20 September 2024 at 15:00 [followed by drinks reception]

Venue: Room 500, Department of Mathematics, University College London, *25 Gordon Street, London, UK
*25 Gordon Street can be identified by the UCL student union branding, which also shares the building.

Organisers:

Yiannis Petridis (UCL) and Ian Petrow (UCL)

Quadratic Characters with Non-negative Partial Sums

Kannan Soundararajan, Professor of Mathematics, Stanford University, USA

Registration is free but required. Please register by 18 September 2024.

Are there infinitely many quadratic characters (for instance, the Legendre symbol mod p) for which the partial sums are always non-negative? Although only 0% of characters can have this property, numerical work (most recently by Kalmynin) suggests that such characters are nevertheless plentiful. For instance, computations show that there are many more examples than may be expected by modeling such sums by a simple random walk. I will discuss joint work with Angelo and Xu which obtains new upper bounds for the number of such characters, by studying a related problem on maxima of L-values (closely connected to the Fyodorov-Hiary-Keating conjectures). I will give a heuristic explanation for why such characters are plentiful, and which suggests that our upper bounds may not be too far from the truth.

About the Speaker: Kannan Soundararajan is the Anne T. and Robert M. Bass Professor of Mathematics at Stanford University. His research is in number theory, especially L-functions and multiplicative number theory. He received the Salem Prize in 2003, the SASTRA Ramanujan Prize in 2005, the Infosys prize in 2011, and the Ostrowski prize in 2011. He gave an invited talk at the International Congress of Mathematicians in 2010 and was invited as a plenary speaker of the 2022 ICM.

---

For more information please email the Heilbronn events team at  heilbronn-coordinator@bristol.ac.uk

Information on past and future colloquia is available here

Join the Heilbronn Event mailing list to keep up to date with our upcoming events