The aim of this lecture is to present a relationship between finite Markov chains and spanning trees of graphs. Then we will explore in more detail the
mechanism of this result and give some applications to enumeration of multitype forests.
The aim of this masterclass is to extend to the class of (possibly singular and/or non-compact) semi-algebraic sets some classical results of differential topology and differential geometry, such as the Poincaré-Hopf theorem or the Gauss-Bonnet theorem. We will provide the students with tools and techniques
of semi-algebraic geometry and apply them to get interesting results
on the topology and geometry of (possibly singular and/or non-compact) semi-algebraic sets. The content of the course will
be the following:
Background in differential topology and differential geometry
Basic properties of semi-algebraic sets and maps
Results on the topology and geometry of (singular and/or non-compact) semi-algebraic sets
The organization board will cover accommodation, breakfast, and lunch, but not dinner. As for the travel expenses, we will do our best in the limit of our budget.
For a registration request, please fill in the application form here (or by chosing the insciption tab above). The deadline for the registration requests is November 16, 2020.