TeXed Lectures:

Here, you find the lecture notes of the courses I have taken at CEU during my PhD studies. The notes are presented with the permission of the lecturers, but they are TeXed by myself. Thus, all the mistakes and typos are my faults, please write me a mail, if you find one. Also, take into account that the syllabus of each lecture may vary from year to year.

2014 Fall
    Topics in Algebra (lectured by Mátyás Domokos, Dr.)
    last modification: 2015.09.21.
    Topics in Analysis (lectured by Tamás Tasnádi, dr.)
    last modification: 2015.09.21.
    Representation Theory I (lectured by Mátyás Domokos, Dr.)
    last modification: 2015.09.21.
2015 Winter
Topics in Geometry and Topology (lectured by András Stipsicz, Dr.)
    last modification: 2015.08.18.
    Topics in Commutative Algebra (lectured by Tamás Szamuely, Dr.)
    last modification: 2016.01.03
2015 Fall
Basic Algebraic Geometry (lectured by Tamás Szamuely, Dr.)
    last modification: 2016.05.21.
2016 Winter
Language of Schemes (lectured by Tamás Szamuely, Dr.)
    last modification: 2016.04.13.

2017 Winter
Algebraic Groups (lectured by Tamás Szamuely, Dr.)
    last modification: 2017.03.09.


My name is Szabolcs Mészáros, I am a Phd student at the Institute of Mathematics of the Central European University. On this page, you may find some things I learnt or I'm just trying to understand about mathematics.


(joint with T. Banica) Uniqueness results for noncommutative sphere and projective spaces
(Illinois J. Math. 59(1), (2015), 219-233., arxiv:1507.01831)

It is known that, under strong axioms, there are only three orthogonal quantum groups. We prove here similar results for the noncommutative spheres, the noncommutative projective spaces and for the projective orthogonal quantum groups.

Submitted publications/preprints:

Cocommutative elements form a maximal commutative subalgebra in quantum matrices
(submitted, arxiv:1512.04353)

In this paper we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of M_n, GL_n and SL_n are the centralizers of the trace x_(1,1) + ... + x_(n,n) in each algebra, for q being not a root of unity. In particular, it is not only a commutative subalgebra as it was known before, but it is a maximal one.

Poisson centralizer of the trace
(submitted, arxiv:1604.01391)

The Poisson centralizer of the trace element \sum x_{i,i} is determined in the coordinate ring of SL_n endowed with the Poisson structure obtained as the semiclassical limit of its quantized coordinate ring.  It turns out that this maximal Poisson-commutative subalgebra coincides with the subalgebra of invariants with respect to the adjoint action.