Dear all,
Title: Finite Trigonometric Sums: Evaluations, Estimates, Reciprocity Theorems
Speaker: Bruce Berndt (University of Illinois at Urbana Champaign)
When: Mar 16, 2022, 6:00 PM- 7:00 PM IST (7:30 AM - 8:30 AM (CDT))
Organizers: Gaurav Bhatnagar (Ashoka University) , Atul Dixit (IIT, Gandhinagar) and Krishnan Rajkumar (JNU). Contact: sfandnt@gmail.com
Dear all,
The next talk is by B. Ramakrishnan (popularly known as Ramki), formerly of HRI, Allahabad, and now in ISI, Tezpur.
Happy new year.
Dear all,
Tea or Coffee: Please bring your own.
Abstract:
The talk this week is by Nicholas Smoot from the Research Institute of Symbolic Computation (RISC) at Johannes Kepler University (JKU), Linz, Austria. The announcement is below.
Talk Announcement:
Tea or Coffee: Please bring your own.
Abstract:
Since Ramanujan's groundbreaking work, a large variety of infinite congruence families for partition functions modulo prime powers have been discovered. These families vary enormously with respect to the difficulty of proving them. We will discuss the application of the localization method to proving congruence families by walking through the proof of one recently discovered congruence family for the counting function for 5-elongated plane partitions. In particular, we will discuss a critical aspect of such proofs, in which the associated generating functions of a given congruence family are members of the kernel of a certain linear mapping to a vector space over a finite field. We believe that this approach holds the key to properly classifying congruence families.
Our next speaker is Sunil Naik, a grad student in IMSc, Chennai.
Talk Announcement:
Tea or Coffee: Please bring your own.
Abstract:
The non-vanishing as well as primitivity of the values of the Fourier
coefficients of non-CM Hecke eigen forms, in particular the Ramanujan
$\tau$ function is a deep and mysterious theme in Number theory.
In this talk, we will report on our recent work on the number of
distinct prime factors of the values of the Fourier coefficients of
non-CM Hecke eigen forms, in particular the Ramanujan $\tau$ function.
We are happy that Kaneenika Sinha (IISER, Pune) has consented to give a mini-course on Central limit theorems in number theory. The course will comprise two lectures. The announcement is below. Graduate students who are interested in number theory are especially welcome to hear Professor Sinha.
Mini-course announcement
Tea or Coffee: Please bring your own.
Talk 1
Talk Announcement:
Tea or Coffee: Please bring your own.
Abstract:
Cylindric partitions, first introduced by Gessel and
Krattenthaler in 1997, are an affine (or toroidal) analogue of
ordinary plane partitions. Perhaps somewhat surprisingly, cylindric
partitions have a close connection to Rogers--Ramanujan-type $q$-series
identities. In this talk I will try to explain this connection, and report
on some new Rogers--Ramanujan identities for the affine Lie algebra
$\mathrm{A}_2^{(1)}$ that follow naturally from this connection.
We are delighted to welcome Neelam Kandhil (soon to become Dr. Neelam Kandhil) of IMSc, Chennai for our next talk. The talk announcement is below.
Talk Announcement:
Tea or Coffee: Please bring your own.
Abstract:
It is an open question of Baker whether the numbers $L(1, \chi)$ for non-trivial Dirichlet characters $\chi$ with period $q$ are linearly independent over $\mathbb{Q}$. The best known result is due to Baker, Birch and Wirsing which affirms this when $q$ is co-prime to $\varphi(q)$. In this talk, we will discuss an extension of this result to any arbitrary family of moduli. The interplay between the resulting ambient number fields brings in new technical issues and complications hitherto absent in the context of a fixed modulus. In the process, we also extend a result of Okada about linear independence of the cotangent values over $\mathbb{Q}$ as well as a result of Murty-Murty about ${\overline{\mathbb{Q}}}$ linear independence of such $L(1, \chi)$ values.
If time permits, we will also discuss the interrelation between the non-vanishing of Dedekind zeta values and its derivatives.
Our next speaker is Arindam Roy of the University of North Carolina at Charlotte. The talk announcement is below.
Talk Announcement:
Tea or Coffee: Please bring your own.
Abstract:
Our next speaker is Amita Malik of the Max Plank Institute. The talk announcement is below.
Talk Announcement:
Tea or Coffee: Please bring your own.
Abstract:
Our next speaker is Murali Srinivasan of IIT Bombay (at Mumbai). The talk announcement is below.
Talk Announcement:
Tea or Coffee: Please bring your own.
Abstract:
On the coming Thursday, Atul Dixit (IIT, Gandhinagar) and Gaurav Bhatnagar (Ashoka University) will present the talks they presented at the recently concluded JMM meeting held online. Each talk will be approximately 20 minutes followed by 10 minutes for questions. The titles and abstracts are below.
Dear all,