Mathematics seminars at IISER Mohali during the spring of 2026

A series of talks is (ongoing and) planned for the spring semester of ‘26, organized at IISER Mohali.

• path to LoHS and beyond
  • Lebesgue integral (Ch 1, Papa Rudin), (Ch 2, Papa Rudin)
  • Complex measures (Ch 6, Papa Rudin)
  • Following Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler, Thomas Ward sections 2.3-4, 3.5
  • parts of Ch 4
  • sections 6.1-3
  • section 7.1
  • sections 8.1, 8.3-6
• Following [2402.15867] An Invitation to Analytic Group Theory
  • Sections 1.2 and 1.3: $F_2$ is paradoxical
  • Section 1.4
• Fuchsian groups $\leftrightarrow$ hyperbolic/Riemann surfaces
  • Riemann surfaces and their uniformization, hyperbolic surfaces and their uniformization
  • …
  • (main result 1) Geodesic flow on finite volume(?) hyperbolic surfaces is ergodic
• Following Hall’s Quantum Theory for Mathematicians.pdf
• watch party on PDEs: MIT Differential analysis I

special talks related to geometry of spaces and algebra of functions on it §

topics	assuming	advert for
(space) Metric spaces $X$ $\leftrightarrow$ rings of continuous functions $\mathcal{C}(X)$	only Sem 5 courses	the whole philosophy, the course on Rings and modules, the course on topology
(functions) Banach algebras and $\mathsf{c}\ast$-algebras, and how they correspond to locally compact Hausdorff topological spaces (from above)	courses upto Sem 7	LoHS
(space) smooth manifolds $X$ and ${\mathcal{C}}^{\infty }(X)$	smooth manifolds from Sem 7
(functions) “smooth $\mathbb{R}$-algebras”
(space) topological dynamics: Consider $G\to {\mathsf{Top}}_{\ast }\stackrel{{\pi }_1}{\to }\mathsf{Grp}$ and the action $GL(2,\mathbb{Z})\curvearrowright T^2$	Basic algebraic topology like ${\pi }_1$
(functions) measure preserving dynamics and operators on $L^2$ spaces	Basic measure theory	LoHS?
(space) Riemann surfaces	Basic complex analysis	more complex analysis! (Riemann surfaces)
(functions) Field extensions of $\mathbb{C}(t)$