## לפרטים על תואר ראשון ושני

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Curriculum Vitae קורות חיים

**Academic Education**

2005-2006: A post-doctorate student position at the Einstein Institute of Mathematics, the Hebrew university, Jerusalem. Host: Prof. Alex Lubotzky.

2004: Ph.D. Math, Bar Ilan University. Thesis in algebraic combinatorics: Supervisors: Ron Adin and Yuval Roichman. Title: Combinatorial parameters on classical groups.

1999: MSc. Mathemathics, Bar Ilan University.

Thesis in algebraic toplogy: Supervisors: Steven Shnider and Giora Dola. Title: K theory and its applications.

1996: B.Sc . Math and C.s. , Bar Ilan University.

**Academic Appointments [in reverse chronological order]**

2007-Regular appointment. Dept. of Math. Jerusalem college of Technology.

2005-2007-Lecturer, Dept. of Math. Jerusalem college of Technology.

2004-Non-faculty teache. Jerusalem college of Technology.

**Awards and Honors for Academic or Professional Achievement**

Bar Ilan president program for excellent Ph.D. students

**Research and Development Activities Publications**

Recently, in a joint work with D.Garber , we defined what might be called the 'Bruhathedron' which is a type of a deformation of the well known (weak) Bruhat poset for the Coxeter group of type A. The 'Bruhathedron' is a family of ranked posets, indexed by the elements of the group mentioned above which extrapolates the behavior of the original Bruhat poset in such a way that the rank generating functions share the symmetric properties of the original generating function, the Poincare polynomial. We are trying to obtain some more symmetry properties, involving calculation of the Mobiuos function of this poset and manipulating the rank generating function.

There is a cyclic action on the set of reduced expressions of the longest element in the symmetric group S_n which is equivalent to the promotion action on standard Young tableaux of staircase shape. An open question is to find the orbit structure of this action in one (and hence of both) of these actions. A nice target would be to get a parameter defined on the S_n which will enumerate in some sense these orbits, invoking the Cyclic Seiving Phenomena.

With D. Garber we try to generalize the theory of permutation statistics to alternating subgroups of colored permutation groups. A first step in this direction was recently done by us when we found a combinatorial formula for the length function with respect to new ‘Coxeter like’ generators. We considered this group as a union of sieves over some specific colored permutation group. We are planning to use the sieving structure in order to rise known parameters from the colored permutation groups to the group of alternating permutations.

In a joint work with R. Schwarz and R. Biagioli, we started to construct some new parameters for the affine group of type A. Our parameter is connected to the action of this group on its coinvariant algebra and its generating function serves both as the Poincare polynomial of the affine group of type A as well as the Hilbert series of the Coinvariant algebra

**Summary of Past Research and Development Activities**

The Colored permutation groups serve as a generalization of Coxeter groups of type A and B. They have a family of complex reflection groups as subgroups, thus generalizing also Coxeter type D.

A vast part of my research in the last years lies in the theory of permutation statistics of these groups. Together with D. Garber, we generalized results of Ksavrelof and Zeng about the multi distribution of the excedance number of $S_n$ with some natural parameters to the colored permutation group and to the Coxeter group of type $D$. We defined two different orders on these groups which induce two different excedance numbers.

In a joint work with T. Mansour and D. Garber we defined Excedance numbers for complex reflection groups and calculated their distributions over the involutions of these groups.

With A. Butman and D, Garber we generalized the definition of the Excedance numbers to arbitrary finite Abelian groups. We calculated distributions of these parameters over these groups as well.

In another work, with T. Mansour and D. Garber, we defined a new statistic, called: (c,d)-descent on the colored permutation groups and computed the distribution of these statistics on the set of permutations in these groups. We used some combinatorial approaches, recurrence formulas, and generating functions manipulations to obtain our results.

A work in another direction, joint with Y. Cherniavsky, concerned combinatorics of Borel congruence orbits of symmetric matrices which can be indexed by the monoid of partial permutations.

We presented a combinatorial formula for the rank function of the poset of the closure of those orbits.

**Future Directions for Research and Development. **

A very ambitious aim is to find a length function for the infinite family of complex reflection groups. The idea is to present it in a combinatorial way, and this should lead to new parameters on these groups. There is a deep connection between the affine group of type A and this family of groups. We want to use this connection; together with the knowledge we have on the affine group in order to attack the problem of the length function.

**Publications **

**Peer-Reviewed Papers in Refereed Journals ( not conference proceedings) **

**Before latest appointment: **

1. E. Bagno, Kazhdan Constants of some colored permutation groups, Journal of Algebra 282 (2004) 205-231.

2. E. Bagno, Euler-Mahonian Parameters on Colored Permutation groups, Seminar Lotharingien de Combinatoire 51 (2004), Article B51f.

