Monday 13 May, from 2 pm in Room 2109 - U5 Building, the post-docs Federico Fallucca and Romeo Segnan Dalmasso (University of Milano-Bicocca) will hold the following seminars
Speaker: Federico Fallucca
Title: On the classification of regular product-quotient surfaces with p_g=3 and their canonical map
Abstract: A product-quotient surface is the minimal resolution of singularities of a quotient of a product of curves by theaction of a finite group of automorphisms. Introduced by Catanese in a paper from 2000, product-quotient surfaceshave been extensively investigated by several authors. They are valuable tools for constructing new examples ofalgebraic surfaces and exploring their geometry in an accessible way. Consequently, classifying these surfaces byfixing certain invariants such as the self-intersection $K^2$ of the canonical class and the Euler characteristic $\chi$ isnot only inherently interesting but also highly practical in various contexts.
During the talk, I will provide a brief overview on product-quotient surfaces and I will describe the most important toolsthat are developed by some authors to produce a classification of them using a computational algebra system (e.g.MAGMA). I will introduce the results I have obtained to provide a more efficient algorithm. One of the main results is a theoremthat allows us to move from a database of $G$-coverings of the projective line (in pairs), already produced in a recent work by Conti, Ghigi and Pignatelli, to a database of families of product-quotient surfaces.
Using this approach, I have produced a huge list of families of product-quotient surfaces with $p_g=3$, $q=0$, andhigh $K^2$ values. The classification is complete for $K^2\in \{23, ..., 32\}$. Finally, I plan to show as an application how I used this huge list of families to obtain new results on a still openquestion regarding the degree of the canonical map of surfaces of general type.
Speaker: Romeo Segnan Dalmasso
Title: Special structures and spinors on manifolds
Abstract: The study of special structures on (pseudo)-Riemannian manifolds has been of interest for bothmathematicians and physicists for at least a century, the most striking example being the Einstein condition on themetric tensor of the manifold, which is hence called Einstein. The existence of such structures on a given manifold, is closely related to (the existence of) sections of the spinorbundle, called spinors, satisfying some constraint. For instance, the existence of Killing spinors on a Riemannian(spin) manifold implies, among other things, that the metric satisfies the Einstein condition, and the existence ofparallel spinors implies that the Ricci tensor is identically zero. In the pseudo-Riemannian setting the situation is lessstudied, nor as strict, for instance the metric need not be Einstein.
In this talk, I will first give an introduction to the topic, which aims to give a more clear picture of the relation betweenspecial structures and particular spinors. Next, I will present a new method to construct pseudo-Riemannian K\"ahlerEinstein and Sasaki Einstein solvmanifolds, which come equipped with a parallel or Killing spinors respectively.Finally, I will talk about possible future work on the construction of manifolds endowed with parallel or Killing spinors.
This talk is based on joint works with D. Conti and F.A. Rossi.
All interested are invited to participate