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The Eighth Congress of Romanian Mathematicians |
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List of talks
Special session: Local rings and homological algebra. Special session dedicated to Prof. Nicolae Radu
II. Algebraic, Complex and Differential Geometry and Topology
Special session: Geometry and Topology of Differentiable Manifolds and Algebraic Varieties
III. Real and Complex Analysis, Potential Theory
IV. Ordinary and Partial Differential Equations, Variational Methods, Optimal Control
Special session: Optimization and Games Theory
V. Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics
Special session: Spectral Theory and Applications in Mathematical Physics
Special session: Dynamical Systems and Ergodic Theory
VI. Probability, Stochastic Analysis, and Mathematical Statistics
VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences
Special session: Mathematical Modeling of Some Medical and Biological Processes
Special session: Mathematical Models in Astronomy
VIII. Theoretical Computer Science, Operations Research and Mathematical Programming
Special session: Logic in Computer Science
IX. History and Philosophy of Mathematics
Geometry and Topology of Differentiable Manifolds and Algebraic Varieties (special session)
(this list is in updating process)
1.
BERCEANU Barbu Rudolf Barbu.Berceanu@imar.ro
Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania
Title: De la alfabetul Artin la alfabetul Garside (details)
Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania
Title: De la alfabetul Artin la alfabetul Garside (details)
Abstract:
Schimbind generatorii Artin $\{x_1,x_2,\ldots,x_{n-1}\}$ ai grupului braid $B_n$ cu generatorii $\{\delta |\Delta_n\}$ se obtine un sistem finit de relatii derivate ale lui $B_n$.
Schimbind generatorii Artin $\{x_1,x_2,\ldots,x_{n-1}\}$ ai grupului braid $B_n$ cu generatorii $\{\delta |\Delta_n\}$ se obtine un sistem finit de relatii derivate ale lui $B_n$.
2.
BURGHELEA Dan d.burghelea@gmail.com
Ohio State University, U.S.A.
Title: Monodromy / Alexander rational function of a circle valued map (details)
Ohio State University, U.S.A.
Title: Monodromy / Alexander rational function of a circle valued map (details)
Abstract:
Abstract: I will provide an alternative presentation of the monodromy of $(X; xiin H^1(X;mathbb Z)$ based on the linear algebra of "linear relations".This presentation is a source of new invariants derived from any homology/ cohomology type of vector valued homotopy functor. The Alexander polynomial of a knot is a particular example.
Abstract: I will provide an alternative presentation of the monodromy of $(X; xiin H^1(X;mathbb Z)$ based on the linear algebra of "linear relations".This presentation is a source of new invariants derived from any homology/ cohomology type of vector valued homotopy functor. The Alexander polynomial of a knot is a particular example.
3.
MACINIC Anca anca.macinic@imar.ro
INSTITUTE OF MATHEMATICS "SIMION STOILOW" OF THE ROMANIAN ACADEMY, Romania
Title: (Multi)nets and monodromy (details)
INSTITUTE OF MATHEMATICS "SIMION STOILOW" OF THE ROMANIAN ACADEMY, Romania
Title: (Multi)nets and monodromy (details)
Abstract:
The existence of non-trivial monodromy for the comomology of the Milnor fiber F associated to a complex hyperplane arrangement seems to be connected to the existence of a symmetric structure on the intersection lattice of the arrangement. We present instances of this occurence and describe the (combinatorial) monodromy action on $H^1(F)$, in relation to Aomoto-Betti numbers.
The existence of non-trivial monodromy for the comomology of the Milnor fiber F associated to a complex hyperplane arrangement seems to be connected to the existence of a symmetric structure on the intersection lattice of the arrangement. We present instances of this occurence and describe the (combinatorial) monodromy action on $H^1(F)$, in relation to Aomoto-Betti numbers.
4.
MAXIM Laurentiu maxim@math.wisc.edu
University of Wisconsin-Madison, USA
Title: Motivic infinite cyclic covers (details)
University of Wisconsin-Madison, USA
Title: Motivic infinite cyclic covers (details)
Abstract:
To an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold we associate (assuming certain finiteness conditions are satisfied) an element in the equivariant Grothendieck ring of varieties, called motivic infinite cyclic cover, which satisfies birational invariance. Our construction provides a unifying approach for the Denef-Loeser motivic Milnor fibre of a complex hypersurface singularity germ, and the motivic Milnor fiber of a rational function, respectively. This is joint work with M. Gonzalez Villa and A. Libgober.
To an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold we associate (assuming certain finiteness conditions are satisfied) an element in the equivariant Grothendieck ring of varieties, called motivic infinite cyclic cover, which satisfies birational invariance. Our construction provides a unifying approach for the Denef-Loeser motivic Milnor fibre of a complex hypersurface singularity germ, and the motivic Milnor fiber of a rational function, respectively. This is joint work with M. Gonzalez Villa and A. Libgober.
5.
