Dear all,

We are happy to announce our next talk is by Professor Bruce Berndt, the world's biggest authority on Ramanujan's mathematics and related areas.

Please note the special time. It is two hours later than usual. Please circulate this announcement in your department.

Please see a further announcement below.

**Talk Announcement:**

**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))

**Where**: Zoom. Please write to the organisers for the link.

**Live Video Link:**https://youtube.com/live/rCDRKyv_880?feature=share

**Abstract**

First, motivated by a theorem in Ramanujan's lost notebook, Martino Fassina, Sun Kim, Alexandru Zaharescu, and the speaker developed representations for finite sums of products of trig functions for which we provided theorems and several conjectures.

Second, a paper of Richard McIntosh served as motivation. First, he made a very interesting conjecture, which was recently proved by Likun Xie, Zaharescu, and the speaker. Second, he examined a particular trigonometric sum, which inspired Sun Kim, Zaharescu, and the speaker to evaluate in closed form several classes of trigonometric sums, and find reciprocity theorems for others.

**New conference announcement**

A new conference on algebraic combinatorics has been announced by Arvind Ayyer. It is called

Meru Annual Combinatorics Conference

Dates: 29th to 31st May, 2023

Conference website: https://www.imsc.res.in/~amri/meru/