# Real projections of non-standard functions

Università degli Studi Trento

38123 Povo (TN)

Tel +39 04 61/281508-1625-1701-3898-1980.

dept.math [at] unitn.it

**Luogo:** Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari

**Ore** 14:30

**Relatore: **

**Emanuele Bottazzi**(Dottorando Università di Trento)

**Abstract:**

In non-standard analysis, there are many ways to coherently project a non-standard function to a standard real function. The most famous among those projections is the standard part. This procedure maps non-standard functions satisfying a regularity hypothesis called S-continuity to real continuous functions. The first part of the talk is devoted to the presentation of the standard part and to a discussion of S-continuity. In the second part of the talk, we show how a less regular non-standard function can be projected to a distribution. This projection allows a non-standard formulation to many PDEs, paving the way for a definition of generalized solution to PDEs that will be presented at a subsequent date.

This talk is intended as a gentle introduction on the subject: we will focus more on discussing the ideas and providing examples rather than rushing through all the theoretical results. For this reason, we encourage everyone interested in the subject to join the talk.

**Referente: Stefano Baratella**