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Spring Semester 2023

Date / Time Speaker Title Location
24 February 2023
14:15-15:15 		Prof. Dr. Sebastian Herrero
Pontifical Catholic University of Valparaíso / ETH Zürich
Event Details

Number Theory Seminar

Title p-adic asymptotic distribution of CM points
Speaker, Affiliation Prof. Dr. Sebastian Herrero, Pontifical Catholic University of Valparaíso / ETH Zürich
Date, Time 24 February 2023, 14:15-15:15
Location HG G 43
Abstract A CM point in the moduli space of complex elliptic curves is a point corresponding to an elliptic curve with complex multiplication. A classical result of William Duke (1988), complemented by Laurent Clozel and Emmanuel Ullmo (2004), states that CM points become uniformly distributed in the moduli space, with respect to the hyperbolic measure, when the discriminant of the underlying ring of endomorphisms grows. Since CM points are algebraic, it is possible to study p-adic analogues of this phenomenon. In this talk I will present a description of the p-adic asymptotic distribution of CM points in the moduli space of p-adic elliptic curves. In contrast to the complex case, there are infinitely many measures describing the p-adic asymptotic distribution of CM points. This is joint work with Ricardo Menares (Pontificia Universidad Católica de Chile) and Juan Rivera-Letelier (University of Rochester).
p-adic asymptotic distribution of CM pointsread_more
HG G 43
17 March 2023
14:15-15:15 		Dr. Florian Wilsch
Leibniz Universität Hannover
Event Details

Number Theory Seminar

Title Integral points on cubic surfaces via a Hardy–Littlewood heuristic
Speaker, Affiliation Dr. Florian Wilsch, Leibniz Universität Hannover
Date, Time 17 March 2023, 14:15-15:15
Location HG G 43
Abstract An affine cubic surface is defined by an irreducible cubic polynomial f with integer coefficients in three variables, and its integral points correspond to integral roots of this polynomial. These solutions tend to be sparser and much harder to find than in cases of higher dimension or lower degree, as witnessed by the search for representations of integers k as sums of three cubes — that is, the case f = x³ + y³ + z³ - k – whose existence or nonexistence has only recently been settled for the first one hundred integers. To shed new light on this kind of problem, we develop a Hardy–Littlewood heuristic for the number of integral points on affine cubic surfaces, arriving at a prediction that looks similar to Manin's conjecture on rational points and related problems. We compare this heuristic to Heath-Brown's prediction for sums of three cubes, to Zagier's count on the Markoff surface and to Baragar's and Umeda's work on variants of it, as well as to numerical data. This is joint work with Tim Browning.
Integral points on cubic surfaces via a Hardy–Littlewood heuristicread_more
HG G 43
7 April 2023
14:15-15:15
Event Details

Number Theory Seminar

Title No seminar - easter holidays
Speaker, Affiliation
Date, Time 7 April 2023, 14:15-15:15
Location
No seminar - easter holidays
14 April 2023
14:15-15:15
Event Details

Number Theory Seminar

Title No seminar - easter holidays
Speaker, Affiliation
Date, Time 14 April 2023, 14:15-15:15
Location
No seminar - easter holidays
21 April 2023
14:15-15:15
Event Details

Number Theory Seminar

Title No seminar - Promotionsfeier
Speaker, Affiliation
Date, Time 21 April 2023, 14:15-15:15
Location
No seminar - Promotionsfeier
5 May 2023
14:15-15:15 		Prof. Dr. Martin Raum
Chalmers Technical University, Gothenburg
Event Details

Number Theory Seminar

Title Polyharmonic Maass forms and cyclic representations of the Gelfand quiver
Speaker, Affiliation Prof. Dr. Martin Raum, Chalmers Technical University, Gothenburg
Date, Time 5 May 2023, 14:15-15:15
Location HG G 43
Abstract Polyharmonic Maass forms are generalizations of classical elliptic modular forms that obey weaker differential equations than the Cauchy-Riemann equations, and thus form a richer class of functions which accommodate, for instance, some generating series of period integrals. Their differential properties are captured by cyclic Harish-Chandra modules, which are in ono-to-one correspondence with cyclic representations of the two-cyclic and the Gelfand quiver. We show that all latter representations arise from polyharmonic Maass forms, and provide a explicit construction, which has a natural interpretation in terms of tensor products of Harish-Chandra modules.
Polyharmonic Maass forms and cyclic representations of the Gelfand quiverread_more
HG G 43
19 May 2023
14:15-15:15
Event Details

Number Theory Seminar

Title No seminar - Auffahrt
Speaker, Affiliation
Date, Time 19 May 2023, 14:15-15:15
Location
No seminar - Auffahrt
26 May 2023
14:15-15:15 		Prof. Dr. Kevin Hughes
Edinburgh Napier University
Event Details

Number Theory Seminar

Title What to do after Vinogradov's Mean Value Theorems
Speaker, Affiliation Prof. Dr. Kevin Hughes, Edinburgh Napier University
Date, Time 26 May 2023, 14:15-15:15
Location HG G 43
Abstract I will lightly discuss a few problems closely connected to Vinogradov's Mean value theorems going beyond the optimal conjecture thereof (proved by Wooley and Bourgain--Demeter--Guth in 2015). Depending on time and the audience's interest I will focus on one of the problems.
What to do after Vinogradov's Mean Value Theoremsread_more
HG G 43
2 June 2023
14:15-15:15 		Prof. Dr. Tim Browning
ISTA
Event Details

Number Theory Seminar

Title Hasse principle for random varieties
Speaker, Affiliation Prof. Dr. Tim Browning, ISTA
Date, Time 2 June 2023, 14:15-15:15
Location HG G 43
Abstract I'll discuss efforts to understand the solubility of random Diophantine equations, focusing on recent joint work with Sofos and Teräväinen about the integral Hasse principle for random norm form equations defined over the integers.
Hasse principle for random varietiesread_more
HG G 43

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