**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

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-

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,

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 **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**

1. Residue classes for Legendre and IH multisingularities

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

Fiber bundles, characteristic classes, and cobordisms (MI RAS, Spring

Examination problems 19.05.2006