December 19, Wednesday, 18:30, room 306

Fedor Selyanin

Tropical Grassmannian (continued)

Russian version: Тропический грассманиан  (продолжение, см. ниже анонс на русском)

We will identify the tropical Grassmannian with the space of phylogenetic trees. The latter is an interesting combinatorial object, which was first defined and studied in applications of mathematics to biology.

Второй доклад будет посвящён собственно тропикализации грассманового многообразия G(2,n), которая окажется пространством филогенетических деревьев, красивым комбинаторным объектом.

December 12, Wednesday, 18:30, room 306

Fedor Selyanin

Tropical Grassmannian

Russian version: Тропический грассманиан (см. ниже анонс на русском)

The first part of the talk is an introduction to tropical geometry. We explain basic concepts of tropical geometry using concrete examples. The second part of the talk will be devoted to tropicalization of the Grassmannian G(2,n). We identify the tropical Grassmannian with the space of phylogenetic trees. The latter is an interesting combinatorial object, which was first defined and studied in applications of mathematics to biology.

В начале лекции будет введение в тропическую геометрию, на наглядных примерах объясню её базовые понятия. Вторая часть лекции будет посвящена собственно тропикализации грассманового многообразия G(2,n), которая окажется пространством филогенетических деревьев, красивым комбинаторным объектом.

December 5, Wednesday, 18:30, room 306

Yury Rudko

Gelfand-Zetlin bases for representations of SL(n)

We construct Gelfand-Zetlin bases in irreducible representations of SL(n) using the chain of subgroups SL(n)>SL(n-1)>…>SL(2). The key step is reduction of an irreducible representation of SL(n) to SL(n-1). Using reduction we show that basis vectors are labeled by lattice points in a convex polytope (called Gelfand-Zetlin polytope) defined by simpe inequalities. We work out concrete examples such as the adjoint representation of SL(3).