NICOLAESCU Liviu lnicolae08@gmail.com
University of Notre Dame, USA
Title: A stochastic Gauss-Bonnet-Chern formula. (details)
University of Notre Dame, USA
Title: A stochastic Gauss-Bonnet-Chern formula. (details)
Abstract:
A Gaussian ensemble of smooth sections of a smooth vector bundle E determines a metric and a compatible connection on E. If the bundle is oriented, and the base manifold M is compact and oriented, then the zero locus of a random section in the ensemble is a random current in M and we prove that the expectation of this current is equal to the current determined by the Euler form associated to the above connection by the Chern-Weil construction.
A Gaussian ensemble of smooth sections of a smooth vector bundle E determines a metric and a compatible connection on E. If the bundle is oriented, and the base manifold M is compact and oriented, then the zero locus of a random section in the ensemble is a random current in M and we prove that the expectation of this current is equal to the current determined by the Euler form associated to the above connection by the Chern-Weil construction.
6.
PAUNESCU Laurentiu laurentiu.paunescu@sydney.edu.au
The University of Sydney, Australia
Title: Proof of Whitney fibering conjecture (details)
The University of Sydney, Australia
Title: Proof of Whitney fibering conjecture (details)
Abstract:
In this paper we show Whitney fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivialization arc-wise analytic and we show that it can be constructed under the classical Zariski algebro-geometric equisingularity assumptions. Using a slightly stronger version of Zariski equisingularity, we show the existence of Whitney stratified fibration, satisfying the conditions (b) of Whitney and (w) of Verdier. Our construction is based on Puiseux with parameter theorem and a generalization of Whitney interpolation. For algebraic sets our construction gives a global stratification.
In this paper we show Whitney fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivialization arc-wise analytic and we show that it can be constructed under the classical Zariski algebro-geometric equisingularity assumptions. Using a slightly stronger version of Zariski equisingularity, we show the existence of Whitney stratified fibration, satisfying the conditions (b) of Whitney and (w) of Verdier. Our construction is based on Puiseux with parameter theorem and a generalization of Whitney interpolation. For algebraic sets our construction gives a global stratification.
7.
POPESCU Clement Radu radu.popescu@imar.ro
Institutul de Matematica "Simion Stoilow" al Academiei Romane, Romania
Title: Flat connections and resonance varieties of rank larger than 1 (details)
Institutul de Matematica "Simion Stoilow" al Academiei Romane, Romania
Title: Flat connections and resonance varieties of rank larger than 1 (details)
Abstract:
A way of studying the topological and geometrical properties of a connected CW-complex X, is to study the representation variety of the fundamental group $\pi_1(X)$ into a linear algebraic group G. The set of $\underline{g}$ - valued flat connections, $\underline{g}$ - being the Lie algebra of the group G, an infinitesimal version of the representation variety has a filtration by resonance varieties associated to a representation of $\underline{g}$. I present results concerning these resonance varieties of rank larger than 1.
A way of studying the topological and geometrical properties of a connected CW-complex X, is to study the representation variety of the fundamental group $\pi_1(X)$ into a linear algebraic group G. The set of $\underline{g}$ - valued flat connections, $\underline{g}$ - being the Lie algebra of the group G, an infinitesimal version of the representation variety has a filtration by resonance varieties associated to a representation of $\underline{g}$. I present results concerning these resonance varieties of rank larger than 1.
8.
SECELEANU Alexandra aseceleanu2@unl.edu
University of Nebraska-Lincoln, USA
Title: Symbolic powers and line arrangements (details)
University of Nebraska-Lincoln, USA
Title: Symbolic powers and line arrangements (details)
Abstract:
Symbolic powers of ideals play a significant part in algebraic geometry and in commutative algebra, where containment relations between symbolic powers and ordinary powers of ideals have become a focus of interest. In this talk, we consider new algebraic invariants that measure this containment. Examples will focus on the case of ideals of points arising as the singular locus of a planar line arrangement.
Symbolic powers of ideals play a significant part in algebraic geometry and in commutative algebra, where containment relations between symbolic powers and ordinary powers of ideals have become a focus of interest. In this talk, we consider new algebraic invariants that measure this containment. Examples will focus on the case of ideals of points arising as the singular locus of a planar line arrangement.
9.
SUCIU Alexandru a.suciu@neu.edu
Northeastern University, USA
Title: Topology of complex line arrangements (details)
Northeastern University, USA
Title: Topology of complex line arrangements (details)
Abstract:
I will discuss some recent advances in our understanding of the relationship between the topology, group theory, and combinatorics of an arrangement of lines in the complex plane.
I will discuss some recent advances in our understanding of the relationship between the topology, group theory, and combinatorics of an arrangement of lines in the complex plane.
10.
TIBAR Mihai tibar@math.univ-lille1.fr
Université de Lille 1, France
Title: Topology of real polynomial maps (details)
Université de Lille 1, France
Title: Topology of real polynomial maps (details)
Abstract:
The topology of fibres of a real polynomial function may change due to the behavior at infinity. We focus on the detection of those fibres which are asymptotically atypical.
The topology of fibres of a real polynomial function may change due to the behavior at infinity. We focus on the detection of those fibres which are asymptotically atypical.