Sunday, January 24, 2021

Victor Moll (Tulane) - February 4, 2021 -3:55 PM - 5:00 PM (IST)

The next talk will be by Victor Moll of Tulane University. This will be the first mathematician from the US giving a talk in our seminar. Victor has kindly consented to stay awake to make his talk more suitable for Indian timings. But in future, we do expect speakers from the US will speak at times later at night (IST).

At any rate, we hope more speakers from the US will give talks in our seminar. As we have mentioned earlier, our website now contains video recordings of the presentations. This makes it more convenient for the US participants to view the talks.

Talk Announcement

Title:  Valuations of interesting sequences

Speaker: Victor Moll (Tulane)

When: February 4, 2021 - 3:55 PM - 5:00 PM (IST)

ABSTRACT

Given a sequence ${ a_{n} }$ of integers and a prime $p$, the sequence of

valuation $\nu_{p}(a_{n})$ presents interesting  challenges. This talk will discuss a

variety of examples in order to illustrate these challenges and present our approach

to this problem.

Thursday, January 21, 2021

Josef Küstner (University of Vienna) January 21, 2021 - 3:55 - 5:00 PM (IST)

Our next talk is on January 21, 2021. Please do feel free to volunteer to speak, if you have submitted something recently and the topic is suitable for this group.

We have now upgraded the sf-and-nt website a bit. In case a video recording is available, we have embedded it, so you can view the recording at leisure. I wish to thank Shivam Sahu, a recent graduate of the math department of Ashoka University, for help in this activity. In particular, it will be of help when you are reading the associated papers in more detail. Any suggestions for the website are welcome.

The talk for the week is as follows.

Talk Announcement

Title:  Elliptic and q-analogs of the Fibonomial numbers

Speaker: Josef Küstner (University of Vienna)

When: January 21, 2021 - 3:55 PM - 5:00 PM (IST)

ABSTRACT

The Fibonomial numbers are integer numbers obtained from the binomial coefficients by replacing each term by its corresponding Fibonacci number. In 2009, Sagan and Savage introduced a simple combinatorial model for the Fibonomial numbers.

In this talk, I will present a combinatorial description for a q-analog and an elliptic analog of the Fibonomial numbers which is achieved by introducing certain q- and elliptic weights to the model of Sagan and Savage.

This is joint work with Nantel Bergeron and Cesar Ceballos.

Thursday, January 7, 2021

Ramanujan Special: Wadim Zudilin on Thursday, January 7, 2021, 3:55 pm-5 PM

A very happy new year to all. We have decided that the first talk of every year will be a  Ramanujan Special Talk. This year a colloquium talk will be given by Wadim Zudilin. The announcement is below.

We wish you many new theorems, ideas and papers in 2021. Please do send any ideas or suggestions you have for the organisers to make this seminar more successful and help serve the interests of this community.

Talk Announcement

Title: 10 years of q-rious positivity. More needed!

The $q$-binomial coefficients $\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i),$ for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients. This readily follows from the $q$-binomial theorem, or the many combinatorial interpretations of them. Ten years ago, together with Ole Warnaar we observed that this non-negativity (aka positivity) property generalises to products of ratios of $q$-factorials that happen to be polynomials; we prove this observation for (very few) cases. During the last decade a resumed interest in study of generalised integer-valued factorial ratios, in connection with problems in analytic number theory and combinatorics, has brought to life new positive structures for their $q$-analogues. In my talk I will report on this "$q$-rious positivity" phenomenon, an ongoing project with Warnaar.