## Keynote Speakers

**Prof. Luigi Ambrosio**

Scuola Normale Superiore di Pisa, Italy

**About Prof. Luigi Ambrosio:** Luigi Ambrosio is a remarkable mathematician
renowned for his important contributions in the field of partial differential
equations and of the calculus of variation.

Born in Italy in 1963, he is Director of the Scuola Normale Superiore in Pisa
(since 2019) after having served as Professor there since 1998. He has also held
professorships at the universities of Roma Tor Vergata, Benevento and Pavia. He
has received a great many prestigious awards, including the Prize of the Italian
Mathematical Union and the Fermat Prize. He has been invited to give plenary
lectures at the International Congress of Mathematicians, as well as the
European Congress. He is a Member of the Accademia dei Lincei.

Partial differential equations concern the dynamics of quantities that depend on
several parameters, which are most often time and position. There are numerous
examples: a vibrating string, a moving electromagnetic wave, the motion of a
fluid, or more generally, any moving object.

The calculus of variation tries to describe curves or surfaces minimising a
certain quantity. For example, which surface limited by a closed curve has a
minimal area? These “minimal surfaces” are analogous to soap bubbles. What shape
should one give to an airplane wing so as to minimize air resistance? One may
also try to direct a large number of cars in a city in order to minimize traffic
jams.

Luigi Ambrosio’s astonishing capacity for synthesis has allowed him to create
hitherto unimaginable bridges between these two important fields of mathematics.
For example, his discoveries concern transport equations and conservation laws,
optimal transport, evolution equations in geometry, and analysis in metric
spaces. Historically, mathematicians looked for smooth solutions with no
regularities, but unfortunately this does not correspond to physical reality.
Over the past few decades, in particular thanks to Ambrosio, new methods have
made it possible to find non-smooth solutions. This has led to the fundamental
renewal of the venerable field of infinitesimal calculus.

Luigi Ambrosio has introduced functional mathematical spaces, enabling him to
make analyses under very weak conditions of regularity. For example, he has
extended the theory of currents (which goes back to the 1960s) to show the
existence of minimal surfaces beyond Euclidean space to any geometry whatsoever,
something that had not previously been shown. This result was quite a surprise
to the community of scholars in the field of geometric measure theory.

Other important advances include his work on the mathematical curvature of
metric measure spaces as well as on gradient flows in these spaces, which are a
priori not very regular.

The problem of optimal transport, which goes back to Gaspard Monge in 1781,
consists in moving one distribution of masses towards another in the most
efficient way. This problem has had a long and complex history, but thanks to
Luigi Ambrosio’s contribution, some of the bases for definitive proof of the
existence of solutions have been established, precisely in the situation
described by Monge.

Luigi Ambrosio is not only known for his mathematical discoveries. He is an
exceptional teacher who has founded a school of thought and who has trained a
great number of students who today make up a community of mathematicians working
in prestigious universities throughout the world.

Prof. Dashnor Hoxha

Orleans University, France

**About Prof. Dashnor Hoxha:** After obtained an engineer degree from
Polytechnic Univeristy of Tirana and a Bachelor in Physics form Natural Science
Faculty of Tirana, Albanie in 1991, I was awarded Mc. S and Ph. D in
Geomechanics Hydrosystems and Structures from National Polytechnic Institut of
Lorraine (INPL) France in 1998. I worked for ten years in the research and
developing industry before joining the University of Orleans as Head of
Sustainables Constructions Division in 2007. I work actually in the Laboratory
of Pluridisiplinary Research in Engineering Systemes, Mechanics and Energy
(PRISME) and I teach as Professor in Polytechnic School of Orleans. I published
more than 34 papers in refereed international journals and 45 papers in
conferences and 4 book chapiters and I have been involved in many international
conferences as Technical Chair and tutorial presenter.