Info: The AGDM seminar is a joint seminar of the University of Vienna and TU Wien. In winter semesters, we meet on Tuesdays from 15:00 to 16:30 at the University of Vienna. In summer semesters, we meet on Tuesdays from 15:15 to 16:45 at TU Wien.
Since 2025, we use a mailing-list to advertise the seminar. You can register here.
Place: University of Vienna, Oskar-Morgenstern-Platz 1, BZ 09 (first room on the right on the 9th floor)
Time:Tuesday, 15:00-16:30
| Date: | Tuesday 09.12.2025 |
| Title: | On Deciding Transcendence of Power Series |
| Speaker: | Alin Bostan (INRIA, Sorbonne Université) |
| Abstract: | A power series is said to be D-finite (“differentially finite”) if it satisfies a linear differential equation with polynomial coefficients. D-finite power series are ubiquitous in combinatorics, number theory and mathematical physics. In his seminal article on D-finite functions [S1], Richard P. Stanley asked for “an algorithm suitable for computer implementation” to decide whether a given D-finite power series is algebraic or transcendental. Although Stanley insisted on the practical aspect of the targeted algorithm, at the time he formulated the problem it was unknown whether the task of recognizing algebraicity of D-finite functions is decidable even in theory. I will first report on such a decidability result. The corresponding algorithm has too high a complexity to be useful in practice. This is because it relies on the costly algorithm from [S2], which involves, among other things, factoring linear differential operators, solving huge polynomial systems and solving Abel’s problem. I will then present an answer to Stanley’s question based on “minimization” of linear differential equations, and illustrate it through examples coming from combinatorics and number theory. (Work in collaboration with Bruno Salvy and Michael F. Singer.) [S1] R. P. Stanley, "Differentiably finite power series". European J. Combin. 1 (1980), no. 2, 175–188. [S2] M. F. Singer, "Algebraic solutions of nth order linear differential equations". Proc. Queen’s Number Theory Conf. 1979, Queen's Papers in Pure and Appl. Math., 54 (1980), 379–420. |
| Title: | On the Integrality of Some P-recursive Sequences |
| Speaker: | Anastasia Matveeva (École polytechnique) |
| Abstract: | D-finite power series are those whose coefficient sequences are P-recursive ("polynomially recursive"), that is they satisfy linear recurrence relations with polynomial coefficients. Algebraicity of D-finite power series is connected to (quasi-)integrality ("global boundedness") of the coefficient sequence, by a famous result due to Eisenstein [E]. However, while algebraicity of D-finite power series is now proved to be decidable (cf. previous talk), deciding integrality of P-recursive sequences is still a largely open question. This talk addresses a family of subproblems of the integrality question. I will start by revisiting the integrality criterion for the so-called "Motzkin-type sequences" due to Klazar and Luca [KL], and propose a unified approach for analyzing global boundedness and algebraicity within a broader class of P-recursive sequences. The central contribution is an algorithm that finds all algebraic solutions of certain second-order recurrence relations with linear polynomial coefficients. As algebraicity and global boundedness are shown to be equivalent in the special cases considered, the method detects all globally bounded solutions as well. This offers a systematic approach to deciding when a given P-recursive sequence is integral or almost integral - a question that arises naturally in combinatorics and differential algebra. (Based on joint work with Alin Bostan.) [E] G. Eisenstein, "Über eine allgemeine Eigenschaft der Reihen-Entwicklungen aller algebraischen Funktionen”. Berichte Königl. Preuss. Akad. Wiss. Berlin, 1852, pp. 441–443. [KL] M. Klazar and F. Luca, "On integrality and periodicity of the Motzkin numbers". Aequationes Math. 69 (2005), no. 1-2, 68–75. |
Maintaining a respectful environment is essential to fostering meaningful dialogue and intellectual growth. Participants are expected to refrain from any form of disrespectful or inappropriate behaviour, including offensive comments, harassment, or disruptive conduct. Questions and contributions should be constructive, relevant to the topic, and posed in a professional manner that encourages healthy academic exchange. Harassment of any kind—including verbal, moral or physical—will not be tolerated, and all attendees are urged to uphold these principles to ensure a safe and welcoming atmosphere for everyone.
| 16.12.2025 | Atsuro Yoshida | |
| 13.01.2026 | Abdulhafeez Abdulsalam | |
| 20.01.2026 | Markus Reibnegger | |
| 27.01.2026 | Mona Gatzweiler |
| 02.12.2025 | Marcus Schönfelder (University of Vienna) | The $1/4$-phenomenon of placement probabilities of tilings in the Aztec diamond |
| 25.11.2025 | Joshua Jeishing Wen (University of Vienna) | Tesler identities for wreath Macdonald polynomials |
| 18.11.2025 | Fabián Levicán (University of Vienna) | Embeddings of weighted projective spaces |
| 11.11.2025 | Nicolas Allen Smoot (University of Vienna) | Some New Examples of Modular Congruence Multiplicities |
| 04.11.2025 | Eva-Maria Hainzl (TU Wien) | Functional equations with catalytic variable 101 |
| 28.10.2025 | Shane Chern (University of Vienna) | The Koutschan-Krattenthaler-Schlosser determinants and their combinatorics |
| 21.10.2025 | Sergio Alejandro Fernandez de Soto Guerrero (TU Graz) | MathMagic: A positroidal action over a deck of cards |
| 14.10.2025 | Christian Krattenthaler (University of Vienna) | Two Topics, Four Lessons |
| 07.10.2025 | Matija Bucic (University of Vienna) | Equiangular lines via improved eigenvalue multiplicity |