Einstein Institute of Mathematics
מכון איינשטיין למתמטיקה
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The Hebrew University of Jerusalem Einstein Institute of Mathematics |
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האוניברסיטה העברית בירושלים מכון איינשטיין למתמטיקה |
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Held at the Einstein Institute of Mathematics of the Hebrew University. All talks will be held in lecture hall 2 |  Prof. Shimshon A. Amitsur (1921 - 1994) |
יתקיים במכון איינשטיין למתמטיקה, האוניברסיטה העברית
ההרצאות יתקיימו באולם 2 |
| Coordinators:
Avinoam Mann (mann @ math.huji.ac.il) |
מתאמים
א. מן
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| The speakers will be:
O. Holtz (Berkeley) |
מרצים
א. הולץ, ברקלי
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Program
- Wednesday, June 9th
- 9:30 - gathering
10:00 - Miriam Cohen : Conjugacy classes for Hopf algebras
11:00 - Coffee break
11:30 - Elon Lindenstrauss : An effective proof of the Oppenheim Conjecture (Abstract)
12:30 - Tamar Ziegler : An inverse theorem for the Gowers norms (Abstract)
13:30 - Lunch break
15:00 - Uzi Vishne : Realizability and admissibility of groups under extension of fields (Abstract)
16:00 - Michael Larsen : Equations in simple groups
The Symposium dinner will be held in the evening.
- Thursday, June 10th
- 9:30 - Moshe Jarden : Ample fields (Abstract)
10:30 - Coffee break
11:00 - Olga Holtz : Zonotopal combinatorics (Abstract)
12:00 - Leonid Makar-Limanov : Free Poisson algebras (Abstract)
13:00 - Lunch break
14:00 - Alex Lubotzky : Representation growth of arithmetic groups (Abstract)
15:00 - Coffee break
15:30 - Peter Sarnak : Mobius randomness and dynamics (Abstract)
(Sarnak's talk doubles as a departmental colloquium).
Abstracts
- Elon Lindenstrauss (Hebrew University and Princeton University) : An effective proof of the Oppenheim Conjecture
- Abstract: In the mid 80's Margulis proved the Oppenheim Conjecture regarding values of indefinite quadratic forms. I will present new work, joint with Margulis, where we quantify this statement by giving bounds on the size of integer vectors for which |Q(x)|<ε for an irrational indefinite quadratic form Q in three variables.
- Tamar Ziegler (Technion) : An inverse theorem for the Gowers norms
- Abstract: A famous theorem of Dirichlet establishes the existence of infinitely many primes in arithmetic progressions so long as there are no local obstructions. In 2006 Green and Tao set up a programme for proving a multidimensional generalization of this theorem, reducing the multidimensional case to the assertion of two conjectures. The first - the mobius nilsequence conjecture - was resolved by Green and Tao in 2008. In recent joint work with Green and Tao we resolve the second conjecture - the inverse conjecture for the Gowers norms. I will describe the conjecture and give some insights into its proof.
- Uzi Vishne (Bar-Ilan) : Realizability and admissibility of groups under extension of fields
- Abstract: One of the major problems in Galois theory of number fields deals with the realization of a finite group G as a Galois group, over a number field F. Given a Galois extension K/F with this Galois group, one may further ask whether K can be realized as a maximal subfield in a division algebra whose center is F, in which case G is "F-admissible". I will present some problems and methods of this theory, initiated by M.A. Schacher, and discuss the behavior of realizability and admissibility under extension of number fields. As it turns out, in many cases, admissibility goes up together with an easily verified condition on roots of unity. This is a joint work with Danny Neftin.
- Moshe Jarden (Tel-Aviv University) : Ample Fields
- Abstract: A field K is said to be ample if every absolutely irreducible K-curve with a K-rational simple point has infinitely many K-rational points. Equivalently, K is existentially closed in K((t)). For example each PAC field and each Henselian field is ample. The most striking property of an ample field K is the each finite split embedding problem over K(x) has a regular solution. Indeed, no other fields beside ample fields are known to have that property.
- Olga Holtz (UC Berkeley and TU Berlin) : Zonotopal combinatorics
- Abstract: Given a graph G, we consider its associated (linear) matroid X, and associate X with three algebras called external, central, and internal. Each algebraic structure is given in terms of a pair of zero-dimensional homogeneous polynomial ideals in n variables that are dual to each other. Algebraically, one encodes properties of the (generic) hyperplane arrangement H(X) associated to X, while the other encodes by duality the properties of the zonotope Z(X) built from the matrix X. In particular, the Hilbert series of each of the three ideals turn out to be ultimately related to the Tutte polynomial of G, and the grading of the ideals turns out to be related to specific counting functions on subforests or on spanning trees of G. The focus of this talk is on the interplay between the algebra and the combinatorics that arise in this fashion. Joint work with Amos Ron.
- Leonid Makar-Limanov (Wayne State) : Free Poisson algebras
- Abstract: Though the Poisson algebras are very popular, surprisingly little is known about them as algebraic objects. In my talk I'll tell about several new results on free Poisson algebras in characteristic zero case: a description of automorphisms of Poisson algebras of rank 2, a description of (Poisson) centralizers, and the Freiheitssatz.
- Alex Lubotzky (Hebrew University) : Representation growth of arithmetic groups
- Abstract: Let D be a finitely generated group and Rn(D) the number of its n-dimensional complex irreducible representations. Rn(D) may be infinite but it is finite for higher rank arithmetic groups. In fact B. Martin and the speaker showed that the sequence grows polynomially iff D satifies the congruence subgroup property. In this case one can define a ζ-function counting these representation. We will present some results on this function, its Euler factorization and abscissa of convergence (joint work with M. Larsen) as well as a conjecture on its uniformity for lattices in a semisimple Lie group. Some recent work of Avni, Klopsch, Onn and Voll gives further support to this conjecture.
- Peter Sarnak (IAS, Princeton) : Mobius randomness and dynamics
- Abstract: A classical vague principle in number theory asserts that the Mobius function is "random", however this has never been made precise. We use notions from dynamics to formulate a precise conjecture which captures this randomness. The conjecture can be established in a number of cases and a key input is the interplay between Vinogradov's bilinear forms method and selfjoinings.
- Directions:
- How to Reach Us: Edmond J. Safra Campus, Givat Ram
- About Prof. Amitsur:
- Shimshon A. Amitsur / The Mathematics Genealogy Project
Shimshon Avraham Amitsur (1921 - 1994) / The MacTutor History of Mathematics archive
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