There will be talks in Fall 2026. The seminar will take place in Aula INdAM at 12.
2026.10.02. Tuan Ngo Dac (CNRS Université de Caen Normandie)
[Note the different time! This talk will be at 9h30.]
On the algebra of multiple zeta values
Classical multiple zeta values (MZV’s) first studied by Euler in the eighteenth century have been investigated intensively over the past four decades due to their deep connections to various branches of mathematics and physics, including arithmetic geometry, knot theory and high-energy physics. We review central conjectures on the algebra of these values and report on recent progress. We then introduce the analogues of MZV’s in positive characteristic, following the pioneering work of Carlitz and Thakur. After reviewing their basic properties and outlining the main goals of the theory, we report on several new results on their algebraic structure. This is based on joint work with Nguyen Chu Gia Vuong and Pham Lan Huong.
2026.10.23. Gergely Harcos (Rényi Institute)
On the non-spherical sup-norm problem
A central problem in analytic number theory is to estimate the sup-norm of cusp forms on various Lie groups. It is natural to consider the Lie group GL(n,R), but for n>2, the results so far were confined to cusp forms that are right-invariant under the maximal compact subgrop O(n). I will explain how to deal with more general cusp forms on GL(n,R). A key ingredient is a new uniform decay bound for generalized spherical functions. Based on recent joint work with Valentin Blomer, Péter Maga, and Djordje Milićević.
2026.10.30. Youness Lamzouri (Institut Elie Cartan de Lorraine)
A Hilbert space approach to the zeros of the Riemann zeta function and applications
The Riemann hypothesis asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2. In the absence of a proof of the Riemann hypothesis, a fundamental problem is to determine what proportion of the zeros can be shown to lie on the critical line.
In this talk, I will introduce a new Hilbert space approach that establishes a direct connection between Montgomery's pair correlation method and the study of zeros of the Riemann zeta function on the critical line. This approach yields a new, conceptually simpler unconditional proof that more than two thirds of the zeros are simple and lie on the critical line.
I will also discuss several further applications of this method, including the discovery of a surprising rigidity phenomenon linking the simplicity and location of the zeros, a proof that more than 13/20 of the zeros are isolated, and new results on consecutive gaps between their ordinates. Finally, I will explain how these ideas can be used to prove that at least 3/10 of the zeros of certain linear combinations of two primitive Dirichlet L-functions lie on the critical line.
2026.11.06. Alessandra Migliaccio (Università di Ferrara e Università di Parma)
Problems in additive number theory: the Goldbach conjecture and its variants
The talk is devoted to presenting some problems and techniques in additive theory, a specific branch of analytic number theory. More precisely, we begin with an overview of the circle method - a fundamental tool introduced by Hardy, Littlewood and Ramanujan; then, we focus on its application to the Goldbach conjecture, and we underline the role of the so-called density in the study of related additive problems - such as Vinogradov's theorem - compared to this one. In the second part of the seminar, we explore our recent generalizations of two previous results: we first extend to polynomials computed at prime variables, an estimate of M. Cantarini, A. Gambini and A. Zaccagnini (2020) for the average number of representations of an integer as a sum of prime powers. Eventually, starting from the paper of K. Ikeda and A. I. Suriajaya (2025), we move to the arithmetic progressions, and we find the asymptotic behavior for the average number of representations of an integer as a sum of two prime powers and of at least three primes, over multiples of a fixed integer. All of them are joint works with A. Zaccagnini.
2026.11.13. Chiara Bellotti (Max Planck Institute for Mathematics)
On the Gauss sphere problem
The Gauss sphere problem concerns counting integer lattice points inside a three-dimensional ball of radius R. A classical result states that the number of such points is asymptotic to the volume of the ball. A central question in analytic number theory is to determine how small the error term in this approximation can be. Over the years, successive improvements have been obtained by Chen, Vinogradov, Chamizo and Iwaniec, and Heath-Brown, with the latter establishing an error exponent of 21/16. In this talk, I will discuss recent joint work with Bryce Kerr in which we improve Heath-Brown's exponent to 55/42. I will also explain how recent progress on zero-free regions for Dirichlet L-functions leads to a further improvement.
2026.11.27. Christos Katsivelos (University of Patras)
Past Events