Distinguished Lecture

Speaker: Florian Pop (Penn)

"New developments in anabelian geometry I"

Time: 16:00

Room: MC 107

At the beginning of the 1980's, Grothendieck announced his new ideas concerning an "anabelian geometry". His fundamental observation was that algebraic fundamental groups of "complicated" varieties tend to become very rigid objects when endowed with the Galois action of fields of definition of those varieties, and morphisms between such "rigidified objects" tend to originate from geometry and arithmetic. Conjecturally, this would enable us with a completely new tool to attack problems in arithmetic/algebraic geometry, namely by translating them into questions about the category of (etale) fundamental groups via the (etale) fundamental group functor. There are several aspects of these problems, like recovering varieties and points of these from the corresponding fundamental group setting, giving new non-tautological descriptions of absolute Galois groups in purely topological/combinatorial terms, describing the representations of absolute Galois groups, etc. Grothendieck's Esquisse d'un Programme sparked a very intensive research activity. Meanwhile some of the questions have quite satisfactory answers, but some of the most fundamental ones are not answered yet. After an introduction to anabelian geometry, I plan to present some new results, concerning: the birational aspects of the theory, the anabelian geometry of curves, Grothendieck's section conjecture; and to touch upon the problem of describing absolute Galois groups in purely topological/combinatorial terms (thus answering the Ihara Question / Oda-Matsumoto Conjecture).

Distinguished Lecture

Speaker: Florian Pop (Penn)

"New developments in anabelian geometry II""

Time: 15:00

Room: MC 107

At the beginning of the 1980's, Grothendieck announced his new ideas concerning an "anabelian geometry". His fundamental observation was that algebraic fundamental groups of "complicated" varieties tend to become very rigid objects when endowed with the Galois action of fields of definition of those varieties, and morphisms between such "rigidified objects" tend to originate from geometry and arithmetic. Conjecturally, this would enable us with a completely new tool to attack problems in arithmetic/algebraic geometry, namely by translating them into questions about the category of (etale) fundamental groups via the (etale) fundamental group functor. There are several aspects of these problems, like recovering varieties and points of these from the corresponding fundamental group setting, giving new non-tautological descriptions of absolute Galois groups in purely topological/combinatorial terms, describing the representations of absolute Galois groups, etc. Grothendieck's Esquisse d'un Programme sparked a very intensive research activity. Meanwhile some of the questions have quite satisfactory answers, but some of the most fundamental ones are not answered yet. After an introduction to anabelian geometry, I plan to present some new results, concerning: the birational aspects of the theory, the anabelian geometry of curves, Grothendieck's section conjecture; and to touch upon the problem of describing absolute Galois groups in purely topological/combinatorial terms (thus answering the Ihara Question / Oda-Matsumoto Conjecture).

Distinguished Lecture

Speaker: Florian Pop (Penn)

"New developments in anabelian geometry III"

Time: 15:00

Room: MC 107

At the beginning of the 1980's, Grothendieck announced his new ideas concerning an "anabelian geometry". His fundamental observation was that algebraic fundamental groups of "complicated" varieties tend to become very rigid objects when endowed with the Galois action of fields of definition of those varieties, and morphisms between such "rigidified objects" tend to originate from geometry and arithmetic. Conjecturally, this would enable us with a completely new tool to attack problems in arithmetic/algebraic geometry, namely by translating them into questions about the category of (etale) fundamental groups via the (etale) fundamental group functor. There are several aspects of these problems, like recovering varieties and points of these from the corresponding fundamental group setting, giving new non-tautological descriptions of absolute Galois groups in purely topological/combinatorial terms, describing the representations of absolute Galois groups, etc. Grothendieck's Esquisse d'un Programme sparked a very intensive research activity. Meanwhile some of the questions have quite satisfactory answers, but some of the most fundamental ones are not answered yet. After an introduction to anabelian geometry, I plan to present some new results, concerning: the birational aspects of the theory, the anabelian geometry of curves, Grothendieck's section conjecture; and to touch upon the problem of describing absolute Galois groups in purely topological/combinatorial terms (thus answering the Ihara Question / Oda-Matsumoto Conjecture).