Some contributions to the theory of singularities and their characteristic classes

In this Ph.D. thesis, we give some contributions to the theory of singularities, as well as to the theory of characteristic classes of singular spaces. The first part of this thesis is devoted to the theory of singularities of mappings. We obtain formulas for an important analytical invariant, the image Milnor number of a map-germ. The first contribution is a version of the Lê-Greuel formula for the image Milnor number for corank 1 map-germs, which gives a recursive method to compute it. This work is in collaboration with my Ph.D. supervisor J. J. Nuño. In the second work of this thesis, we obtain two formulas for the image Milnor number for weighted-homogeneous map-germs for dimensions four and five. These formulas are obtained by combining the theory of characteristic classes of singular spaces with a recursive method through examples of singularities. This work is in collaboration with Prof. G. Peñafort. The last part which composes the main work of this Ph.D. thesis is the proof for projective varieties of the Brasselet-Schürmann-Yokura conjecture. This conjecture is within the theory of characteristic classes of singular spaces. Characteristic classes of singular varieties are homology classes generalizing the classical cohomological characteristic classes of manifolds. The conjecture states that two different characteristic classes coincide for compact complex algebraic varieties that are rational homology manifolds. This work is in collaboration with my Ph.D. supervisor J. Fernández de Bobadilla. This conjecture is the characteristic class version for rational homology manifolds of the famous Hodge Index Theorem which computes the signature of a compact complex manifold in terms of Hodge numbers

Image Milnor Number Formulas for Weighted-Homogeneous Map-Germs

We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely interpolative method, applied to a result by Ohmoto. We use our approach to recover the formulas for $n=2$ and $3$ due to Mond and Ohmoto, respectively. For $n\geq 6$, the method is valid as long as certain multi-singularity conjecture holds.BERC.2014-2017, MINECO.Severo Ochoa.SEV-2013-0323

Production and characterization of activated carbon from barley straw by physical activation with carbon dioxide and steam

In recent years, the growth of environmental protection policies has generated an increase in the global demand for activated carbon, the most widely used adsorbent in many industrial sectors, and with good prospects of implementation in others such as energy storage (electrodes in supercapacitors) and agriculture (fertilizer production). This demand is driving by the search for renewable, abundant and low-cost precursor materials, as an alternative to traditional fossil sources. This study investigates the production of activated carbon from barley straw using physical activation method with two different activating agents, carbon dioxide and steam. Experimental tests under different conditions at each stage of the process, carbonization and activation, have been conducted in order to maximize the BET surface area and microporosity of the final product. During the carbonization stage, temperature and heating rate have been found to be the most relevant factors, while activation temperature and hold time played this role during activation. Optimal conditions for the activation stage were obtained at 800 °C and a hold time of 1 h in the case of activation with carbon dioxide and at 700 °C and a hold time of 1 h in the case of activation with steam. The maximum BET surface area and micropore volume achieved by carbon dioxide activation were of 789 m2/g and 0.3268 cm3/g while for steam activation were 552 m2/g and 0.2304 cm3/g, which represent respectively an increase of more than 43% and 42% for the case of activation with carbon dioxide