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The Ninth Amitsur Memorial Symposium

Location:

Einstein Institute of Mathematics of the Hebrew University.

Dates:

Wednesday and Thursday, June 23rd and 24th (Tamuz 4th and 5th).

The speakers will be:

Tzvi Arad (Nethanya)
Michael Belolipetsky (Jerusalem)
Shai Haran (Technion)
Marcel Herzog (Tel - Aviv)
Michael Larsen (Indiana)
Anna Melnikov (Haifa)
Shulamit Solomon (Jerusalem)
Evgenii Plotkin (Bar-Ilan)
Alexei Kanel-Belov (Jerusalem)
David Kazhdan (Jerusalem)
Michah Sageev (Technion)

Wednesday

10:00 - D.Kazhdan: Crystaline bases and geometric crystals.

10:50 - Coffee break.

11:10 - M.Larsen: The inverse Galois problem for Mordell-Weil modules.

12:10 - T.Arad: Some topics in table algebra theory.

13:10 - Lunch break: all participants are invited for lunch at Beit Belgia, on campus.

15:00 - S.Haran: The mysteries of the Real prime.

16:00 - A.Melnikov: Combinatorial descriptions of orbital varieties closure inclusions. (Abstract)

16:50 - Coffee break.

17:10 - M.Sageev: Groups and CAT(0) cubical complexes.

18:30 - A buffet dinner at the courtyard of the Institute of Mathematics, all participants are invited.

Thursday

10:00 - M.Herzog: Finite groups with exactly two character degrees.

10:50 - Coffee break.

11:10 - M.Belolipetsky: Finite groups and hyperbolic manifolds. (Abstract)

12:10 - S.Solomon: Linear group-subgroup pairs with the same invariants. (Abstract)

13:10 - Lunch break (as above).

15:00 - A.Kanel-Belov: Polynomial endomorphisms and the generalized cancellation conjecture. (Abstract)

16:00 - E.Plotkin: Engel-like characterization of radicals in finite groups and finite dimensional Lie algebras. (Abstract)

End of the Symposium.

Mikhail Belolipetsky: Finite groups and hyperbolic manifolds

The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n > 1, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n = 3 have been proved before by Greenberg and Kojima, respectively. Our argument uses counting results on subgroup growth and arithmetic of the lattices in PO(n,1), it applies uniformly for all the dimensions n > 1. This is a joint result with Alex Lubotzky.

Alexei Belov: Polynomial endomorphisms and the generalized cancellation conjecture

The talk is devoted to some questions related to the Jacobian and cancellation conjectures.

Suppose that A[t] is isomorphic toB[s]. Then A and B may be not isomorphic. However, if there is an embedding of A[t] in B[s] then A can be embedded in B. Moreover, if the isomorphism sends t to s, then A and B are isomorphic. This answers the so-called Samuel conjecture. Another implication is: suppose V \times K \equivK^4. Then the algebraic variety V is byrationally equivalent to K^3.

Anna Melnikov: Combinatorial description of orbital varieties closure inclusions

Young tableaux play a central role in the theory of primitive ideals in U(sl(n)), since they describe them. The order relation on Young tableaux describing the inclusion of primitive ideals is given by Kazhdan-Lusztig data. The question is how to describe this order in terms of Young tableaux only and how to describe the order relation on orbital variety closures which should coincide with the order on primitive ideals. In my talk I would like to tell about the progress in this field during the last few years.

Eugene Plotkin: Engel-like characterization of radicals in finite groups and finite dimensional Lie algebras

The following theorem by R.Baer is well-known: in any finite group its nilpotent radical coincides with the set of all Engel elements. We discuss the approaches to a similar characterization of the solvable radical of a finite group (finite dimensional Lie algebra).

Joint work with T.Bandman, M.Borovoi, F.Grunewald, B.Kunyavskii

Shulamit Solomon: Linear group-subgroup pairs with the same invariants

We consider the problem of finding all linear algebraic group-subgroup pairs, such that the rational invariants of the group and of the subgroup coincide. We call such pairs exceptional.

One can compare a classification of exceptional pairs to the main theorem of the Galois theory, establishing a bijection between subgroups of the Galois group of a field extension L/K and subfields of L containing K. In other words, a finite group is uniquely determined by its invariants. By classifying exceptional pairs we establish that a group is almost always uniquely determined by its invariants, for other classes of groups, namely, irreducible and orthogonal groups.

There is no registration fee, and everybody is welcome!

Directions:

How to Reach Us: Edmond J. Safra Campus, Givat Ram

• 8th Amitsur Memorial Symposium, Hebrew University, 2002
• 7th Amitsur Memorial Symposium, Ben Gurion University, 2001
  • Amnon Yekutieli (Ben Gurion University of the Negev): Derived Picard groups of finite dimensional algebras
• 6th Amitsur Memorial Symposium, Hebrew University, 1999
  • A. Magid: The Picard-Vessiot antiderivative closure
• 5th Amitsur Memorial Symposium, Hebrew University, 1999
• 4th Amitsur Memorial Symposium, Bar-Ilan University, 1998

About Prof. Amitsur:

Shimshon A. Amitsur / The Mathematics Genealogy Project