Diffeology: A gentle introduction

Abstract: Diffeological spaces, introduced in 1985 by Iglesias-Zemmour, are general spaces on which one can do differential calculus. The notion is very weak, permitting even a structureless set to be a diffeological space but, more meaningfully, making it possible to do differential calculus on spaces of smooth functions. In this talk, we will discuss the basic definitions and examples in the subject.

Speakers' bios: Ambar Sengupta studied mathematics at Presidency College, Calcutta, and then obtained his PhD in Mathematics at Cornell University in 1990. After a post-doctoral appointment at Princeton University, he was on the faculty at LSU 1991-2016, and since then has been at the University of Connecticut. Sengupta's mathematical work has spanned a wide range, with much of the inspiration coming from mathematical physics. His recent interests include nonstandard analysis, classical analysis, and category-theoretic geometry.

Dion Mann is currently studying mathematics through the Ph.D. program at the University of Connecticut. Previously, he obtained a bachelor’s in physics and mathematics at the University of Colorado, Boulder. His mathematical interests broadly include mathematical physics and differential topology.

Moderator's bio: Irfan Alam is an autistic mathematician, currently working as a postdoctoral fellow in the Department of Computer and Mathematical Sciences at University of Toronto Scarborough. He completed the BMath and MMath programs at the Indian Statistical Institute (2009-2014), before joining Louisiana State University as a graduate student, where he obtained his PhD in Mathematics as well as MA in Philosophy in 2021. Irfan’s mathematical focus is on applications of nonstandard analysis to standard mathematics, especially in probability theory, topology, and lately in the foundations of machine learning. He also works on the philosophy of mathematical practice, with particular interests in the history of infinitesimals and in epistemic injustices in mathematics caused by various socio-cultural norms.

Computer scienceMathematics

Audience: researchers in the topic

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Relatorium seminar

Series comments: The name "Relatorium" combines "relator" with the Latin root "-ium," meaning "a place for activities" (as in "auditorium" or "gymnasium"). This seminar series is a platform to relate ideas, interact with math, and connect with each other.

In this series, we explore math beyond what we usually hear in standard talks. These sessions fall somewhere between a technical talk and a podcast: moderately formal, yet conversational. The philosophy behind the series is that math is best learned by active participation rather than passive listening. Our aim is to “engage and involve,” inviting everyone to think actively with the speaker. The concepts are accessible, exploratory, and intended to spark questions and discussions.

The idea of relatability has strong ties to compassion — creating space for shared understanding and exploration - which is the spirit of this seminar! This is a pilot project, so we’re here to improvise, learn, and evolve as we go!

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