My research interests are in computational and combinatorial aspects of finite simple groups, mainly in the properties of the product replacement algorithm graph, Aut(Fn)-actions on group presentations, word maps, and applications to Beauville surfaces.
Papers and preprints
- T. Bandman and S. Garion, Surjectivity and Equidistribution of the word x^ay^b on PSL(2,q) and SL(2,q), Internat. J. Algebra Comput. 22, No. 2 (2012). (pdf)
- T. Bandman, S. Garion and F. Grunewald, On the surjectivity of Engel words on PSL(2,q), to appear in Groups, Geometry and Dynamics. (pdf)
- S. Garion and Y. Glasner, Highly Transitive Actions of Out(Fn), to appear in Groups, Geometry and Dynamics. (pdf)
- S. Garion, M. Larsen and A. Lubotzky, Beauville surfaces and finite simple groups, to appear in J. Reine Angew. Math. (pdf)
- S. Garion and M. Penegini, Beauville surfaces, moduli spaces and finite groups. (pdf)
- S. Garion and M. Penegini, New Beauville surfaces and finite simple groups. (pdf)
- S. Garion, On Beauville structures for PSL(2,q). (pdf)
- S. Garion and A. Shalev, Commutator maps, measure preservation and T-systems, Trans. Amer. Math. Soc. 361 (2009), 4631-4651. (pdf)
- S. Garion, Connectivity of the product replacement algorithm graph of PSL(2,q), J. Group Theory 11 (2008), 765-777. (pdf)
- N. Avni and S. Garion, Connectivity of the product replacement graph of simple groups of bounded Lie rank, J. Algebra 320 (2008), 945-960. (pdf)
Ph.D. Thesis: Properties of the product replacement algorithm graph. (pdf)
M.Sc. Thesis: Descent via 3-isogeny of the elliptic curve X3+Y3=AZ3.
Presentations
- Computational and combinatorial aspects of finite simple groups (pdf)
- Triangle groups, finite simple groups and applications to Beauville surfaces (pdf)
- New Beauville surfaces, moduli spaces and finite groups (pdf)
- The product replacement algorithm graph of finite simple groups (pdf)
- Connectivity properties of the product replacement algorithm graph of finite simple groups (pdf)
- Aut(Fn)-actions on group presentations and representations (pdf)
Conference talks & Organization
- Co-organizer of the workshop Beauville surfaces and groups 2012, in Newcastle, UK, June 2012; jointly with Ingrid Bauer and Alina Vdovina.
- Workshop on Geometric presentations of finite and infinite groups, in Birmingham, UK, July 2011.
- The Kortrijk workshop on Discrete Groups and Geometric Structures, with Applications IV (CGG VI), in Oostende, Belgium, June 2011.
- Norddeutsches Gruppentheorie-Kolloquium, in Halle, Germany, June 2010.
- Combinatorics, Groups, Algorithms, and Complexity Conference in honor of Laci Babai's 60th birthday, in Columbus, Ohio, March 2010.
- Lis Gaines workshop on Action of Aut(Fn) on representation varieties, in Sde-Boker, Israel, January 2009.
Positions and scholarships
Postdoctoral:
- From May 2011: Postdoctoral position at Universität Münster, Germany, in the framework of the SFB 878 "Groups, Geometry & Actions" .
- April 2010 - April 2011: EPDI Fellowship at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France.
- April 2009 - March 2010: EPDI Fellowship at the Max-Planck-Institute for Mathematics in Bonn, Germany.
During my Ph.D. studies:
- April 2008 - March 2009: DAAD scholarship for foreign doctoral students in Germany.
- 2007/8: Fellowship for women Ph.D. students in science and technology from the Israel Ministry of Science and Technology.
- 2004 - 2009: Ph.D. studies in Mathematics at The Hebrew University of Jerusalem.
Teaching
I have been a teaching assistant at the Einstein Institute of Mathematics in the Hebrew University. Here is the list of the courses I taught.- Infinitesimal calculus 1 (Fall 2006/7, Fall 2007/8)
- Infinitesimal calculus 2 (Spring 2006)
- Discrete Math (Fall 2005/6)
- Linear algebra 2 (Spring 2005)
- Linear algebra 1 (Fall 2004/5)
Other activities and volunteer work
- Reviewer for Zentralblatt MATH and some mathematical journals.
- Fall 2007/8: Mentored a small group of Atidim students, who study for a bachelor degree in mathematics and education.
- Fall 2007/8: Organized the Amitsur Algebra Seminar at the Hebrew University.
- 2006 - 2008: I have been a member of the board of the Teaching Assistants Organization in the Hebrew University.