3. E. Bagno & R. Biagioli, Combinatorics and Representations of Complex Reflection Groups G(r,p,n), to appear in Israel Journal of Math.

4. E. Bagno & D. Garber, On the Excadence numebr of colored permuataion groups, Seminar Lotharingien de Combinatoire 53 (2006), Article B53f.

5. E. Bagno & Y. Cherniavsky, Permutation representations on invertible matrices, Linear Algebra and its Applications, 419 (2006) 494-518.

**Since latest appointment: **

6. E. Bagno, D. Garber & T. Mansour, Excedance number for involutions in Complex reflection groups, Seminaire Lotharingien de Comibinatoire 56 (2007), Article B56d.

7. E. Bagno, A. Butman, & D. Garber, Statistics on the multi-colored permutation groups, The Electronic Journal of Combinatorics, 14, (2007), #R24.

8. E. Bagno & Y. Cherniavsky, Sign Balance for finite groups of Lie type. Linear Algebra and applications. 429 (1), 2008 , 224-233.

9. E. Bagno, D. Garber & T. Mansour, Counting descent pairs with prescribed colors in the colored permutation groups, Seminar Lotharingien de Combinatoire 60 (2009), Article B60e.

**Peer-Reviewed Papers in Refereed Conference Proceedings ( not abstracts) **

**Before latest appointment: **

1. Exact Kazhdan Constants of Some Coxeter Groups and Wreath Products. Proceedings of the Conference on formal power series and algebraic combinatorics, University of Melbourne,2002.

2. E. Bagno & Y. Cherniavsky, Sign balance for finite groups of Lie type. Proceedings of the 2004’ Formal Power Series & Algebraic Combinatorics Conference

3. E. Bagno & R.Biagioli, Combinatorics and Representations of Complex Reflection Groups G(r,p,n). Proceedings of the 2005’ Formal Power Series & Algebraic Combinatorics Conference.

4. E. Bagno & D. Garber, On the Excadence numebr of colored permutation groups. Proceedings of the 2005’ Formal Power Series & Algebraic Combinatorics Conference.

5. E. Bagno & Y. Cherniavsky, Permutation representations on invertible matrices. Proceedings of the 2005’ Formal Power Series & Algebraic Combinatorics Conference..

6. E. Bagno, D. Garber, & T. Mansour, On the excedance number for involutions in colored permutation groups, *26th International Colloquium on group Theoretical Methods in Physics*, City, University of New York, New York, June 26-30, 2006 (6pp.).

**Since latest appointment**

7. E. Bagno, Y. Cherniavsky, Involutions of the Symmetric Group and Congruence B-Orbits. 2010’ Formal Power Series & Algebraic Combinatorics Conference.

**Presentations at Conferences with Published Proceedings. **

**Before latest appointment **

1. 2002: The 48-th Seminaire Lotharingien de Combinatoire -02, Ottrot, France 10. 3-13.3 2002. (Sponsored by Bar Ilan University). (gave a lecture).

2. 2002: Formal Power Series & Algebraic Combinatorics, University of Melbourne, 8.7-12.7 2002. (Sponsored by Bar Ilan University). (presented a poster).

3. 2003: The 50-th Seminaire Lotharingien de Combinatoire -03, Ottrot, France 23. 3 - 27.3 2002. (Sponsored by Bar Ilan University). (gave a lecture).

4. 2004: Formal Power Series & Algebraic Combinatorics, University of British Columbia (Vancouver B.C., Canada). .June 28 - July 2, 2004. (Sponsored by the conference). (presented a poster)

5. 2005: Formal Power Series & Algebraic Combinatorics, Taoromina, Sicily. June 20 - June 25 (Sponsored by Ace). (presented 3 posters).

**Funded Projects , Grants or Contracts **

**Since latest appointment **

2007-2009: NEW PRESENTATIONS AND STATISTICS ON SUBGROUPS OF THE COLORED PERMUTATION GROUP.

Granted by: Israeli – France fellowship.

Recipient names: Eli Bagno, Toufik Mansour, David Garber, Ricardo Biagioli, Frederic Jouhet, Jiang Zeng.

My function: Head of Israeli team.

**Referee reports for the following journals: **

1. Advances in applied Math.

2. The bulletin of the L.M.S.

3. Journal of combinatorial theory A.

4. The Fpsac conference.

**Courses Taught: **

Discrete Mathematics, Linear Algebra, Statistics, Linear Structures ,Mathematical Logic, Calculus, Galois theory, Topology, Analytical Geometry, Differential Equations.

**Instruction of Courses: **

Discrete Mathematics, Linear