Subgroups of Finite Abelian Groups (Lecture 2) by Amritanshu Prasad

Program: Combinatorial Methods in Enumerative Algebra

ORGANIZERS: Angela Carnevale (University of Galway, Ireland), Uri Onn (Australian National University, Canberra, Australia), Amritanshu Prasad (IMSc, Chennai, India), Pooja Singla (IIT Kanpur, India) and Christopher Voll (Bielefeld University, Germany)
DATE & TIME: 02 December 2024 to 13 December 2024
VENUE: Ramanujan Lecture Hall, ICTS Bengaluru

Many algebraic counting problems give rise to integer sequences that hold information which is best accessed by encoding these numbers in appropriate generating functions. Numerous classical zeta and L-functions testify to this principle: Dirichlet’s zeta function enumerates ideals of a number field; Witten’s zeta function counts representations of Lie groups; Hasse– Weil zeta functions encode the numbers of rational points of algebraic varieties over finite fields. Analytic and arithmetic properties of these zeta functions hold or are expected to hold, the key to a treasure trove of information about the underlying structures.

Zeta functions of groups and rings are invaluable tools in asymptotic group theory and ring theory. Often, they admit Euler product decompositions, with rational local factors that reflect regularity of structure in the underlying data.

We aim to bring together experts in the various relevant subject areas, including those in zeta functions of groups and rings and—crucially—in adjacent combinatorial areas, enabling them to address some of the outstanding problems in this field.

We will train young researchers to invite them to this vibrant area of enumerative algebra, give them the tools to both contribute to this area of asymptotic group and ring theory and relate it to their own area of expertise.

Partially supported by TRR358.

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