Note: In-person seminars will be held at `Übungsraum 2' of the Mathematical Institute subject to requirements and guidelines of the University of Cologne on COVID-19. In particular, we have limited room for participants. So please contact `cnazarog@math.uni-koeln.de' in advance to check for room availability if you would like to participate.



Seminare und Vorträge im SS 2022

am Montag, 04. April :

Oberseminar Zahlentheorie

Petru Constantinescu
Title: Dissipation of Correlations of Automorphic Forms
Abstract: Mass equidistribution of eigenfunctions is a central topic in quantum chaos and number theory. In this talk we highlight a generalisation of the Quantum Unique Ergodicity for holomorphic cusp forms in the weight aspect. We show that correlations of masses coming from off-diagonal terms dissipate as the weight tends to infinity. This corresponds to classifying the possible quantum limits along any sequence of Hecke eigenforms of increasing weight.

14:00 Übungsraum 2

am Montag, 25. April :

Oberseminar Zahlentheorie

Ian Wagner
Title: Laguerre-Pólya type functions with applications in combinatorics and number theory
Abstract: We define a new class of functions which puts the recent work of Griffin, Ono, Rolen, and Zagier into a framework analogous to the classical Laguerre-Pólya class. The main result is a classification of functions in this new class involving multiplier sequences, Jensen polynomials, and generalized Laguerre inequalities. Finally, we discuss some applications and open problems connected to functions in this class with a focus on partitions and the Riemann Xi-function.

14:00 Übungsraum 2

am Montag, 23. Mai :

Oberseminar Zahlentheorie

Jan Bruinier
Title: Special cycles on toroidal compactifications of orthogonal Shimura varieties
Abstract: We report on joint work with Shaul Zemel and Markus Schwagenscheidt. We define special cycles on orthogonal Shimura varieties and prove a modularity result for the corresponding generating series. It turns out that the multiplicities of the irreducible components of the boundary divisors are given by special values of regularized theta lifts of Lorentzian and positive definite lattices. There are explicit formulas for these multiplicities, which can be viewed as generalizations of the Kronecker class number relations.

14:00 Übungsraum 2

am Montag, 30. Mai :

Oberseminar Zahlentheorie

Taylor Garnowski
Title: Asymptotic Analysis of Mixed Mock Modular Forms and Related q-products (PhD Defense)
Abstract: This thesis contains results of three research projects which study asymptotics for the Fourier coefficients of mixed mock modular forms and twisted q-products arising in combinatorics. To begin, we compute an asymptotic distribution for generalizations of unimodal sequences called odd-balanced unimodal sequences which were defined by Kim, Lim, and Lovejoy in 2016. We find the interesting result that the odd-balanced unimodal sequences with certain restrictions on their rank, are asymptotically related to the overpartition function. This is in contrast to strongly unimodal sequences which are asymptotically related to the partition function. In the second part of this thesis, we compute asymptotic estimates for the Fourier coefficients of two mock theta functions originating from Bailey pairs derived by Lovejoy and Osburn in 2012. We encounter cancellation in our estimates for one of the functions, which requires a careful study of secondary asymptotic terms. We deal with this by using higher order asymptotic expansions for the Jacobi theta functions. In our final result, we find asymptotic estimates for the complex Fourier coefficients of the product \((\zeta q;q)^{-1}_\infty\), with \(\zeta\) a root of unity. This result has interesting applications in analysis and combinatorics. For large \(n\), we are able to predict sign changes of arbitrary linear combinations of the function \(p(a,b;n)\) for fixed \(b\), where \(p(a,b;n)\) counts the number of partitions of \(n\) where the number of parts is congruent to \(a\) modulo \(b\). We see that simple differences of the type \(p(a_1,b;n)-p(a_2,b;n)\) have sign change patterns that oscillate like a cosine.

14:00 Übungsraum 2

am Montag, 13. Juni :

Oberseminar Zahlentheorie

Jeremy Lovejoy

14:00 Übungsraum 2

am Montag, 20. Juni :

Oberseminar Zahlentheorie

Ioana Coman

14:00 Übungsraum 2

am Montag, 27. Juni :

Oberseminar Zahlentheorie

TBD

14:00 Übungsraum 2

am Montag, 11. Juli :

Oberseminar Zahlentheorie

Peter Paule

14:00 Übungsraum 2

am Montag, 18. Juli :

Oberseminar Zahlentheorie

Amanda Folsom

14:00 Übungsraum 2

Archiv

Seminare und Vorträge im WS 2021/2022
Seminare und Vorträge im SS 2021
Seminare und Vorträge im WS 2019/2020
Seminare und Vorträge im SS 2019
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Seminare und Vorträge im SS 2013
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Seminare und Vorträge im WS 2011/2012
Seminare und Vorträge im SS 2011
Seminare und Vorträge im WS 2010/2011
Seminare und Vorträge im SS 2010
Seminare und Vorträge im WS 2009/2010
Seminare und Vorträge im SS 2009
Seminare und Vorträge im WS 2008/2009
Seminare und Vorträge im SS 2008 und früher