Summer semester 2005
Speaker: Lior Fishman
Title: Schmidt's Game.
Abstract:
We give a brief introduction (omitting proofs) to the notion of
badly approximable numbers and follow Schmidt's paper from 1966 in which a
proof that the set of badly approximable numbers on the real line is a
winning set (in Schmidt's sense)..
Date and Time: Tuesday, 21 June, 2005 at 12:00
Place: Room 201, Mathematics Building (58), BGU
Honor guest: Prof. Matatiyahu Rubin.
Speaker: Yona Maissel
Title: Amenable groups.
Abstract:
We will give definitions and prove some basic properties of amenable groups
and some related classes of groups.
Date and Time: Wednesday, 29 June, 2005 at 13:30
Place: Room 201, Mathematics Building (58), BGU
Speaker: Yona Maissel
Title: Amenable groups - continued.
Date and Time: Wednesday, 6 July, 2005 at 13:30
Place: Room -101, Mathematics Building (58), BGU
Speaker: Eli Shamovich
Title: p-adic Numbers and Valuation Theory
Abstract: We will study the basics of valuation
theory and the construction of
the field of p-adic numbers via completions of Q with respect to a
certain metric. We will briefly review basic properties of the p-adics
and compare these properties with R."
The recommended books are "Algebraic Number Theory" by J. Neukirch (in
my opinion it is the best book on the subject) part 2 and "Algebraic
Number Theory" by S. Lang. Other books that might be useful are "A
course in Arithmetics" by J.P. Serre and "Number Theory" by Ireland
and Rosen. However the lecture will be based on the exposition in
Neukirch' book
Date and Time: Wednesday, 13 July, 2005 at 13:30
Place: Room -101, Mathematics Building (58), BGU
Speaker: Andrey Melnikov.
Title: The word problem for Semigroup varieties.
Source: S. Margoulis, J. Meakin, M. Sapir, "Algorithmic problems in groups, semigroups and inverse semigroups", J. Fountain (ed.), Semigroups, Formal languages and Groups, 1995, 190-199 (the article is 147-214).
Abstract: The aim of the talk is to prove the famous Novikov's theorem, that there doesn't exist an universal algorithm, deciding for a finitely generated free group with finite number of relations, whether a given word is identity. In order to do it one has to study the following topics:
It is important to emphasize that it is only a beginning. Construction of such a semigroup, having the undecidability property is highly difficult and quite popular today.
Date and Time: Wednesday, 20 July, 2005 at 13:30
Place: Room -101, Mathematics Building (58), BGU
Speaker: Andrey Melnikov.
Title: Growth conditions in Groups and Supramenability
Source: S. Wagon, "The Banach-Tarskii paradox"
Abstract: The notion of supramenable group is connected to the rate of growth of a group, that is, the speed at which new elements appear when one considers longer and longer words, using letters from a fixed finite subset of a group. The approach through supramenability sheds light on a basic difference between Abelian and Solvable groups. Both are amenable, but their growth properties can be quite different.
Date and Time: Wednesday, 3 August, 2005 at 13:30
Place: Room -101, Mathematics Building (58), BGU
Speaker: Eli Shamovich
Title: An Introduction to the Jacobian Conjecture
Source: 1. Bass, Connell, Wright: "The Jacobian Conjecture: Reduction of Degree and Formal Expansions of the Inverse." 2. van den Essen "The Exotic World of Injective Polynomial Maps."
Abstract:
We shall roughly follow the following schedule:
- The origin of the problem.
- The statement of the problem over $\mathbb{C}$.
- The general problem.
- Counterexamples to the conjecture in certain cases of the general problem.
- The "Lefshetz Principle" or how the case of $\mathbb{C}$ covers the most.
- Some known results.
- Some hunches about the truth of the conjecture.
Date and Time: Wednesday, 10 August, 2005 at 13:30
Place: Room -101, Mathematics Building (58), BGU
Speaker: Elliot Brenner
Title: Dirichlet theorem
Abstract:
The subject of my talk will be the theorem that in every arithmetic progression
{a+nq}, where a and q are positive integers having no common factor, and n
ranges over the integers from 1 to infinity, there are infinitely many primes.
I will define the Dirichlet characters \xi and Dirichlet L-functions L(xi,s).
I will show that the non-vanishing of the Dirichlet L-function associated to
particular \xi at s=1 is equivalent to the statement that there are infinitely
many primes in {a+nq}. I will start giving the proof that the L(xi,s) in
question does not vanish at s=1
Date and Time: Wednesday, 28 September, 2005 at 13:30
Place: Room -101, Mathematics Building (58), BGU
Speaker: Elliot Brenner - continue
Title: Dirichlet theorem
Abstract: see above.
Date and Time: Wednesday,
19 October, 2005 at 13:30
Place: Room -101, Mathematics Building (58), BGU
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