Algebra Seminar
Speaker: Prof. Gurmeet Bakshi (Panjab University, Chandigarh)
Host: Sudhir R. Ghorpade
Title: Classical Problems to Modern Perspectives: Units in Integral Group Rings
Time, day and date: 4:00:00 PM - 5:00:00 PM, Monday, September 22
Venue: Ramanujan Hall
Abstract: The question of determining the unit group of an integral group ring has a long and fascinating history of more than eighty years. Despite important contributions by Higman, Bass, Milnor, Ritter, Sehgal, and many others, a full description remains a challenge even for cyclic groups. In this talk, I will trace the development of the subject from its classical origins to recent progress. Central to modern approaches are Shoda pairs and their refinements, which provide effective tools to analyze the rational group algebra and construct explicit units. I will present results on generalized strongly monomial groups, highlighting their role in understanding primitive idempotents, central units, and finite index subgroups of unit groups. Alongside these theoretical advances, I will also touch upon computational aspects. We will also see how old problems continue to inspire new algebra.

Special Colloquium
Speaker: N.S. Narasimha Sastry, Kerala School of Mathematics
Host: Dipendra Prasad
Title: `Monster is fabulous'
Time, day and date: 5:15:00 PM - 6:15:00 PM, Monday, September 22
Venue: Ramanujan Hall
Abstract: So said Simon Norton! True Indeed!! This enigmatic, Monster finite simple group, emerged during the last phase of the classification of finite simple groups, one of the major achievements of twentieth century mathematics. The existence of Monster ties together many unique situations in Mathematics including highly transitive permutation groups (Mathieu groups) , perfect sphere packings in finite vector spaces and Golay codes, the exceptional 24-dimensional Leech lattice, some exceptional non split group extensions, special strongly regular graphs, a unique decomposition of Lie algebra of type E_8 and so on. Further, twenty of the sporadic simple groups and non-split group extensions (many, then unknown),, apart from few classical groups appear as quotients of subgroups of the Monster. Also, it seems to highlight the role of extraspecial groups (finite p-groups which are finite analogue of the Heisenberg group) in the emergence of sporadic simple groups..  
Apart from Its enormous size, its permutation or linear representations only possible on objects of very large size; and its very intricate structure, it has deep connections with many other mathematical structures including modular functions, affine E_8-root system, Vertex operator algebras; and string theory.

In this talk, I will try to present some striking features of this group,, mention some (group theoretic) foundational steps in the classification, state its connection to modular functions (the so-called `Monster Moonshine'), the affine E_8 connection, and some brief remarks on the initial steps leading to its construction. (Paucity Of knowledge prevents me from making any references to its connections between the Monster group and String theory which seems to be very substantial.) 

I will try to make the talk as simple (if not, simpler!) as possible.. .