### Departmental Weekly Events

__March 20 – March 24, 2023__

AGENDA

__Monday, March 20__

**Algebra Seminar**,*“Factorization beyond Factorization Theory I.”*., Laura Cossu from University of Graz, Austria.__12:30PM - 1:30PM__. SH 235 and Zoom. Link:**944 6111 4862**

**Abstract: **Many problems in algebra involve the decomposition of certain elements of a ring (or more generally of a monoid) into a product of certain other elements (hereinafter generically referred to as "building blocks") that are in some sense minimal. The classical theory of factorization investigates factorizations in which the building blocks are atoms, i.e., non-unit elements of a monoid that are not products of two non-units. For example, it is well known that every non-zero non-unit of a Dedekind domain (more generally, of a Noetherian domain) can be written as a finite product of atoms and that in general such decompositions are not unique. On the other hand, examples of factorizations that lie beyond the scope of the classical theory include additive decompositions into multiplicative units in rings; cyclic decompositions of permutations in the symmetric group of degree n; idempotent factorizations of the "singular elements'' of a monoid; and so on.

We combine the language of monoids and preorders to make first steps towards the construction of a "unified theory of factorization". In particular, we prove an abstract factorization theorem that recovers, among others, a classical theorem of Cohn on atomic factorizations in cancellative monoids and a classical result of Anderson and Valdes-Leon on "irreducible factorizations" in commutative monoids. Moreover, we generalize the notion itself of factorization and some of the most studied arithmetical invariants of the classical theory (including sets of lengths and elasticities). The talks are based on joint work with S. Tringali.

__Tuesday, March 21__

**No Events**

__Wednesday, March 22__

**Faculty Meeting**,*All College Track and Tenure Track.,*John Harding.__12:30PM - 1:30PM__. Zoom. Link:**941 2833 9147**

__Thursday, March 23__

**No Events**

__Friday, March 24__

**No Geometry & Topology Seminar**

**Colloquium**,*“Data is Nothing Without Control: On Building IoT Architectures for a Sustainable Society.”*., Marco Aiello from University of Stuttgart, Germany.__12:15PM - 1:30PM__. Science Hall 107 and Zoom. Link:**985 2970 4531**

**Abstract: **The availability of data in digital form is at unprecedented levels and is enabling a new way of building systems that are transforming our society. But data by itself is not enough to provide useful systems. In this talk, I will overview recent and current research efforts at the Service Computing Department of the Institute of Architecture of Application Systems of the University of Stuttgart. The research efforts revolve around the design of architectures that go beyond the mere collection of data and can support humans in smart ways. The applications of these systems are in the field of energy and sustainability, in particular: Smart Buildings, Smart Grids, and Smart Data Centers.

__Notes:__

None

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