# Antonio CAUSA

##### Contacts

**Office:** Dipartimento di Matematica e Informatica, ufficio 332**Email:** causa@dmi.unict.it**Phone:** 095 7383067**Fax:** ++39 095 330094**Skype:** antonio.causa5

##### Office Hours

Tuesday from 09:00 to 11:00 | Thursday from 11:00 to 13:00 Meetings can be scheduled by email.Antonio Causa was born in 1968, graduated in Physics at University of Catania in 1992 and he is a researcher in Geometry at University of Catania since 1997.

He has taught courses of Geometry, Linear Algebra, Coding Theory at Faculty of Engineering, Mathematics, Informatics of the University of Catania since 1998.

His research interests mainly concern Algebraic Geometry, Coding Theory, Variational Inequalities.

**N.B.**the number of publications can affect the loading time of the information

##### Academic Year 2021/2022

- DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE

Master's Degree in Architecture and Building Engineering - 1^{st}Year**GEOMETRIA** - DEPARTMENT OF PHYSICS AND ASTRONOMY

Bachelor's Degree in Physics - 1^{st}Year**GEOMETRIA A - L**

##### Academic Year 2020/2021

- DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE

Master's Degree in Architecture and Building Engineering - 1^{st}Year**GEOMETRIA** - DEPARTMENT OF PHYSICS AND ASTRONOMY

Bachelor's Degree in Physics - 1^{st}Year**GEOMETRIA M - Z**

##### Academic Year 2019/2020

- DEPARTMENT OF CHEMICAL SCIENCES

Bachelor's Degree in Chemistry - 1^{st}Year**MATHEMATICS 1 A - L**

##### Academic Year 2018/2019

- DEPARTMENT OF BIOLOGICAL, GEOLOGICAL AND ENVIRONMENTAL SCIENCES

Bachelor's Degree in Biology - 1^{st}Year**ISTITUZIONI DI MATEMATICHE - canale 1**

##### Academic Year 2017/2018

- DEPARTMENT OF BIOLOGICAL, GEOLOGICAL AND ENVIRONMENTAL SCIENCES

Bachelor's Degree in Biology - 1^{st}Year**ISTITUZIONI DI MATEMATICHE - canale 1**

##### Academic Year 2016/2017

- DEPARTMENT OF BIOLOGICAL, GEOLOGICAL AND ENVIRONMENTAL SCIENCES

Bachelor's Degree in Biology - 1^{st}Year**ISTITUZIONI DI MATEMATICHE - canale 1**

##### Academic Year 2015/2016

- DEPARTMENT OF BIOLOGICAL, GEOLOGICAL AND ENVIRONMENTAL SCIENCES

Bachelor's Degree in Biology - 1^{st}Year**ISTITUZIONI DI MATEMATICHE A - L**

My research interests mainly concern Algebraic Geometry, Coding Theory, Variational Inequalities.

Some results have been obtained on the "Waring problem" for real binary symmetric tensors.

The Waring problem for symmetric tensors deals with the following problem: given a degree n polynomial in m variables find the (Waring) rank of f, i.e. the minimum number of summands that achieve the following equality: f=a_{1}l_{1}^{n} +...+ a_{k}l_{k}^{n} with a_{i} real coefficients and l_{i} linear forms in m variables.

In the context of Variational Inequalities it has been studied the regularity of the solution of some classes of variational inequalities.

Let K be a nonempty, closed and convex subset of the n-dimensional Euclidean space R^{n}, F : U → R^{n }a continuous mapping. The variational inequality problem (VI) is the problem of finding a point x* in K such that

F(x*)(y − x*) ≥ 0 ∀y in K.

If the set K and the mappings F are dependent by a (usually real) parameter t one can ask which properties solution x*(t) fulfills.

When the convex set K(t) is a polytope, i.e. a bounded intersection of a finite set of half-spaces, it has been studied Lipschitz continuity of solution x*(t).

During the last decades many scholars have been studying the connections between commutative algebra and combinatorics. It has been noted that problems in the former can be translated in the language of the latter and vice versa.

As a starting point some combinatorial objects as graphs and hypergraphs can be used to construct particular monomial ideals called Edge ideals and Covering ideals. In this context we are interested in studying some algebraic invariants such Betti numbers, Hilbert function, Castelnuovo-Mumford regularity, Waldschmidt constant of Edge ideals and Covering ideals associated to matroids or Steiner systems.

A Matroid is a hypergraph which consists of a a finite set M of elements together with a family of subsets of M, called independent sets, such that the empty set is independent, every subset of an independent set is independent, for every subset A of M, all maximum independent sets contained in A have the same number of elements.

Another interesting problem is the Ideal containment problem for Edge ideals and Covering ideals, i.e. decide for which m and r there is the containment I^{(m) } is a subset of I^{r}, where I^{(m)} is the symbolic power of the ideal I and I^{r} is the regular power of I.