Abstract: The Chabauty method is a remarkable tool which employs p-adic analitic methods (in particular Colman integration.) To study rational points on curves. However the method can be applied only when the genus of the curve in question is larger than its Mordell-Weil rank. Kim developed a sophisticated "nonableian" generalisation. We shall present the classical methid, and give an approachable introduction to Kim's method. I'm basically going to follow http://math.mit.edu/nt/old/stage_s18.html

Abstract: I will discuss applications of algebraic results to combinatorics, focusing in particular on Lefschetz theorem, Decomposition theorem and Hodge Riemann relations. Secondly, I will discuss proving these results combinatorially, using a technique by McMullen and extended by de Cataldo and Migliorini. Finally, I will discuss Lefschetz type theorems beyond positivity. Recommended prerequisites: basic commutative algebra

Abstract: I will discuss applications of algebraic results to combinatorics, focusing in particular on Lefschetz theorem, Decomposition theorem and Hodge Riemann relations. Secondly, I will discuss proving these results combinatorially, using a technique by McMullen and extended by de Cataldo and Migliorini. Finally, I will discuss Lefschetz type theorems beyond positivity. Recommended prerequisites: basic commutative algebra

Abstract: The Chabauty method is a remarkable tool which employs p-adic analitic methods (in particular Colman integration.) To study rational points on curves. However the method can be applied only when the genus of the curve in question is larger than its Mordell-Weil rank. Kim developed a sophisticated "nonableian" generalisation. We shall present the classical methid, and give an approachable introduction to Kim's method. I'm basically going to follow http://math.mit.edu/nt/old/stage_s18.html

Abstract: I will discuss applications of algebraic results to combinatorics, focusing in particular on Lefschetz theorem, Decomposition theorem and Hodge Riemann relations. Secondly, I will discuss proving these results combinatorially, using a technique by McMullen and extended by de Cataldo and Migliorini. Finally, I will discuss Lefschetz type theorems beyond positivity. Recommended prerequisites: basic commutative algebra

Abstract: The Chabauty method is a remarkable tool which employs p-adic analitic methods (in particular Colman integration.) To study rational points on curves. However the method can be applied only when the genus of the curve in question is larger than its Mordell-Weil rank. Kim developed a sophisticated "nonableian" generalisation. We shall present the classical methid, and give an approachable introduction to Kim's method. I'm basically going to follow http://math.mit.edu/nt/old/stage_s18.html

Abstract: I will discuss applications of algebraic results to combinatorics, focusing in particular on Lefschetz theorem, Decomposition theorem and Hodge Riemann relations. Secondly, I will discuss proving these results combinatorially, using a technique by McMullen and extended by de Cataldo and Migliorini. Finally, I will discuss Lefschetz type theorems beyond positivity. Recommended prerequisites: basic commutative algebra

The main goal of my talk will be to introduce adeles and ideles and to formulate the global class field theory both for number fields and function fields. Key words: adeles, ideles, class field theory, algebraic curves.

The goal of my talk will be to formulate local and global Langlands conjectures Key words: smooth representations of p-adic groups, supercuspidal representations, automorphic representations, cusp forms, Galois representations.

The goal of my talk will be to introduce the local and the global the Class field theory. Though definitions of all basic objects (inverse limits, p-adic numbers, adeles, ideles, etc.) will be briefly recalled, it is recommended that the participants review these notions before the lecture. The talk will be independent of the first lecture

Speaker: Michael Chapman, HU Title: Graphs which are expanders both locally and globally Abstract:

Speaker: Michael Simkin, HU Title: The threshold problem for Latin squares

 Automorphisms of meet-trees


Abstract: A meet-tree is a partial order such that the set of vertices below any vertex is linearly ordered, and for every pair of vertices there is a greatest element smaller than or equal to each of them. I'll talk on a work in progress with Itay Kaplan and Tomasz Rzepecki mainly showing that the universal homogeneous countable meet-tree admits generic automorphisms.