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Lecture Series Announcement Date: 25, 27 and 28 March 2024 Time: 2:00 to 3:15 PM Venue: Lecture Hall 202 An introduction to mapping class groups Kashyap Rajeevsarathy IISER Bhopal. 27-03-24 Abstract Let $S = S_{g,b,p}$ denote the closed orientable surface of genus $g$ with $b$ boundary components and $p$ punctures. The mapping class group of $S$ (denoted by $\text{Mod}(S)$) is defined to be the group of isotopy classes of orientation preserving self-homeomorphisms of $S$ that restrict to the identity on $\partial S$ and preserve the set of punctures in $S$. In this three-part lecture series, we will introduce various concepts and ideas that lie at the foundation of the theory of mapping class groups. We will also explore some of its connections with hyperbolic geometry, braid groups, Teichmuller theory, geometric group theory, and $3$-manifolds. We will conclude the series with a short discussion on infinite-type surfaces and their associated mapping class groups, also known as big mapping class groups. The past decade has witnessed a burgeoning interest in studying these groups as they are far more intricate than their finite-type counterparts. While some analogs of results in $\text{Mod}(S)$ have been derived in this setting, many fundamental questions remain open. We will survey some of the recent developments in this direction.
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