Saturday, March 19, 2022

Soumyarup Banerjee (IIT, Gandhinagar) - Thursday, Mar 24, 2022 - 3:55 PM

Our next speaker is Soumyarup Banerjee of IIT, Gandhinagar. The talk announcement is below.

Talk Announcement:

Title: Finiteness theorems with almost prime inputs

Speaker: Soumyarup Banerjee (IIT, Gandhinagar)
 
When: Thursday, Mar 24, 2022 - 4:00 PM - 5:00 PM (IST) 

Where: Zoom. Please write to the organizers for the link.

Live Link: https://youtu.be/Fd2gNRyK04I

Tea or Coffee: Please bring your own.

Abstract:  

The Conway–Schneeberger Fifteen theorem states that a given positive definite integral quadratic form is universal (i.e., represents every positive integer with integer inputs) if and only if it represents the integers up to 15. This theorem is sometimes known as “Finiteness theorem" as it reduces an infinite check to a finite one. In this talk, I would like to present my recent work along with Ben Kane where I have investigated quadratic forms which are universal when restricted to almost prime inputs and have established finiteness theorems akin to the Conway–Schneeberger Fifteen theorem.


Saturday, March 5, 2022

Wenguang Zhai (China Inst. of Mining and Tech, Beijing, PRC) - Thursday, Mar 10, 3:55 PM (IST)

Our next speaker of Wenguang Zhai of the China Institute of Mining and Technology, Beijing, who will speak on recent work with Xiadong Cao (Beijing Institute of Petro-Chemical Technology, Beijing) and Yoshio Tanigawa (Nagoya, Japan).

Talk Announcement:


Title: The MC-algorithm and continued fraction formulas involving ratios of Gamma functions

Speaker: Wenguang Zhai (China Institute of Mining and Technology, Beijing, PRC)
 
When: Thursday, Mar 10, 2022 - 4:00 PM - 5:00 PM (IST) 

Where: Zoom. Please write to the organizers for the link.

Live Link: https://youtu.be/C6jzvD2NPuo

Tea or Coffee: Please bring your own.

Abstract:  

Ramanujan discovered many continued fraction expansions about ratios of the Gamma functions. However, Ramanujan left us no clues about how he discovered these elegant formulas. In this talk, we will explain the so-called MC-algorithm. By this algorithm, we can not only rediscover many of Ramanujan's continued fraction expansions, but also find some new formulas.