Seminare und Vorträge im WS 2019/2020

am Dienstag, 08. Oktober:

Oberseminar Zahlentheorie

Yingkun Li (Technische Universität Darmstadt),
CM values of modular functions and factorization
Abstract: The theory of complex multiplication tells us that the values of the j-invariant at CM points are algebraic integers. The norm of the difference of two such values has nice and explicit factorization, which was the subject of the seminal work of Gross and Zagier on singular moduli in the 1980s. In this talk, we will recall this classical result, review some recent factorization formula for other modular functions, and report some progress on a conjecture of Yui and Zagier. This is joint work with Tonghai Yang.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 29. Oktober:

Oberseminar Zahlentheorie

Winston Heap (MPIM Bonn),
The max of ζ(1+it)

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 12. November:

Oberseminar Zahlentheorie

Haowu Wang (MPIM Bonn),
Theta block conjecture for Siegel paramodular forms
Abstract: The theta-block conjecture proposed by Gritsenko–Poor–Yuen in 2013 characterizes Siegel paramodular forms which are simultaneously Borcherds products and additive Jacobi lifts. In this talk, I prove this conjecture for two infinite series of theta blocks of weights 2 related to root systems A_4 and A_1+B_3.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 19. November:

Oberseminar Zahlentheorie

Eugenia Rosu (MPIM Bonn),
Special cycles on orthogonal Shimura varieties
Abstract: Extending on the work of Kudla-Millson and Yuan-Zhang-Zhang, together with Yott we are constructing special cycles for a specific GSpin Shimura variety. We further construct a generating series that has as coefficients the cohomology classes corresponding to the special cycle classes on the GSpin Shimura variety and show the modularity of the generating series in the cohomology group over C.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 26. November:

Oberseminar Zahlentheorie

Peter Koymans (MPIM Bonn),
On Chowla’s conjecture over function fields
Abstract: Let chi be a quadratic Dirichlet character. Then Chowla’s conjecture states that L(1/2, chi) is non-zero. Over function fields this conjecture has recently been disproved by Wanlin Li. The main result of this talk is that for many values of s we have that L(s, chi) is not zero for 100% of the characters chi. This is work in progress with Carlo Pagano and Mark Shusterman.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 10. Dezember:

Oberseminar Zahlentheorie

Moritz Dittmann (TU Darmstadt),
Harmonic theta series and the Kodaira dimension of A_6
Abstract: The quotient A_n of the Siegel upper half plane H_n by the group of symplectic 2nx2n matrices with integral entries is a coarse moduli space for principally polarized abelian varieties of dimension n over the complex numbers. Its Kodaira dimension has been known for over 35 years for all n ≠ 6. In this talk we present an algorithm to compute Fourier coefficients of harmonic Siegel theta series and use it to prove that the Kodaira dimension of A_6 is not negative. This is joint work with Riccardo Salvati Manni and Nils Scheithauer.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 14. Januar:

Oberseminar Zahlentheorie

Hongbo Yin (MPIM Bonn),
Borcherds Product and CM Value of Lambda function
Abstract: In this talk, we will talk about Gross-Zagier's type factorization formulas for the CM value of special modular functions using the Borcherds product and Bruinier-Kudla-Yang's big CM value formula. We will illustrate the method using the Lambda modular function which is a joint work with Tonghai Yang and Peng Yu.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 21. Januar:

Oberseminar Zahlentheorie

Marc Munsch (MPIM Bonn),
Small GCD sums
Abstract: In recent years, the question of maximizing GCD sums regained interest due to its firm link with large values of L-functions, leading for instance to the breakthrough improvement of Bondarenko and Seip concerning the maximum of the Riemann zeta function on the critical line. In this talk, we address the counterpart problem of minimizing GCD sums and present several results with applications. We consider as well a related optimization question regarding the usual multiplicative energy of a subset of the first N integers. This is a joint work with de la Bretèche and Tenenbaum.

14:00 Seminarraum 3 des Mathematischen Instituts

am Dienstag, 28. Januar:

Oberseminar Zahlentheorie

Jens Funke (Durham University),
The construction of Green currents and singular theta lifts for unitary groups
Abstract: In this talk we describe how singular theta lifts for the reductive dual pair U(p, q) × U(1, 1) can be employed to construct two different kinds of Green forms for codimension q-cycles in Shimura varieties associated to unitary groups. In particular, we establish an adjointness result between the singular theta lift and the Kudla-Millson theta lift and discuss further applications in the context of the Kudla Program. This is joint work with Eric Hofmann.

14:00 Seminarraum 3 des Mathematischen Instituts

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Seminare und Vorträge im SS 2019
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