Schedule and Courses

MONDAY 
TUESDAY 
WEDNESDAY 
THURSDAY 
FRIDAY 
SATURDAY 
9:00 
. 
BREAKFAST 
BREAKFAST 
BREAKFAST 
BREAKFAST 
BREAKFAST 
9:3011:30 
A 
COURSE 1 S. GUSEINZADE 
COURSE 1 S. GUSEINZADE

COURSE 1 S. GUSEINZADE

COURSE 1 S. GUSEINZADE

D 
11:3012:00 
R 
COFFEE 
COFFEE 
COFFEE 
COFFEE 
E 
12:0014:00 
R 
COURSE 2
S. ISHII

COURSE 2
S. ISHII

COURSE 2
S. ISHII

COURSE 2
S. ISHII

P

14:00 
I 
LUNCH 
LUNCH 
LUNCH 
LUNCH 
A 
15:0017:30 
V 
FREE TIME
APPLICATIONS

FREE TIME
APPLICATIONS

FREE TIME
APPLICATIONS

FREE TIME
APPLICATIONS

R

17:3019:30 
A 
COURSE 3 I. OJEDA

COURSE 3 I. OJEDA

COURSE 3 I. OJEDA

COURSE 3 I. OJEDA

T 
19:30 
L 
COFFEE 
COFFEE 
COFFEE 
COFFEE 
U 
20:0021:00 
OPEN TALK 
MATHEMATICAL
DISCUSSIONS

MATHEMATICAL
DISCUSSIONS

MATHEMATICAL
DISCUSSIONS

MATHEMATICAL
DISCUSSIONS

R 
21:00 
DINNER 
DINNER 
DINNER 
DINNER 
DINNER 
E 
COURSES
AND GENERAL TOPICS
Open talk: Equisingularity.
Javier Fernández de Bobadilla (CSIC, Madrid).
Course 1: Integration with respect to the Euler characteristic and its applications.
Sabir M. GuseinZade (Moscow State University). Euler characteristic is additive with respect to the union of spaces. This permits to use it as a (nonpositive) measure on an algebra of sets and to construct the notion of integration with respect to the Euler characteristic. This notion can be used both for formulation of mathematical statements and for proof of new ones. E.g. it turns out to be effective for computing zeta functions of monodromy transformations and Poincare series of some filtrations. Integration with respect to the Euler characteristic is also a starting point for the notion of motivic integration.
Course 2: Introduction to arc spaces and the Nash problem.
Shihoko Ishii (Tokyo Institute of Technology). The concepts jet scheme and arc space over an algebraic variety or an analytic space was introduced by Nash in his preprint in 1968 which was later published in 1995. The study of these spaces was further developed by Kontsevich, Denef and Loeser as the theory of motivic integration. These spaces are considered as something to represent the nature of the singularities of the base space. In these lecture, I provide the beginners with the basic knowledge of these spaces and the Nash problem.
Course 3: Monomial algebras and binomial ideals.
Ignacio Ojeda (Universidad de Extremadura). The course is intended to be an introduction to computational and combinatorial commutative algebra. The exposition will mainly concerns combinatorially defined ideals and their quotients, with special emphasis on numerical invariants and resolutions. More precisely, we will focus our attention on the rationality of the Poincare Series, short rational functions, the Koszul property, quadratic Gröbner bases, and primary decompostions of monomial and torics ideals. Also some applications will be discussed, for instance, classification of graphical models.
Mathematical Discusions: A free space to discuss your own work, anything arising from the courses or simply share ideas! You can prepare a poster or a talk.
On Saturday at 9:30, there is a bus from Sedano to Burgos supported by the organization. The bus stops either in the railway and bus stations for those participants without car who have to travel in the morning, the expected arrival time is 10:1510:30.
