations between space groups: Subgroups of space groups: types of subgroups of space groups; Hermann theorem; maximal subgroups; series of isomorphic subgroups. Coset decomposition.

4th Day, Thursday, morning session:

Lecturers: Leopoldo Suescun, Maria Cristina Nonato, Arbelio Penton-Madrigal, Ernesto Estevez Rams.

  • Reciprocal space
  • Crystallographic calculations in reciprocal space
  • Introduction to diffraction


4th Day, Thursday, afternoon session

Lecturers: Leopoldo Suescun, Maria Cristina Nonato, Arbelio Penton-Madrigal, Ernesto Estevez Rams.

  • Diffraction symmetry: Laue classes, Friedel's law, resonant scattering.
  • Integral, zonal and serial reflection conditions and their use to determine the space-group type. Special reflection conditions.

Poster session: Thursday, 16:00 -18:30


5th Day, Friday, morning session:

Lecturers: Gemma de la Flor Martín, tutor Leopoldo Suescun

  • Maximal subgroups data and related computer applications: (i) Introduction and use of the databases of the IT-Online server and the Bilbao Crystallographic server of maximal subgroups, series of isomorphic subgroups and minimal supergroups; (ii) General group-subgroup relations between space groups: computer programs on the IT-Online server and the Bilbao Crystallographic Server.
  • Relations of Wyckoff positions for a group-subgroup pair. Supergroups of space groups.


5th Day, Friday, afternoon session

Lecturers: Gemma de la Flor Martín, tutor Leopoldo Suescun

  • Crystal-structure descriptions I. Basis transformations and crystal-structure descriptions; structure descriptions compatible with symmetry reduction (the program TRANSTRU). Descriptions of crystal structures with respect to different ITA settings of the space groups (the program SETSTRU). Equivalent crystal structure descriptions (the programs EQUIVSTRU and COMPSTRU).
  • Crystal-structure relations. Group-subgroup relations between space groups and the construction of structure family trees (Baernighausen trees (the program STRUCTURE RELATIONS).


Closing lecture: María Cristina Nonato

Fragment screening by X-ray crystallography, an important tool to develop new therapies against infectious diseases.

Gender Equity and Diversity Policy

Herewith, we the organizers of International School on Fundamental Crystallography. Seventh MaThCryst School in Latin America endorse the IUCr GEDC Code of Conduct.


Statement on Gender Balance at International School on Fundamental Crystallography. Seventh MaThCryst School in Latin America.

The International School on Fundamental Crystallography. Seventh MaThCryst School in Latin America Organizing Committee fully supports and promotes gender equality in accordance with the IUCr policy

We will ensure gender equality in our committees (including the Organizing Committee itself), among our lecturers and participants and pay special attention to the gender balance in evaluating bursary applications.

Our gender statistics on female participation in the schools conducted are shown in the following graph. In this context and in accordance with IUCr policies and according to the observed behavior, in the present school we will emphasize female participation. For further information, our gender equity and diversity advisor is MSc. Maria Luisa Cerón Loayza (e-mail:

Further information can be found on the web site of IUCR’s Gender Equity and Diversity Committee GEDC ( This page contains a code of conduct, a GEDC conference speaker statement and a toolkit for conference organizers.


Scientific Freedom Policy Statement

The Organizing Committee of International School on Fundamental Crystallography. Seventh MaThCryst School in Latin America shall observe the basic policy of non-discrimination and affirms the right and freedom of scientists to associate in international scientific activity without regard to such factors as ethnic origin, religion, citizenship, language, political stance, gender, sex or age, in accordance with the Statutes of the International Council for Science. At International School on Fundamental Crystallography. Seventh MaThCryst School in Latin America no barriers will exist which would prevent the participation of bona fide scientists.


Diversity, Equality and Inclusion Statement

We welcome all crystallographers and scientists working in related fields, regardless of their ethnic origin, race, citizenship, language, political views, gender, sex, sexual preferences, physical disabilities and age. We strive to create a culture of diversity, equality and inclusion.

Important dates / Deadlines

School  registration Opens: March 01, 2024
Early registration deadline: July 12, 2024
Regular and on-site registration: July 12 to August 12, 2024
Submission of poster contribution deadline: July 12, 2024
Notification of poster acceptance/rejection: July 19, 2024
Applications for travel & support deadline: July 122024
Notification for travel & support acceptance/rejection: July 19, 2024


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Certificate and materials of event

In order to secure a certificate, access to materials, and a coffee break, a single payment as specified in the table is necessary. 


Under graduate or post-graduate students.

Retiree or post-doctoral fellows within five (5) years of receiving a graduate degree.

SOPERFI member
SOPERFI member

The prices listed do not account for currency conversion or bank fees. You have the option to pay the entire fee in US dollars or Peruvian soles, and payment instructions can be found by clicking the link.

Abstract submission

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International Program Committee

  • Mois I. Aroyo, University of the Basque Country, Spain
  • Massimo Nespolo, Université de Lorraine, France
  • Gemma de la Flor Martín, Karlsruhe Institute of Technology, Germany
  • María Cristina Nonato, University of São Paulo, Brazil
  • Leopoldo Suescun, Universidad de la República, Uruguay
  • Arbelio Penton-Madrigal, Universidad de la Habana, Cuba


Local Organizing Committee

  • Dr. Justiniano Quispe Marcatoma, Universidad Nacional Mayor de San Marcos
  • Dr. Maria Quintana Caceda, Universidad Nacional de Ingenieria
  • Dr. Carlos Landauro Saenz, Universidad Nacional Mayor de San Marcos
  • MSc. Maria Luisa Ceron Loayza, Universidad Nacional Mayor de San Marcos
  • Dr. Victor Peña Rodríguez, Universidad Nacional Mayor de San Marcos
  • Dr. Gladys Ocharan Velasquez. National University of San Agustin
  • Dr. Hector Loro Ramirez. National University of Engineering
  • MSc. Silvia Espinoza Suarez, Universidad Nacional Mayor de San Marcos
  • Dr. Juan Carlos Gonzalez Gonzalez, Universidad Nacional Mayor de San Marcos
  • Dr. Lyda la Torre Riveros, Universidad Nacional de San Antonio de Abad del Cusco
  • Dr. Veronica Carranza Oropeza, Universidad Nacional Mayor de San Marcos
  • Dr. Elvira Zeballos Velasquez, Universidad Nacional Mayor de San Marcos




Travel & Support

Review the bases to apply for the financial support provided by the organization and sponsors (link)

  • Applications for travel & support deadline: July 12,2024
  • Notification for travel & support  acceptance / rejection: July 19,2024


For any inquiries related to the scientific program and about the organization, please contact:

Dr. Justiniano Quispe Marcatoma

Universidad Nacional Mayor de San Marcos.





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