Discrete Mathematics Working Group (Arbeitsgemeinschaft Diskrete Mathematik, AGDM)
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, the seminars are held in TU Wien.
From 2025, we will be using a new mailing-list to advertise the seminar. You can register here.
Place: TU Wien (Freihaus, Wiedner Hauptstr. 8-10, 1040 Wien): Room DA 08 B19 (Dissertantenzimmer), 8th floor, Tower A (green)
Time: Tuesday, 15:15-16:45
Next talk
| Date: |
Tuesday 10.06.2025 |
| Title: |
Perfect matching enumeration and Kasteleyn‘s method |
| Speaker: |
Marcus Schönfelder (University of Vienna) |
| Abstract: |
A perfect matching of a graph $G=(V,E)$ is a covering set of matchings $\mu\subseteq E$ such that every vertex of $G$ is contained in exactly one edge $e\in \mu$. The number of perfect matchings for a given graph and its asymptotics show connections to various other areas of science including electrostatics, statistical mechanics and chemistry. From mathematical and especially combinatorial point of view, perfect matching enumeration is a highly multi-facetted problem whose complexity is heavily influenced by the structure of the underlying graph. A first successful attempt to give a general solution was achieved by Kasteleyn in the 1960s. By assigning a certain orientation on the edges of $G$ he was able to express the perfect matching generating function $M(G)$ of any PLANAR graph $G$ as plus or minus a Pfaffian form of its skew-symmetric adjacency matrix. After a brief introduction to the theory of Pfaffian forms, we will study Kasteleyn's method together and use the strong correspondence between perfect matchings and Pfaffians to directly translate identities of Pfaffian forms into formulas for perfect matchings. Extending the work of Markus Fulmek (2010) this provides an algebraic approach to proving condensation formulas for perfect matchings as an alternative to the purely combinatorial method. While Fulmek used involutions on superposition cycles to translate Pfaffian formulas into the language of perfect matchings, we will take the slightly more technical path by explicitly deducing the translation signs of the respective Pfaffians, which allows us to translate formulas of higher degree even where the involution-approach is no longer applicable. In the end, if time allows, we mention the complications that occur when poking holes of odd size into our planar graph. We explore a possible solution to this problem by connecting holes of odd size to larger holes of even size via certain well-behaved paths. |
Code of conduct
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.
Upcoming talks
| 17.06.2025 | Atsuro Yoshida |
| 24.06.2025 | Alessandro Iraci |
Talks in the past years
Talks of years 2005 - 2024
Past talks of this year
| Datum: |
03.06.2025 |
| Titel: |
Positive $m$-divisible non-crossing partitions and their cyclic sieving |
| Speaker: |
Christian Krattenthaler (University of Vienna) |
| Datum: |
27.05.2025 |
| Titel: |
Scaling limits of multitype Bienaymé trees |
| Speaker: |
Philipp Beltran (TU Wien) |
| Datum: |
20.05.2025 |
| Titel: |
Quilts of alternating sign matrices |
| Speaker: |
Matjaž Konvalinka (University of Ljubljana) |
| Datum: |
13.05.2025 |
| Titel: |
Color rules for cyclic wreath products and semigroup algebras from projective toric varieties |
| Speaker: |
Fabián Levicán (University of Vienna) |
| Datum: |
08.05.2025 |
| Titel: |
Schur's 1926 partition theorem - new variations and recent advances |
| Speaker: |
Krishnaswami Alladi (University of Florida) |
| Datum: |
15.04.2025 |
| Titel: |
On the Unexpected Connections in the Arithmetic Properties of POND and PEND Partitions |
| Speaker: |
James Sellers (University of Minnesota Duluth) |
| Datum: |
08.04.2025 |
| Titel: |
Dual transform, PSD codes and self-dual bent functions |
| Speaker: |
Stefka Bouyuklieva (University of Veliko Tarnovo) |
| Datum: |
01.04.2025 |
| Titel: |
Newton polytopes of some symmetric polynomials |
| Speaker: |
Candice Zhang 张旭彤 (Chinese Academy of Sciences, Beijing) |
| Datum: |
18.03.2025 |
| Titel: |
Combinatorial problems arising from representation theory of $GL_n$ over a $p$-adic field |
| Speaker: |
Erez Lapid (Weizmann Institute of Science) |
| Datum: |
11.03.2025 |
| Titel: |
Hall-Littlewood polynomials, affine Schubert series, and lattice enumeration |
| Speaker: |
Christopher Voll (Universität Bielefeld) |
| Datum: |
04.03.2025 |
| Titel: |
The number of monotone trapezoids with prescribed bottom row |
| Speaker: |
Ilse Fischer (Universität Wien) |
| Datum: |
28.01.2025 |
| Titel: |
Cohomology of perfect Lie algebras and partitions |
| Speaker: |
Dietrich Burde (Universität Wien) |
| Datum: |
21.01.2025 |
| Titel: |
Rook equivalence and a multisum extension of the Sears $_4\phi_3$ transformation |
| Speaker: |
Michael Schlosser (Universität Wien) |
| Datum: |
14.01.2025 |
| Titel: |
Short presentations and posters |
| Speaker: |
Students |
| Datum: |
07.01.2025 |
| Titel: |
Separated variables on plane algebraic curves |
| Speaker: |
Manfred Buchacher (JKU Linz) |
| Datum: |
17.12.2024 |
| Titel: |
Murnaghan–Nakayama rlies for symplectic, orthogonal and orthosymplectic Schur functions |
| Speaker: |
Nishu Kumari (Universität Wien) |
| Datum: |
10.12.2024 |
| Titel: |
Number systems and fractals |
| Speaker: |
Lucía Rossi (TU Wien) |
| Datum: |
03.12.2024 |
| Titel: |
Cluster structures on spinor helicity and momentum twistor varieties |
| Speaker: |
Jianrong Li (Universität Wien) |
| Datum: |
26.11.2024 |
| Titel: |
An Unexpected Symmetry on Graphs |
| Speaker: |
Florian Fürsinn (Universität Wien) |
| Datum: |
19.11.2024 |
| Titel: |
Phase transitions of block-weighted planar maps |
| Speaker: |
Zéphyr Salvy (TU Wien) |
| Datum: |
12.11.2024 |
| Titel: |
Polyominoes from operators on symmetric functions |
| Speaker: |
Marino Romero (Universität Wien) |
| Datum: |
05.11.2024 |
| Titel: |
Folding lemma and its applications in Number Theory |
| Speaker: |
Nikita Shliga (La Trobe University Melbourne) |
| Datum: |
29.10.2024 |
| Titel: |
Growth diagram proofs for the Littlewood identities |
| Speaker: |
Florian Schreier-Aigner (Universität Wien) |
| Datum: |
22.10.2024 |
| Titel: |
A central limit theorem for a card shuffling problem |
| Speaker: |
Shane Chern (Universität Wien) |
| Datum: |
15.10.2024 |
| Titel: |
$p(5n+4)$ again! Parity bias and it's unintended arithmetic consequences |
| Speaker: |
Manosij Ghosh Dastidar (TU Wien) |
| Datum: |
08.10.2024 |
| Titel: |
Lattice points and rational $q$-Catalan numbers |
| Speaker: |
Drew Armstrong (University of Miami) |