Lucas Fresse

Department of Mathematics
the Weizmann Institute of Science
Rehovot 76100, Israel

e-mail: lucas.fresse(at)weizmann.ac.il


I am post-doc at the Hebrew University of Jerusalem, and I am consultant within the Department of Mathematics at the Weizmann Institute of Science.

Here is my CV in English, including the list of my publications and a description of my research interests and works.
Here is my CV in French.


Research

I am doing my research on the geometry of flag varieties and nilpotent orbits. Specifically, I have worked on the geometry of Springer fibers and orbital varieties.
This subject is related to different fields as algebraic geometry, representation theory (representations of Weyl groups, primitive ideal of enveloping algebras), combinatorics.

Here is my PhD thesis, entitled Une étude combinatoire de la géométrie des fibres de Springer de type A (in French),
defended on 12th December 2007 at the University Lyon 1, under the supervision of Prof. Olivier Mathieu.


Articles

• Nombres de Betti des fibres de Springer de type A, C. R. Acad. Sci. Paris, Ser. I   347 (2009) 283-287 (website).
• Composantes singulières des fibres de Springer dans le cas deux-colonnes, C. R. Acad. Sci. Paris, Ser. I   347 (2009) 631-636 (website).
• Betti numbers of Springer fibers in type A,  J. Algebra  322 (2009) 2566-2579 (website).
• Singular components of Springer fibers in the two-column case, Ann. Inst. Fourier (Grenoble)  59 (2009) 2429-2444 (website).
• A unified approach on Springer fibers in the hook, two-row and two-column cases, Transform. Groups  15 (2010) 285-331 (website).
• On the singularity of the irreducible components of a Springer fiber in sl(n) (with Anna Melnikov), Selecta Math. (N.S.)  16 (2010) 393-418 (website).
• On the singularity of some special components of Springer fibers, J. Lie Theory  21 (2011) 205-242 (website).
• Some characterizations of singular components of Springer fibers in the two-column case (with Anna Melnikov), to appear in Algebras and Representation Theory (website).
• On geometric properties of orbital varieties in type A (with Anna Melnikov), C. R. Acad. Sci. Paris, Ser. I, in press (website).


(cette page en français: ici)