Invited Lectures

Pierre Berger, PhD.
Université Paris 13 Sorbonne Paris Cité, France

Pierre Berger graduated from Ecole Normale Supérieure in Paris, has done his PhD with J.C. Yoccoz at Univ. Paris XI and College de France. He has been ERC laureate for the program "Emergence of wild differentiable dynamical systems" which aims to describe the statistical complexity of dynamical systems. He is now CNRS research director at Sorbonne University. He was also formed at École nationale supérieure des Arts Décoratifs. He was the main coordinator of many national and international exhibitions, showing images, installations and movies made alone or in collaboration with scientists and artists. These exhibitions shed light on the sensations and mysteries provided by research in mathematics. The artworks are based on new discoveries in pure mathematics.

Esthétopies
The exhibit “esthétopies” gathers artworks representing spaces from contemporary mathematics, which are called 3-manifolds. These representations are based on research at the interface of pure mathematics and informatics, which solved problems opened by Thurston's school at the Geometry Center in the 90's. The artworks aim to offer new sensitive explorations and to present the unsayable of mathematical features (geodesic flows, sonorities of manifolds, topological surgery etc). Some of these artworks were produced in collaborations with the artists Pierre-Yves Fave, Sergio Krakowski, Vincent Martial and Jimena Royo-Letelier. http://esthetopies.ihp.fr/

Mgr. Michal Zamboj, Ph. D.
Faculty of Education, Charles University in Prague, Czech Republic

Michal Zamboj received the Ph.D. degree from the Faculty of Mathematics and Physics, Charles University in Prague with a focus on synthetic projective geometry. In his dissertation, the method of double orthogonal projection to visualize the four-dimensional space was introduced. Currently, he is an assistant professor of mathematics at the Faculty of Education, Charles University with a focus on various kinds of geometry. His research consists mainly of visualization of four-dimensional mathematical phenomena and their synthetic constructions. He also contributes to the mathematical theory of juggling with scientific and popularizing mathematical lectures.

Visualizing Objects of Four-Dimensional Space: From Flatland to the Hopf Fibration
One of the fundamental questions of a three-dimensional geometer is how to imagine a four-dimensional object. And yet he draws pictures of three-dimensional objects in the two-dimensional paper. Moreover, would a two-dimensional geometer understand our sketches? Based on analogies, we give an overview of methods of examination of four-dimensional objects. We emphasize visualization as the main element of perception of four-dimensional space. For this purpose, we describe the double orthogonal projection of the four-dimensional space onto two mutually perpendicular three-dimensional spaces as a generalization of the classical Monge’s projection. In such a projection, we construct a four-dimensional playground for convenient synthetic creation of four-dimensional objects. All our constructions are easily accessible with the 3-D modeling software GeoGebra. Furthermore, we apply the method of projection to an intuitive investigation of various four-dimensional mathematical phenomena – polytopes, four-dimensional quadrics, three-sphere and its stereographic projection, complex plane, and the Hopf fibration.

Prof. Araceli Queiruga Dios
School of Industrial Engineering, University of Salamanca, Spain

Araceli Queiruga-Dios obtained his Ph.D. in Mathematics at the University of Salamanca (Spain) when she was working for a telecommunications multinational company. Her major field of research is public key cryptography, together with educational tools and mathematical applications for engineering students. She is Professor at the Department of Applied Mathematics at the School of Industrial Engineering in the University of Salamanca. She has participated as coordinator and collaborator in several research projects at national and European level. She is co-author of over 50 papers, more than 70 contributions to workshops and conferences, and 1 patent related to RSA parameters. She is currently the coordinator of the Erasmus+ project: RULES_MATH (New rules for assessing mathematical competencies).

Assessment standards and activities: Some results
During the last 2 years a team made of 9 European institutions have been working to define assessment standards for Mathematics in engineering degrees. Mathematics courses in engineering degrees are a challenge. Different methodologies such as team work, project-based learning, or learning by games, are daily part of our classes. The big “problem” dealing with engineering students is that they need mathematics as a tool for other disciplines. Mathematics is not a goal, but a means to become a professional. Our competencies-based learning methods take students to change their minds and discover a new educational paradigm. We have proposed different assessment activities as a result of our work. This assessment is the consequence of using different methodologies. One of these methodologies is the use of games for learning Mathematics. Our students like playing video games and also board games. Is it possible to think that they could learn and acquire competencies by playing games? We present here our results about the evaluation of engineering students from engineering degrees.