Ex Numera Undergraduate Student Seminar: Elvin Meng

Description

Join Ex Numera, the undergraduate mathematics club, for a talk by Elvin Meng entitled "Limitless Calculus and the Foundation of Mathematics." There will be a general body meeting following the seminar.

Abstract: This talk will give an introduction to an alternative formulation of analysis known as Infinitesimal Analysis or Synthetic Differential Geometry (SDG). The idea is to introduce infinitesimal objects that aligns with intuitive notions of the infinitely small into the real line in such a way that, under constructivist logic, standard operations and constructions such that differentiation, integration, and Taylor series can be defined (with their usual properties) without δ formulations or limit computations. The talk will first motivate the Kock-Lawvere Axiom that allows the existence of infinitesimal objects, and then reconstruct roughly two semesters of calculus (hopefully in under 40 minutes) within this new framework. We will also provide a brief description of constructivist logic as an alternative mathematical paradigm. We will end by discussing manifolds in this framework and topos theory as the correct universe of discourse for models of this theory.

Prerequisities: Two semesters of calculus. Knowledge of analysis, logic, and algebraic geometry is beneficial but by no means necessary.