David Hartman | Charles University Prague |

## David Hartman |
Everything is both simpler
than we can imagine, and more complicated that we can conceive. Johann Wolfgang von Goethe |

My research is divided into several areas. The first area is represented by *combinatorial theory of complex networks*. This deals mainly with research
of graph theoretical properties of complex networks or corresponding models.

- Extremal propeerties of CN characteristics
- Specific properties of CN such as sparsity or clustered nature
- Algorithms for CN

Another topic from graph theory is the analysis of *symmetrical relational structures* and particularly those meeting homogeneity condition. Within this area the interesting parts are:

- Homomorphism-homogeneity of various structures
- Classes defined by various types of homogeneity
- Relational and lift complexity

Another area is area of *interval optimization*, where the main areas are:

- Extending linear algebra with interval aritmetics
- Solvability of interval (linear) systems

Last area is that of *dynamical systems* with application to neurology, climatology, and cybersecurity where the main area of interests are:

- Reliability of complex network construction
- Modelling of complex network and graph limits
- Utilization of complex network measure to analyse real-world phenomena

*ERC DYNASNET*- ERC Synergy Grant

Dynamics and Structure of Networks, see pages.*GACR 19-11753S*- Czech Science Foundation standard research grant

Computational neuroscience grant in cooperative with Institute of Physiology*GACR 19-16066S*- Czech Science Foundation standard research grant

Nonlinear interaction and information transfer in complex systems*FP7 BRAINSYNCH*- EU 7th Framework Research Programme

Large scale interactions in brain networks and their breakdown in brain diseases.*ERC CZ CORES*- ERC grant

ERC grant on Complex Structures: Regularities in Comb. and Discrete Math*CE-ITI*- Czech Science Foundation center of excellence

Centrum of Excelence - Institute for Theoretical Computer Science*GACR P103/11/J068*- Czech Science Foundation bilateral research grant with Germany

Interactions, information transfer and complex structures in the dynamics of changing climate.*GACR P402/13-10660S*- Czech Science Foundation standard research grant

Interval methods for optimization problems

*Homomorphism-homogeneity classes of countable L -colored graphs*, EUROCOMB 2019, Bratislava, Slovakia, 2019*Maximization of a Convex Quadratic Form on a Polytope: Factorization and the Chebyshev Norm Bounds*, WCGO 2019, Mety, France, 2019*Complexity of computing powers for various classes of interval matrices*, MATTRIAD 2019, Liblice, Czech Republic, 2019*Plausible ways to compute powers of interval matrices*, ICMAA 2019, Reno, Nevada, 2019*On equality of two classes of homomorphism-homogeneous relational structures*, BANFF 2018 Unifying Themes in Ramsey Theory, Banff, 2018*Equality of classes MH and HH*, ICMS 2018 From permutation groups to model theory workshop, Edingurgh, 2018*Computing powers of interval matrices*, SCAN 2018, Tokyo, 2018*Disturbing effects within construction of stock networks*, Dresden, Germany, 2018