Dr. Luigi Ferraro
Department of Mathematics
Texas Tech University

Department of Mathematics
Texas Tech University
One of my research interests is in commutative algebra, in particular in the use of homological tools to study commutative rings. I am also interested in non-commutative algebra, in particular in the actions of Hopf algebras on rings and the homological properties of quotients of skew polynomial rings.
Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra. Here is a list of packages I co-wrote:
Stable cohomology of local rings and Castelnuovo-Mumford regularity of graded modules.
CHAMP is a weekly online seminar series; its main goal is to give graduate students and other early career researchers on the job market a platform to give a 50 minutes talk about their research. This is the seminar that I gave at CHAMP, based on my paper The homotopy Lie algebra of a Tor-independent tensor product.
Here is a counterexample answering the question that Eloisa asked at the end of the talk: let k be a field, let R=k[[x,y]] be a power series ring and let I1=(x2,xy),I2=(y2) be ideals of R. Set S1=R/I1, S2=R/I2 and S=R/(I1+I2). Then $\pi$(S) is a free Lie algebra since the square of the maximal ideal of $S$ is zero. While
$\pi$(S1)$\times$$\pi$(R)$\pi$(S2) is not free because an element of degree 2 of $\pi$(S1) commutes with an element of degree 2 of $\pi$(S2); this follows from the fact that R is regular and so $\pi$(R) is concentrated in degree 1.
Teaching (WFU)
Graduate courses taught as principal instructor:
Undergraduate courses taught as principal instructor:
Teaching (UNL)
Undergraduate courses taught as principal instructor:
Recitations