Kazarian, Maxim Eduardovich

V.A.Steklov Institute of Mathematics RAS
    (Department of geometry and topology)
& Moscow Independent University
    (College of Mathematics)

119991  8, Gubkina St., Moscow, Russia
Office: 536
Phone: (095) 135 14 90
Fax:     (095) 135 05 55
E-mail: kazarian@mccme.ru

Principal fields of research:
geometry, topology, singularity theory, characteristic classes

 Vita and Education
 
Employment
 
Mathematical papers
 
Output of Mathematica programs and other resources
 
Mathematical courses lecture notes
 

Vita and Education:
    Born: 11.04.1965 (Moscow)
    1982-1988 Study in Moscow Aviation Institute, Department of Applied Mathematics,
    1988-1991 Aspirantura, the Steklov Institute of Mathematics, supervisor Prof. V.I.Arnold
    1991 Candidate of Science (=PhD) in Physics and Mathematics,
Dissertation title: "Bifurcations of flattenings of space curves and singularities of boundaries of fundamental systems"
    1998-2001 Doctorantura, the Steklov Institute of Mathematics,  
Habilitation thesis "Characteristic classes in Singularity Theory" (2003)

    1984 Married, 3 children,  1 son and 2 daughters.

Employment:
    1991-1994 The staff at the Moscow Transportation Institute RAS
    1994-        Mathematical College of Moscow Independent University
    2001-        Research fellow at the Steklov Institute of Mathematics

 

 

Selected papers:

1. Classifying spaces of singularities and Thom polynomials, in: New developments in
Singularity Theory (Cambridge 2000), NATO Sci.Ser. II
Math.Phys.Chem, 21, Kluwer Acad. Publ.,  Dordrecht, 2001, 117-134.

2. Thom polynomials for Lagrange, Legendre, and critical point function singularities,
Proc. LMS. (3) 86 (2003) 707--734.

3. Multisingularities, cobordisms, and enumerative geometry (Russian), Uspekhi Math. Nauk,
58
(4), 2003, 665-724. In the English translation in RMS a number of mistakes
have been introduced for which the author has no responsibility. Some of them are removed in
the
author's translation.

4. Characteristic Classes in Singularity theory (Russian), Doctoral Dissertation (habilitation thesis)
Steklov Math. Inst., 2003, 275pp, 
Author's summary (Russian), 28 pp.

5. Thom polynomials, Lecture notes of three talks given in Singularity Theory Conference,
Sapporo, 2003, 38pp. (revised 01.04.2004)

6. (joint with S.K.Lando) Towards the Intersection Theory on Hurwitz Spaces,
    Izv. Ross. Akad. Nauk Ser. Mat., 68 (2004), no. 5, 82-113,
math.AG/0410388

7. (joint with S.K.Lando) An algebro-geometric proof of Witten's conjecture,
   
math.AG/0601760

8. Morin maps and their characteristic classes, preprint 2006.

9. KP hierarchy for Hodge integrals, preprint 2007.

 

Output of Mathematica programs for computing
characteristic classes of multisingularities
1. Residue classes for Legendre and IH multisingularities
   
Mathematica programme
   
Tables of  residue polynomials

2. Adjacency exponents and Thom polynomials for local Legendre and IH singularities
   
Mathematica programme

3. Application of Legendre multisingularity theory to projective enumerative geometry
    3a. Enumeration of singular curvs on surfaces
       
Linear systems on general surfaces
       
Enumeration of singular plane curves
    3b. Enumeration of tangencies of k-planes with a hypersurface in the projective n-space
       
Source Mathematica programme and some examples
       
Tables for hypersurfaces up to n=7 and various k

4. Localized Thom polynomials and residue classes for maps of relative dimension l
   
Source Mathematica programme
   
Residue polynomials for Legendre maps
   
Residue polynomials for l=-1
   
Residue polynomials for l=0
   
Residue polynomials for l=1

5. Derived Porteous-Thom classes and Thom polynomials for $\Sigma^{a,b}$-singularities



Lecture Notes of some mathematical courses
Calculus on Manifolds (Moscow Independent University, MIM programme,  Fall 2003)
Differential Geometry (Moscow Independent University, MIM programme, Spring 2004)
Introduction to Homology Theory (MI RAS,  Fall 2005, in Russian)
Fiber bundles, characteristic classes, and cobordisms (MI RAS,  Spring 2006, in Russian)
                           
Examination problems 19.05.2006