Devadatta Ganesh Hegde
TIFR, Mumbai
September 18, 2025
Poles of Eisenstein Series in Langlands’ Early Work.: In 1964, Robert Langlands drafted a manuscript entitled \emph{``On the Functional Equations Satisfied by Eisenstein Series}'', addressing the spectral decomposition of spaces such as \[L^{2}\left(SL(n,\mathbb{Z})\backslash SL(n,\mathbb{R})\right).\] Published in 1976 with only minor revisions, this manuscript became a cornerstone of the Langlands program---yet, as Langlands himself remarked, \textquotedblleft it has proven almost impenetrable.\textquotedblright{}
In this talk, I will discuss the simplest cases of this work, focusing on the poles of Eisenstein series, which form a crucial first step toward understanding the general theory. I will also present some of my recent results in this direction.
Sudipta Das
TIFR, Mumbai
September 18, 2025
Asymptotic colength for families of ideals: In this talk, we will discuss the concept of asymptotic colengths for families of $m$-primary ideals within a Noetherian local ring $(R,m)$. We will explore the significance of these colengths in the fields of commutative algebra and algebraic geometry. In any characteristic, we will generalize graded families to weakly graded families of ideals. In prime characteristic, we will investigate various families, including weakly $p$-families. The primary objective of this talk is to present a new analytic method for proving the existence of these limits. If time permits, we will also discuss Brunn-Minkowski type inequalities, positivity results, and volume = multiplicity formulas for these families of ideals. This talk is based on a joint work with Cheng Meng.
TIFR, Mumbai
September 18, 2025
Poles of Eisenstein Series in Langlands’ Early Work.: In 1964, Robert Langlands drafted a manuscript entitled \emph{``On the Functional Equations Satisfied by Eisenstein Series}'', addressing the spectral decomposition of spaces such as \[L^{2}\left(SL(n,\mathbb{Z})\backslash SL(n,\mathbb{R})\right).\] Published in 1976 with only minor revisions, this manuscript became a cornerstone of the Langlands program---yet, as Langlands himself remarked, \textquotedblleft it has proven almost impenetrable.\textquotedblright{}
In this talk, I will discuss the simplest cases of this work, focusing on the poles of Eisenstein series, which form a crucial first step toward understanding the general theory. I will also present some of my recent results in this direction.
Sudipta Das
TIFR, Mumbai
September 18, 2025
Asymptotic colength for families of ideals: In this talk, we will discuss the concept of asymptotic colengths for families of $m$-primary ideals within a Noetherian local ring $(R,m)$. We will explore the significance of these colengths in the fields of commutative algebra and algebraic geometry. In any characteristic, we will generalize graded families to weakly graded families of ideals. In prime characteristic, we will investigate various families, including weakly $p$-families. The primary objective of this talk is to present a new analytic method for proving the existence of these limits. If time permits, we will also discuss Brunn-Minkowski type inequalities, positivity results, and volume = multiplicity formulas for these families of ideals. This talk is based on a joint work with Cheng Meng.