## Upcoming Seminars

### February 2, 2023: TU Graz

Location: HS BE01, Steyrergasse 30

Schedule:

13:30-14:30: Efthymios Sofos (Glasgow University): "Averages of arithmetic functions over values of multivariable polynomials"

Abstract:

In joint work with Destagnol and Hochfilzer we show that if an arithmetic function is equidistributed in arithmetic progressions then one can estimate asymptotically its values over values of polynomials in many variables.

As applications we count asymptotically the number of solutions of certain exponential Diophantine Equations and also give asymptotics for new cases of the Loughran--Smeets conjecture.

14:30-15:00: Tea break

15:00-16:00: Jakob Glas (ISTA): "Rational points on del Pezzo surfaces over function fields"

Abstract:

Manin's conjecture gives a prediction for the number of rational points of bounded height on del Pezzo surfaces. However, when the degree of the surface is small, the conjecture remains far beyond the reach of current techniques. When the degree is 3, Heath-Brown has provided the sharpest general upper bounds conditionally on a conjecture about the growth of the rank of elliptic curves.

In this talk I will report on joint work with Hochfilzer, in which we prove the analogue of Heath-Brown's result over function fields unconditionally and generalise it to del Pezzo surfaces of smaller degree.

16:00-16:15: Break

16:15-17:15: Shuntaro Yamagishi (ISTA): "On Poonen's question regarding polynomial representing all natural numbers"

Abstract:

In 2009, Bjorn Poonen asked on MathOverflow whether there exists a polynomial $f \in \mathbb{Z}[x,y]$ such that $f(\mathbb{Z} \times \mathbb{Z}) = \mathbb{N}$. As far as we know, this question is still open. I will talk about a modest progress on the problem in my joint work with Stanley Yao Xiao (UNBC, Canada).

18:00: Dinner at Sägewerk, Schlögelgasse 1